Real-time high-rate GNSS techniques for earthquake monitoring and early warning

Transcription

1 Real-time high-rate GNSS technique for earthquake monitoring and early warning vorgelegt von Dipl.-Ing. Xingxing Li au Hubei, China Von der Fakultät VI Planen Bauen Umwelt der Technichen Univerität Berlin zur Erlangung de akademichen Grade Doktor der Ingenieurwienchaften - Dr. Ing. - genehmigte Diertation Promotionauchu: Voritzender: Prof. Dr. Frank Flechtner Gutachterin: Prof. Dr. Harald Schuh Gutachterin: Prof. Dr. Ur Hugentobler Gutachterin: Dr. Maorong Ge Tag der wienchaftlichen Auprache: 14. July 2015 Berlin 2015

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3 Abtract In recent time increaing number of high-rate GNSS tation have been intalled around the world and et-up to provide data in real-time. Thee network provide a great opportunity to quickly capture urface diplacement, which make them important a potential contituent of earthquake/tunami monitoring and warning ytem. The appropriate GPS real-time data analyi with ufficient accuracy for thi purpoe i a main focu of the current GNSS reearch. The objective of thi thei i to develop high-preciion GNSS algorithm for better eimological application. The core reearch and the contribution of thi thei are ummarized a following: With the availability of real-time high-rate GNSS obervation and precie atellite orbit and clock product, the interet in the real-time Precie Point Poitioning (PPP) technique ha greatly increaed to contruct diplacement waveform and to invert for ource parameter of earthquake in real time. Furthermore, PPP ambiguity reolution approache, developed in the recent year, overcome the accuracy limitation of the tandard PPP float olution and achieve comparable accuracy with relative poitioning. In thi thei, we introduce the real-time PPP ervice ytem and the key technique for real-time PPP ambiguity reolution. We ae the performance of the ambiguity-fixed PPP in real-time cenario and confirm that poitioning accuracy in term of root mean quare (RMS) of 1.0~1.5 cm can be achieved in horizontal component. For the 2011 Tohoku-Oki (Japan) and the 2010 El Mayor-Cucapah (Mexico) earthquake, the diplacement waveform, etimated from ambiguity-fixed PPP and thoe provided by the accelerometer intrumentation are conitent in the dynamic component within few centimeter. The PPP fixed olution not only can improve the accuracy of coeimic diplacement, but alo provide a reliable recovery of earthquake magnitude and of the fault lip ditribution in real time. We propoe an augmented point poitioning method for GPS baed hazard monitoring, which can achieve fat or even intantaneou precie poitioning without relying on data of a pecific reference tation. The propoed method overcome the limitation of the currently motly ued GPS proceing approache of relative poitioning and global precie point poitioning. The advantage of the propoed approach are demontrated by uing GPS data, which wa recorded during the 2011 Tohoku-Oki earthquake in Japan. We propoe a new approach to quickly capture coeimic diplacement with a ingle GNSS receiver in real-time. The new approach can overcome the convergence problem of precie point poitioning (PPP), and alo avoid the integration proce of the variometric - iii -

4 approach. Uing the reult of the 2011 Tohoku-Oki earthquake, it i demontrated that the propoed method can provide accurate diplacement waveform and permanent coeimic offet at an accuracy of few centimeter, and can alo reliably recover the moment magnitude and fault lip ditribution. We invetigate three current exiting ingle-receiver approache for real-time GNSS eimology, comparing their obervation model for equivalence and aeing the impact of main error component. We propoe ome refinement to the variometric approach and epecially conider compenating the geometry error component by uing the accurate initial coordinate before the earthquake to eliminate the drift trend in the integrated coeimic diplacement. We propoe an approach for tightly integrating GPS and trong motion data on raw obervation level to increae the quality of the derived diplacement. The performance of the propoed approach i demontrated uing 5 Hz high-rate GPS and 200 Hz trong motion data collected during the El Mayor-Cucapah earthquake (Mw 7.2, 4 April, 2010) in Baja California, Mexico. The new approach not only take advantage of both GPS and trong motion enor, but alo improve the reliability of the diplacement by enhancing GPS integer-cycle phae ambiguity reolution, which i very critical for deriving diplacement with highet quality. We alo explore the ue of collocated GPS and eimic enor for earthquake monitoring and early warning. The GPS and eimic data collected during the 2011 Tohoku-Oki (Japan) and the 2010 El Mayor-Cucapah (Mexico) earthquake are analyzed by uing a tightly-coupled integration. The performance of the integrated reult are validated by both time and frequency domain analyi. We detect the P-wave arrival and oberve mall-cale feature of the movement from the integrated reult and locate the epicenter. Meanwhile, permanent offet are extracted from the integrated diplacement highly accurately and ued for reliable fault lip inverion and magnitude etimation. Keyword: High-rate GNSS; GNSS Seimology; Real-time GNSS; Precie Point Poitioning; PPP Ambiguity Reolution; Coeimic Diplacement; Fault Slip Inverion; Geohazard monitoring; Relative Poitioning; Dene Monitoring Network; Augmented PPP; Temporal Point Poitioning; Variometric approach; Seimic Senor; Tightly-integrated Filter; Integrated Diplacement; Earthquake Monitoring; Earthquake Early Warning. - iv -

5 Table of Content Abtract... iii Table of Content... v Lit of Abbreviation... vii Lit of Related Publication... ix 1 Introduction High-rate GNSS eimology uing real-time PPP with ambiguity reolution Introduction Real-time PPP ytem and algorithm Real-time PPP ervice ytem Obervation Model Real-time precie point poitioning Real-time etimation of the uncalibrated phae delay Ambiguity reolution for precie point poitioning Accuracy aement in real-time cenario Application to the 2011 Tohoku-Oki earthquake GPS data and analyi Comparing GPS and eimic waveform Fault lip inverion Application to the 2010 E1 Mayor-Cucapah earthquake GPS data and analyi Comparing GPS and eimic waveform Fault lip inverion Concluion Augmented PPP for eimological application uing dene GNSS network Introduction Augmented PPP approach Application of augmented PPP approach and reult Concluion Temporal point poitioning approach for GNSS eimology uing a ingle receiver Introduction Temporal point poitioning approach Application of TPP approach and reult Single-receiver approache for real-time GNSS eimology v -

6 4.4.1 Comparion of analyi method Error analyi and preciion validation Application to the 2011 Tohoku-Oki earthquake Concluion Tightly-integrated proceing of raw GNSS and accelerometer data Introduction Overview of combining GPS and accelerometer data The tightly-integrated algorithm Reult Comparion of GPS, eimic and integrated waveform Detection of P-wave arrival Extraction of permanent offet and fault lip inverion Concluion Concluion and outlook Reference vi -

7 Lit of Abbreviation AC ARP BDS BKG C/A CDDIS CODE CORS DCB DD DF DFG DOD ECMWF ESA EU EEW Galileo GEO GFZ GIM GLONASS GLOT GMF GNSS GPS GPST GSI IAR IGR IGS IGSO Analyi Center Antenna Reference Point the Chinee BeiDou navigation Satellite Sytem Federal Agency for Cartography and Geodey, Germany Coare/Acquiition code Crutal Dynamic Data Information Sytem Centre of Orbit Determination in Europe Continuouly Operating Reference Station Differential Code Biae Double Difference Dual-Frequency Deutche Forchunggemeinchaft (i.e. German Reearch Foundation) the U.S. Department of Defene European Centre for Medium-Range Weather Forecat European Space Agency European Union Earthquake Early Warning the European Union atellite navigation ytem Satellite in Geotationary Orbit Helmholtz-Centre Potdam-GFZ German Reearch Centre for Geocience Global Ionopheric Map the Ruian GLObal Navigation Satellite Sytem GLONASS time Global Mapping Function Global Navigation Satellite Sytem Global Poitioning Sytem GPS Time Geopatial Information Authority Integer Ambiguity Reolution IGS Rapid orbit International GNSS Service Inclined Geoynchronou Orbit - vii -

8 IGU IGS Ultra-rapid orbit IOV In-Orbit Validation IPP Ionopheric Pierce Point ITRF International Terretrial Reference Frame LC Ionophere-free Linear Combination LEO Low Earth Orbit MEO Medium altitude Earth Orbit MET Meteorology MW_WL MW Widelane Linear Combination NASA National Aeronautic and Space Adminitration NRTK Network-baed Real Time Kinematic poitioning OMC Obervation Minu Computation PCO Phae Centre Offet PCV Phae Centre Variation PNT Poitioning, Navigation and Timing PPP Precie Point Poitioning PPP-RA Precie Point Poitioning Regional Augmentation RMS Root Mean Square RTK Real-Time Kinematic SAPOS Satellite Poitioning Service of the German State Survey SD Single Difference SP3 IGS Standard Product 3 SPS Standard Poitioning Service STD Slant Total Delay UD Un-differenced UPD Un-calibrated Phae Delay UTC Coordinated Univeral Time WL Widelane Combination WGS-84 Word Geodetic Sytem 1984 ZHD Zenith Hydrotatic Delay ZTD Zenith Total Delay ZWD Zenith Wet Delay - viii -

9 Lit of Related Publication 1. Li, X., M. Ge, X. Zhang, Y. Zhang, B. Guo, R. Wang, J. Klotz, and J. Wickert (2013), Real-time high-rate co-eimic diplacement from ambiguity-fixed precie point poitioning: Application to earthquake early warning, Geophy. Re. Lett., 40(2), , doi: /grl Li, X., M. Ge, Y. Zhang, R. Wang, P. Xu, J. Wickert, and H. Schuh (2013), New approach for earthquake/tunami monitoring uing dene GPS network, Sci. Rep., 3, 2682, doi: /rep Li, X., M. Ge, B. Guo, J. Wickert, and H. Schuh (2013), Temporal point poitioning approach for real-time GNSS eimology uing a ingle receiver, Geophy. Re. Lett., 40(21), , doi: /2013gl Li, X., M. Ge, Y. Zhang, R. Wang, B. Guo, J. Klotz, J. Wickert, and H. Schuh (2013), High-rate coeimic diplacement from tightly integrated proceing of raw GPS and accelerometer data. Geophy J Int. 5. Li, X., X. Zhang, and B. Guo (2013), Application of collocated GPS and eimic enor to earthquake monitoring and early warning. Senor 13: Li, X., M. Ge, C. Lu, Y. Zhang, R. Wang, J. Wickert, and H. Schuh (2014), High-rate GPS eimology uing real-time precie point poitioning with ambiguity reolution. IEEE tranaction on Geocience and remote ening, pp Li, X., B. Guo, C. Lu, M. Ge, J. Wickert, and H. Schuh (2014), Real-time GNSS eimology uing a ingle receiver. Geophy. J. Int. doi: /gji/ggu113 In thi thei, the paper 1 and 6 contributed to the Chapter 2, the paper 2 contributed to the Chapter 3, the paper 3 and 7 contributed to the Chapter 4, and the paper 4 and 5 contributed to the Chapter 5. - ix -

10 1 Introduction Recent detructive earthquake that truck Sumatra, Indoneia (Mw 9.2) in 2004, Wenchuan, China (Mw 7.9) in 2008, Maule, Chile (Mw 8.8) in 2010 and Tohoku, Japan (Mw 9.0) in 2011 have once again brought u to focu the urgent need for earthquake monitoring and early warning. Rapid ource and rupture inverion for large earthquake i critical for eimic and tunamigenic hazard mitigation (Allen and Ziv, 2011; Ohta et al., 2012), and earthquakeinduced ite diplacement i key information for uch ource and rupture inverion. For earthquake early warning (EEW) ytem, the etimation of accurate coeimic diplacement and waveform i needed in real-time. Traditionally, diplacement are obtained by double integration of oberved accelerometer ignal or ingle integration of velocitie oberved with broadband eimometer (Kanamori, 2007; Epinoa-Aranda et al., 1995; Allen and Kanamori, 2003). The broadband eimometer are likely to clip the ignal in cae of large earthquake. Although trong-motion accelerometer intrument do not clip, the diplacement converted from acceleration could be degraded ignificantly by drift caued by tilt and the non-linear behavior of the accelerometer (Trifunac and Todorovka, 2001; Boore, 2001). Since Remondi (1985) firt demontrated cm-level accuracy of kinematic GPS, Hirahara et al. (1994) labeled kinematic GPS a GPS eimology, which ha ince attracted more and more attention and application in eimology (ee, e.g., Ge et al. 2000; Laron et al., 2003). High-rate GNSS (e.g., 1 Hz or higher frequency) meaure diplacement directly and can provide reliable etimate of broadband diplacement, including tatic offet and dynamic motion of arbitrarily large magnitude (Laron et al., 2003; Bock et al., 2004). GPS-baed eimic ource characterization ha been demontrated in near- and far-field with remarkable reult (Nikolaidi et al., 2001; Laron et al., 2003; Bock et al., 2004; Ohta et al., 2008; Yokota et al., 2009; Avallone et al., 2011; Melgar et al., 2012; Crowell et al., 2012). GNSS-derived diplacement can be ued to quickly etimate earthquake magnitude, model finite fault lip, and alo play an important role in earthquake/tunami early warning (Blewitt et al., 2006; Wright et al., 2012; Hoechner et al., 2013). Conequently in the recent year, dene GPS monitoring network have been built in eimically active region, e.g., Japan GEONET (the GPS Earth Obervation Network Sytem, and UNAVCO Plate Boundary Obervatory (PBO, Thee network are complementary to eimic monitoring network and contribute ignificantly to earthquake/tunami early warning and hazard rik mitigation (Blewitt et al., 2006; Crowell et al., 2009)

11 Currently, two proceing trategie are mainly ued in mot of the tudie related to GPS eimology and tunami warning: relative baeline/network poitioning (e.g., Nikolaidi et al., 2001; Laron et al., 2003; Bock et al., 2004, Blewitt et al., 2006) and precie point poitioning (PPP) (Zumberge et al., 1997). For relative kinematic poitioning, at leat one nearby reference tation hould be ued for removing mot of biae and recovering integer feature of ambiguity parameter by forming double-differenced ambiguitie. Conequently, ambiguitie can alway be fixed to integer even intantaneouly for achieving high poitioning accuracy of few cm (Bock et al., 2011; Ohta et al., 2012). Therefore, it i already applied in real-time diplacement monitoring (e.g., Crowell et al., 2009). The technique of intantaneou poitioning (Bock et al., 2000) i one typical real-time relative poitioning method and i integrated into EEW ytem (Crowell et al., 2009) and i demontrated by applying the reult for centroid moment tenor (CMT) computation (Melgar et al., 2012), finite fault lip inverion (Crowell et al., 2012) and P wave detection by combining collocated accelerometer data and the GPS diplacement uing a Kalman filter (Bock et al., 2011; Tu et al., 2014). The real-time kinematic (RTK) technique i alo utilized by Ohta et al (2012) to analyze the diplacement of the 2011 Tohoku-Oki earthquake. All of the previouly mentioned tudie ued the relative poitioning technique, which i able to guarantee a high accuracy at 1 cm level. However, for the relative poitioning technique, GPS data from a network i analyzed imultaneouly to etimate tation poition. It i complicated by the need to aign baeline, overlapping Delaunay triangle, or overlapping ub-network. Thi i a ignificant limitation for the challenging imultaneou and precie real-time analyi of GPS data from hundred or thouand of ground tation. Furthermore, intermittent tation dropout complicate the network-baed relative poitioning. Relative poitioning alo require a local reference tation, which might itelf be diplaced during a large eimic event, reulting in mileading GPS analyi reult. In the cae of large earthquake, uch a the Mw 9.0 Tohoku-Oki event in Japan, the reference tation may alo be ignificantly diplaced, even when it i everal hundred kilometer away from the event. The reference tation hould be ufficiently far from the focal region, but mut alo be part of a ub-network that ha relatively hort baeline (uually within everal ten of kilometer). A the baeline length increae, the accuracy of relative poitioning would be ignificantly reduced becaue the atmopheric effect and atellite ephemeri error become le common and thu cannot be effectively cancelled out by double-difference technique. PPP provide a new concept of poitioning ervice by uing precie orbit and clock product generated from a global reference network (Kouba and Héroux, 2001). Kouba (2003) demontrated that PPP uing the orbit and clock product of the International GNSS Service (IGS) can be ued to detect eimic wave and atify the requirement of the GPS eimology

12 Wright et al. (2012) ued PPP in real-time mode with broadcat clock and orbital correction to give tation poition every 1 ec and then carry out a imple tatic inverion to determine the portion of the fault that lipped and the earthquake magnitude. The PPP technique can provide abolute coeimic diplacement with repect to a global reference frame (defined by the atellite orbit and clock) with a tand-alone GPS receiver. A PPP proceing ytem ue information from a global reference network, which i applied to the monitoring tation, conequently the derived poition are referred to the global network, which itelf i hardly affected by the earthquake diplacement. Thank to the development of JPL Global Differential GPS Sytem (GDGPS) and the International GNSS Service (IGS) real-time pilot project (RTPP), real-time precie atellite orbit and clock product are now available online and PPP i widely recognized a a promiing poitioning technique (Caiy 2006; Dow et al., 2009; Bar-Sever et al., 2009). However, tandard PPP (float ambiguity) ha limited accuracy in real-time application becaue of unreolved integer-cycle phae ambiguitie. PPP ambiguity reolution developed in recent year provide an important promie to achieve comparable accuracy with relative/network poitioning (Ge et al., 2008; Li et al., 2013a). The German Reearch Center for Geocience (GFZ), a one of the IGS data analyi center, i operationally providing GPS orbit and clock, uncalibrated phae delay (UPD) and differential code biae (DCB) for real-time PPP ervice with ambiguity-fixing (Ge et al., 2011; Li 2012). The performance i further enhanced by new algorithm for peeding up the reconvergence through etimation of ionopheric delay (e.g., Geng et al., 2010; Zhang and Li, 2012; Li et al., 2013a). Although a convergence period of about 20 min i till required, PPP i able to achieve cm-level poitioning accuracy in real-time without the need for dedicated reference tation (Li et al., 2013b). Coloimo et al. (2011) propoed a variometric approach to determine the change of poition between two adjacent epoch (namely delta poition) baed upon the time ingle-difference of the carrier phae obervation, and then diplacement of the tation are obtained by a ingle integration of the delta poition. Thi approach doe not uffer from convergence proce, but the ingle integration from delta poition to diplacement i accompanied by a drift due to the potential uncompenated error. Uually, a limited duration of 3-4 minute may be enough for large diplacement retrieving. Under the aumption that the variometric-baed diplacement ha a linear trend within few minute, the etimated diplacement after linear trend removal are demontrated to be at a level of a few centimeter (Branzanti et al., 2013). Recent advance in the performance of real-time high-rate GPS, etimate of permanent diplacement directly, mean that it ue can potentially be complementary to the eimic-baed methodologie for earthquake early warning. The main weaknee of current GPS - 3 -

13 meaurement are the lower ampling rate (1~50Hz) and the larger high-frequency noie contribution, and o the GPS-derived dynamic motion are not accurate enough to identify the firt arrival wave (P-wave) with only millimeter-level amplitude. The noie of GPS diplacement i baically white acro the whole eimic frequency band. While trong motion enor are able to ample at very high rate (e.g. 200Hz) and perform very well in the high-frequency range a it i much more enitive to ground motion than GPS receiver, epecially in the vertical direction. However, the acceleration i accompanied by unphyical drift due to enor rotation and tilt (Trifunac and Todorovka, 2001; Lee and Trifunac, 2009), hyterei (Shakal and Peteren, 2001), and impreciion in the numerical integration proce (Boore et al., 2002; Smyth and Wu, 2006). It noie level, viewed in term of diplacement, will rie with decreaing frequency: at ome frequency thi noie level will exceed that of GPS. Therefore, GPS and eimic intrument can be mutually beneficial for eimological application becaue weaknee of one obervation technique are offet by trength in the other. The complementary nature of GPS and eimic enor for tation diplacement etimation and P-wave detection are well recognized and the integrated proceing of the two dataet i a hot topic in GPS eimology for obtaining more accurate and reliable diplacement and P- wave arrival time. Several looely-integrated approache have been propoed to fue accelerometer with collocated GPS diplacement data (Emore et al., 2007; Bock et al., 2011). A the GPS coordinate are already etimated prior to integration with the accelerometer, the precie dynamic information provided by accelerometer cannot be ued to enhance the GPSonly olution in thee integration algorithm. Currently, the available real-time high-rate GNSS data tream have the potential to contribute to EEW ytem. GFZ ha been working on the real-time precie poitioning for geohazard monitoring for year. The EPOS-RT oftware ha been developed for providing worldwide real-time PPP ervice. The accuracy and reliability of the global PPP hould be improved for better monitoring of geohazard, epecially for thoe cauing rather mall diplacement. It i a big challenge to achieve precie and reliable diplacement in real-time. Thu thi thei will focu on the development of high-preciion GNSS algorithm for better eimological application. We alo integrate the accelerometer data into the GNSS data proceing in order to combine all the advantage of GPS and eimic enor. Thi thei include the following chapter, Firtly, Chapter 1 preent the motivation, background and reearch objective of thi thei and pecifie the contribution of thi reearch

14 In the Chapter 2, the ambiguity-fixed PPP method i developed to etimate high-rate coeimic diplacement in real-time. Thi ambiguity-fixed PPP algorithm i decribed in detail. The PPP diplacement waveform are analyzed and compared with eimic waveform and the application of PPP waveform to EEW i decribed. Chapter 3 propoe a novel method for fat or even intantaneou poitioning, making full ue of the currently available global PPP ervice and regional GPS monitoring network. The derived atmopheric correction at the tation with fixed ambiguitie then can be provided to other monitoring tation for intantaneou ambiguity reolution, o that precie diplacement can alway be achieved within a few econd. The new method doe not depend on a pecific reference tation and therefore the analyi reult will not be affected by imultaneou haking of any particular tation. It alo ha better flexibility and efficiency compared to complicated network/ubnetwork analyi. Chapter 4 propoe a new approach for etimating coeimic diplacement with a ingle receiver in real-time. The approach overcome not only the diadvantage of the PPP and RP technique, but alo decreae the decribed drift in the diplacement derived from the variometric approach. The coeimic diplacement could be etimated with few centimeter accuracy uing GNSS data around the earthquake period. The efficiency of the new approach i validated uing 1 Hz GNSS data, collected during the Tohoku-Oki earthquake (Mw 9.0, 11 March, 2011) in Japan. Chapter 5 propoe an approach of integrating the accelerometer data into the GPS data proceing in order to take full ue of the complementary of GPS and eimic enor. Intead of combing the GPS-derived diplacement with the accelerometer data, a tightly-integrated filter i developed to etimate eimic diplacement from GPS phae and range and accelerometer obervation. The performance of the propoed tightly-integrated approach wa validated by the 2010, Mw 7.2 El Mayor-Cucapah earthquake (Mw 7.2, 4 April, 2010) in Baja California, Mexico and the Tohoku-Oki earthquake (Mw 9.0, 11 March, 2011) in Japan. Finally, Chapter 6 ummarize the main reult a obtained in the previou chapter, preent the final concluion and ugget recommendation for the future work

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16 2 High-rate GNSS eimology uing real-time PPP with ambiguity reolution 2.1 Introduction Earthquake-induced ite diplacement i key information for locating the epicentre and etimating the magnitude of earthquake. For earthquake early warning (EEW) ytem, the etimation of accurate coeimic diplacement and waveform i needed in real-time. Traditionally, diplacement are obtained by double integration of oberved accelerometer ignal or ingle integration of velocitie oberved with broadband eimometer (Kanamori, 2007; Epinoa-Aranda et al., 1995; Allen and Kanamori, 2003). Compared to eimic intrument that are ubject to drift (accelerometer) or that clip the ignal in cae of large earthquake (broadband eimometer), GPS receiver oberve diplacement directly, making it particularly valuable in cae of large earthquake (Laron et al., 2003; Blewitt et al., 2006). Until now, pot-proceing or imulated real-time relative kinematic poitioning i utilized in mot of the tudie related to GPS eimology (e.g., Nikolaidi et al., 2001; Laron et al., 2003; Bock et al., 2004) and tunami warning (e.g., Blewitt et al., 2006). For relative kinematic poitioning, at leat one nearby reference tation hould be ued for removing mot of biae and recovering integer feature of ambiguity parameter by forming doubledifferenced ambiguitie. Conequently, ambiguitie can alway be fixed to integer even intantaneouly for achieving high poitioning accuracy of few cm (Bock et al., 2011; Ohta et al., 2012). However, the relative poitioning technique relie on reference tation located cloely. To monitor large region, conequently a large number of reference tation i required which increae cot and ytem complexity. More critical i the fact that the derived diplacement alo depend on the earthquake-induced movement of the reference tation. Thank to the development of JPL Global Differential GPS Sytem (GDGPS) and the International GNSS Service (IGS) real-time pilot project (RTPP), real-time precie atellite orbit and clock product are now available online and PPP i widely recognized a a promiing poitioning technique (Caiy 2006; Dow et al., 2009; Bar-Sever et al., 2009). However, tandard PPP (float ambiguity) ha limited accuracy in real-time application becaue of unreolved integer-cycle phae ambiguitie. In recent year, integer ambiguity fixing approach for PPP ha been developed to improve it performance (Ge et al., 2008; Li et al., 2013)

17 In thi chapter, we introduce the ytem tructure of the real-time PPP ervice by taking the operational real-time PPP ervice, developed at the German Reearch Center for Geocience (GFZ) for both precie poitioning and geophyical application a an example. The GPS data proceing trategie including the obervation model, real-time PPP, and PPP ambiguity reolution are decribed in detail. The poitioning preciion i carefully aeed in real-time cenario. We etimate high-rate coeimic diplacement in imulated real-time PPP mode for 1 Hz GPS data, collected during the Tohoku-Oki earthquake (Mw 9.0, March 11, 2011) in Japan and 5 Hz GPS data, collected during El Mayor-Cucapah earthquake (Mw 7.2, April 4, 2010) in Mexico. The derived diplacement waveform are analyzed, compared with eimic waveform, and finally applied for fault lip inverion to further validate the real-time PPP ervice with ambiguity reolution. 2.2 Real-time PPP ytem and algorithm Real-time PPP ervice ytem In a global real-time PPP ervice ytem, real-time data from a global reference network with a certain number of evenly ditributed tation i eential for generating precie orbit and clock for precie poitioning at the deired location. The real-time orbit i uually predicted baed on orbit determined in a batch-proceing mode uing the latet available obervation (generally 5 min ampling interval) due to the dynamic tability of the atellite movement. More challenging i the etimation of the atellite clock correction, which mut be updated much more frequently due to their hort-term fluctuation (Zhang et al., 2011). Under the framework of the IGS RTPP, data from a global real-time network of more than 100 tation i available and the related data communication for the obervation, retrieving and product cating wa etablihed (Caiy 2006). Furthermore, everal real-time analyi center (RTAC) were etablihed and have been running operationally to contribute their real-time product for comparion and combination. Mot of the RTAC ue a proceing procedure imilar to that for generating the IGS ultra-rapid orbit, but the update time of 6 hour could be hortened for a better orbit accuracy. The atellite clock product are etimated every 5 econd together with receiver clock, ambiguity and zenith tropopheric delay (ZTD) parameter with fixed or tightly contrained atellite orbit and tation coordinate. A in both the orbit determination and clock etimation, tation coordinate are fixed, obervation affected by earthquake-induced diplacement will have large reidual and be rejected a outlier. A the diplacement will not occur at the ame time for mot of the tation, precie atellite orbit and clock are till available during the earthquake time

18 With the real-time orbit and clock, tandard PPP can be carried out at the uer-end where ionopheric delay are uually eliminated uing the ionophere-free combination and ZTD mut be etimated a unknown parameter. Uually, it need an initialization time of about 30 min to obtain poition of cm-level accuracy. Initialization mut be repeated if mot of the atellite loe lock which i referred a to re-convergence and might occur during earthquake. Moreover, a in relative poitioning, the float olution could be further improved by integer ambiguity reolution. For recovering the integer feature of the ambiguitie at the uer-end, uncalibrated phae delay (UPD) at the atellite or imilar product hould be etimated and tranmitted to uer. The approach for thi UPD etimation and integer ambiguity reolution at the uer-end will be preented in detail in the following ection. Taking the operational real-time PPP ervice, developed at GFZ, a example (Ge et al., 2011; Li et al., 2013), the data tream of about 80 globally ditributed IGS tation are proceed in real-time by uing the EPOS-RT oftware for generating and broadcating orbit and clock for tandard PPP ervice. Furthermore, for reolving the integer ambiguity at uer-end, UPD correction are generated and updated in real-time with the ame data et which are ued to etimate orbit and clock product. The data flow at the erver-end, including precie GPS orbit determination, clock etimation and UPD retrieval i hown in Fig Figure 2.1: Data flow at the erver-end of a global real-time PPP ervice. The GPS clock and orbit are baic product and UPD i for PPP ambiguity reolution at the uer-end. At the uer-end, the real-time product tream of orbit and clock are received and applied to the obervation for tandard PPP. If UPD i alo available, PPP with integer ambiguity reolution then can be performed. Due to the product tranmiion delay and higher ampling - 9 -

19 rate (e.g., 1Hz) at uer-end, a linear extrapolation of a few econd will be applied. The data flow at the uer-end i hown in Fig Figure 2.2: Data flow at the uer-end for tandard PPP and PPP with integer ambiguity reolution Obervation Model The obervation equation for undifferenced (UD) carrier phae L and peudorange P repectively, can be expreed a following: L t t ( b b ) N I T (2.1) r, j r g r j r, j j j r, j r, j r r, j P t t c( d d ) I T e (2.2) r, j r g r r, j j r, j r r, j where indice, r, and j refer to the atellite, receiver, and carrier frequency, repectively; t and t r are the clock biae of atellite and receiver; N, r j i the integer ambiguity; br, j dr, jand and bj are the receiver- and atellite-dependent UPD; j i the wavelength; d j are the code biae of the receiver and the atellite; Ir, j i the ionopheric delay of the ignal path at frequency j ; Tr i the correponding and frequency independent tropopheric delay; er, jand r, jare meaurement noie of the peudorange and carrier phae obervation. Furthermore, denote the geometric ditance between the phae center of the g atellite and receiver antenna at the ignal tranmitting and receiving epoch, repectively. Thi mean, that the phae center offet and variation and tation diplacement by tidal loading mut be conidered. Phae wind-up and relativitic delay mut alo be corrected according to

20 the exiting model (Kouba and Héroux, 2001), although they are not included in the equation. A idereal filter can be ued to effectively reduce the impact of multipath error (Choi et al., 2004). The lant tropopheric delay conit of the dry and wet component and both can be expreed by their individual zenith delay and mapping function. The tropopheric delay i uually corrected for it dry component with an a priori model, while the reidual part of the tropopheric delay (conidered a zenith wet delay Z ) at the tation r i etimated from the obervation. r, j r g r j r, j j j r, j r, j r r r, j r L t t ( b b ) N I m Z (2.3) P t t c( d d ) I m Z e (2.4) r, j r g r r, j j r, j r r r, j where m i the wet mapping function. r For multi-frequency obervation, the ionopheric delay at different frequencie can be expreed a, I I ; / (2.5) 2 2 r, j j r,1 j j 1 At the uer-end, the real-time product tream of orbit and clock are received and applied to the obervation for tandard PPP. If UPD i alo available, PPP with integer ambiguity reolution then can be performed. Due to the product tranmiion delay and higher ampling rate (e.g., 1Hz) at uer-end, a linear extrapolation of a few econd will be applied. The data flow at the uer-end i hown in Fig The ionopheric delay can be eliminated by forming the linear combination of obervation at different frequencie. Uually, the ionophere-free obervation i employed in PPP (Kouba and Héroux, 2001). Alternatively, the dual-frequency data can be proceed by etimating the lant ionopheric delay in raw obervation a unknown parameter (Schaffrin and Bock 1988). The line-of-ight ionopheric delay on the L1 frequency I r,1 are taken a parameter to be etimated for each atellite and at each epoch. In order to trengthen the olution, a priori knowledge about thee delay can be utilized a contraint on the ionopheric parameter. The temporal change of the lant ionopheric delay of a atellite-tation pair can be repreented by a tochatic proce according to their temporal correlation. Ionopheric gradient parameter could be ued to take into account the patial ditribution of the ionopheric delay. The temporal correlation, patial characteritic and ionopheric model contraint are comprehenively conidered to peed up the convergence in PPP ambiguity

21 reolution (Li et al., 2013c). Thee contraint, to be impoed on obervation of a ingle tation can be ummarized a: I I w w N 2 rt, rt, 1 t, t ~ (0, wt) vi I / f a a dl a dl a db a db, I r r vi I, 2 r r I ripp, (2.6) where t i the current epoch; t 1 i the previou epoch; w t i a zero mean white noie with variance of 2 wt (generally a few millimeter for 1Hz ampling and an elevation-dependent weighting trategy i applied); vi r i the vertical ionopheric delay with a variance of f 2 vi ; ripp, i the mapping function (Schaer et al., 1999) at the ionopheric pierce point (IPP); the coefficient 0,1, 2,3, 4 a i decribe the planar trend, the average value of the ionopheric i delay over the tation; a 1, a 2, a 3, and a 4 are the coefficient of the two econd-order polynomial that ued to fit the eat-wet and outh-north horizontal gradient; dl and db are the longitude and latitude difference between the IPP and the tation location; I r i the 2 ionopheric delay obtained from external ionopheric model with a variance of I Real-time precie point poitioning Intead of the ionophere-free linear combination, we ue the raw carrier phae and peudorange obervation of Eq (2.3), (2.4), and (2.5) and etimate the lant ionopheric delay a unknown parameter with ionopheric contraint of (2.6). The linearized equation for (2.3) and (2.4) can be repectively expreed a following, l u r t t ( b b ) N I m Z (2.7) r, j r r j r, j j j r, j j r,1 r r r, j p u r t t c( d d ) I m Z e (2.8) r, j r r r, j j j r,1 r r r, j where l r, jand pr, jdenote oberved minu computed phae and peudorange obervable from atellite to receiver r at the frequency j ; u r i the unit vector of the direction from receiver to atellite; r denote the vector of the receiver poition increment. With the received real-time correction of GPS atellite orbit, clock and differential code biae (DCB), the correponding term in the obervation equation can be removed. The raw obervation equation then can be implified a, l u r t B I m Z (2.9) r, j r r j r, j j r,1 r r r, j p u r t c d I m Z e (2.10) r, j r r j r,1 j r,1 r r r, j

22 B N b b (2.11) r, j r, j r, j j where B r, ji the real-valued undifferenced ambiguity. At the epoch k, obervational equation for all the atellite can be expreed a, where the etimated parameter are, Y A X N (2.12) 2 k k k Y, ~ (0, ) k Y Y X r Z t d I ) B ) B ) (2.13) T T T r r r,1 r,1 r,1 r,2 A equential leat quare filter i employed to etimate the unknown parameter for realtime proceing. Pk denote the weight matrix at epoch k, X ˆ P A PY P X ˆ (2.14) 1 T k Xˆ k k k ˆ k 1 k X k1 Q P ( A P A P ) (2.15) 1 T 1 Xˆ Xˆ k k k Xˆ k k k1 The increment of the receiver poition r are etimated epoch by epoch without any contraint between epoch for retrieving rapid tation movement. The tropopheric zenith wet delay Z i decribed a a random walk proce with noie of about 2-5 mm / r T hour. The receiver clock i etimated epoch-wie a white noie and the carrier-phae ambiguitie B r, j are etimated a contant over time Real-time etimation of the uncalibrated phae delay From the carrier phae obervational equation of (2.9), one can ee that undifferenced phae ambiguitie cannot be fixed to integer becaue of the exitence of UPD. The real-valued ambiguitie can be expreed by integer number plu the UPD at receiver and atellite a Eq. (2.11). Recent tudie how, that the UPD can be etimated with high accuracy (Ge et al., 2008; Li and Zhang, 2012) or aimilated into clock parameter (Collin et al., 2008; Lauricheee et al., 2008). In our procedure of real-time UPD etimation, the PPP float olution i firtly carried out for all tation of the reference network. In thi PPP proceing, the coordinate of the reference tation are fixed to well-known value, for example, determined from weekly olution in advance, o that the undifferenced (UD) float ambiguitie could be obtained with higher quality. Aume that we have a network with n tation (generally more than 15 tation for regional network or more than 80 tation for a global network) tracking m atellite, the UD float

23 ambiguitie at each tation are etimated a B, we have the obervation equation in the form of Eq. (2.16) for thee ambiguitie (Li and Zhang, 2012), i N1 B1 I R1 S1 N2 B2 I 0 R2 S2, Q (2.16) 0 I Nn B n I Rn Sn br b where B i the UD float ambiguity vector for tation i ; i vector for tation i ; b r and N i i the UD integer ambiguity b are the UPD for receiver and atellite; R i and Si are the coefficient matrice for receiver and atellite UPD repectively; Q i the co-variance matrix of the UD float ambiguitie; In matrix R i one column with all element i 1 and the other are zero. For matrix S i each line i one element of -1, the other are zero. Under the condition that all the integer ambiguitie are exactly known and one UPD i fixed to zero, other UPD can be etimated by mean of the leat quare adjutment. Furthermore, for integer ambiguity reolution, the fractional part of UPD i ufficient intead of UPD itelf a the integer part can be aborbed by the ambiguity parameter anyway. Therefore, we will not ditinguih UPD and UPD fractional part hereafter. Aume the receiver UPD at the firt arbitrarily elected tation i zero, then the nearet integer of the UD ambiguitie at thi tation are their integer ambiguitie and the fractional part are etimate of the related atellite UPD. Applying thi atellite UPD to the common atellite of the next tation, the corrected UD ambiguitie hould have very imilar fractional part. The mean value of the fractional part of all the common atellite i taken a UPD of the receiver. With thi UPD, the UPD of the upcoming atellite, oberved at the tation, can be etimated. Repeating thi procedure for all tation, we can have the approximate UPD for all receiver and atellite. After correcting the UD float ambiguitie with the UPD, they hould be very cloe to integer, thu ambiguity reolution can be attempted. Replacing integer ambiguity parameter with their fixed value in equation (2.16), the remaining parameter can be etimated and the UPD etimate are urely improved and will help to reolve more integer ambiguitie. The above decribed procedure can be done iteratively until no more integer ambiguitie can be fixed. The UPD of the lat iteration are the information needed for the uer ide for PPP ambiguity reolution. Finally, we broadcat the atellite UPD to PPP uer together with orbit,

24 clock and DCB product tream, o that PPP with integer ambiguity reolution can be performed at a ingle tation Ambiguity reolution for precie point poitioning Integer ambiguity reolution for PPP require not only precie atellite orbit and high-rate atellite clock correction but alo the above mentioned UPD. With the received UPD correction, atellite UPD are removed at the uer-end and the obervational equation of (2.9) can be implified a, l u r t N b I m Z (2.17) r, j r r j r, j j r, j j r,1 r r r, j The receiver UPD can be eaily eparated by adapting one UD ambiguity to it nearet integer. Afterward, the UD ambiguitie have integer feature and the L1 and L2 ambiguitie can be fixed imultaneouly uing integer etimation method (ee, e.g., Teunien 1995; Xu et al., 2012). The ratio of the econd minimum to the minimum quadratic form of reidual i applied to decide the correctne and confidence level of integer ambiguity candidate (the threhold for the ratio tet i et to 3 a uual). 2.3 Accuracy aement in real-time cenario For aeing the preciion of our real-time product tream, fifteen real-time GPS tation (1Hz ampling), which are not ued for erver-ide product generation, are elected a uer tation. The PPP float olution and PPP with ambiguity reolution are carried out in parallel for thee tation from day 325 to (November 20 to 29, 2012). The ame orbit and clock correction are ued to feed the float PPP and the ambiguity-fixed PPP. Compared with GFZ final product (be regarded a truth), the 3D RMS (root mean quare) of orbit error i about 4.0 cm, the RMS of clock error i about 5.1cm, and the RMS of uer range error (URE) i about 3.5cm. The tation coordinate are etimated epoch-by-epoch without any contraint between epoch for teting the real-time kinematic performance. The etimated coordinate are compared with the coordinate derived from pot-proceed daily olution to ae the poitioning accuracy. A a typical example, the difference of the etimated poition with repect to their daily olution for tation A17D (Potdam) on day 326 are exemplarily hown in Figure 2.3. Figure 2.3a how the poition difference (with repect to pot-proceed daily olution) of the PPP float olution in the north, eat and up component. The difference are within 10 and 15 cm for the horizontal and vertical component, repectively. The vertical i, a expected, the noiiet component, due to the atellite contellation geometry and the high correlation between zenith tropopheric delay and the height component. There are long-term variation

25 and hort-term fluctuation in the poition erie even after a long convergence period of 24 hour (day 325). The poition difference of the fixed olution are hown in Figure 2.3b. The improvement i ignificant, when compared with the related float olution. In the ambiguityfixed olution, the fluctuation are much maller than thoe in the float olution and there are not obviou biae. A poition accuracy of better than 5 and 10 cm in horizontal and vertical component i repectively achieved once the ambiguitie are uccefully fixed. Comparion of the PPP float and fixed olution for tation BELL on day 326 are hown in Figure 2.4 and imilar improvement are achieved in the ambiguity-fixed olution. Figure 2.3: Real-time kinematic PPP olution for tation A17D (Potdam) on day (a), PPP without ambiguity-reolution; (b), PPP with fixed ambiguitie. The north, eat and up component are indicated by the green, red and black line, repectively

26 Figure 2.4: Real-time kinematic PPP olution for tation BELL on day (a), PPP without ambiguity-reolution; (b), PPP with fixed ambiguitie. The north, eat and up component are indicated by the green, red and black line, repectively. The RMS, tandard deviation (STD) and mean bia of the poition difference erie are calculated a tatitical indicator for the accuracy aement. The tatitical reult of the poition difference erie of day 326 to (November 21 to 29, 2012) for tation A17D and BELL are ummarized in Table 1. The RMS of the elected fifteen uer tation for both PPP float and fixed olution are alo hown in Figure 2.5. From Fig. 2.5, the poition RMS in north, eat and vertical direction of the float olution are improved from about 3, 5 and 6 cm to 1, 1 and 3 cm, repectively, by integer ambiguity reolution. Among thee ignificant improvement the larget i in the eat component. The STD of float olution are reduced from about 2 and 5 cm for the horizontal and vertical component to 1 and 2.5 cm, repectively. It i worth to mention that the biae are alo

27 decreaed evidently by ambiguity reolution, epecially in the eat component from about 3-4 cm to everal mm. Table 2.1: Statitical reult including RMS, STD and mean biae. Station RMS (cm) STD (cm) Mean bia (cm) &Accuracy Float Fixed Float Fixed Float Fixed North(A17D) Eat(A17D) Up(A17D) North(BELL) Eat(BELL) Up(BELL)

28 Figure 2.5: RMS of the poition difference of day 326 to (November 21 to 29, 2012) for the elected fifteen uer tation (Global). The RMS of north, eat and up component are hown in the top, middle and bottom ub-figure. The float olution are in blue and the fixed one in red. 2.4 Application to the 2011 Tohoku-Oki earthquake GPS data and analyi The Mw 9.0 Tohoku-Oki earthquake occurred on March 11, 2011 at 05:46:24 UTC in the north-wetern Pacific Ocean at a relatively hallow depth of 30 km, with it epicenter approximately 72 km eat of the Ohika Peninula of Tohoku, Japan. The Tohoku-Oki event i one of the bet recorded large earthquake in hitory a Japan ha one of the denet GPS network in the world. The Geopatial Information Authority of Japan (GSI) operate more than 1,200 continuouly recording GPS tation (collectively called the GPS Earth Obervation Network Sytem, GEONET) all over Japan ( The GEONET data provide an ideal opportunity to evaluate the performance of real-time PPP derived coeimic diplacement. We proce 1 Hz data of about 80 globally ditributed real-time IGS tation uing the EPOS-RT oftware of GFZ in imulated real-time mode (data i edited in real-time proce without pre-clean) for providing GPS orbit, clock and UPD correction at 5 ampling interval. Compared with GFZ final product, the 3D RMS of orbit error i about 4.1 cm, the RMS of clock error i about 5.3 cm, and the RMS of URE i about 3.6 cm. Baed on thee correction, we replayed the 1 Hz GPS data collected at the GEONET tation during the 2011 Tohoku-Oki earthquake. In the near future, it i difficult for mot countrie at threat from large earthquake and tunami to afford uch a dene GPS network a Japan GEONET. To tet the utility of a pare GPS network for earthquake/tunami early warning (Wright et al., 2012), ixty high-rate GPS tation are elected from the GEONET for fault lip inverion in thi tudy. The ditribution of the elected GPS tation i hown in Figure

29 Figure 2.6: Location of the 2011 Tohoku-Oki earthquake epicenter and the ditribution of the elected high-rate GPS tation and trong motion tation. The epicenter i marked by the red tar. The blue circle repreent tation with GPS only, wherea the gray triangle are for tation with collocated GPS and trong motion eimometer. We calculated the RMS of the poition difference of the ixty elected GPS tation over the 2 hour before the earthquake event for the PPP float and fixed olution, repectively. It reveal that RMS in eat, north and vertical of the float olution of about 2.8, 4.4 and 9.7 cm are improved to 1.9, 1.9 and 4.0 cm, correpondingly by integer ambiguity reolution. Similarly, we alo calculated the RMS of the diplacement-derived velocitie over thee two hour for the ixty GPS tation which are 2.7, 1.8 and 4.6 mm/ repectively in the north, eat and up component. The diplacement waveform from PPP fixed olution and the velocitie of five tation are hown a example in Figure 2.7a and 2.7b, repectively

30 Figure 2.7: PPP diplacement and velocity waveform at GPS tation 0008, 3031, 0318, 0804 and 0177 during the Tohoku-Oki earthquake on March 11, The north, eat and up component are repectively hown by red, green and black line Comparing GPS and eimic waveform Japan ha one of the denet eimometer network in the world, and preently include the F- Net, with 84 broadband tation; the K-NET, with 1,000 trong motion tation; the Hi-Net, with 777 high enitivity tation (borehole intallation); and the KiK-Net, co-located with the Hi-Net. We found about fifteen collocated GPS and trong motion tation pair (Fig. 2.6). The trong motion recording are firtly proceed uing the automatic empirical baeline correction cheme propoed by Wang et al. (2011). The velocity and diplacement eimogram are then derived from the baeline-corrected trong motion recording and compared with the GPS reult at thee collocated pair

31 The nearet tation pair between the trong motion and GPS network, that i, K-NET tation AKT006 ( N, E) and the GEONET tation 0183 ( N, E), being eparated by 20 m. The PPP and eimic diplacement waveform from 0183 and AKT006 for the Tohoku-Oki earthquake are exemplarily compared in Figure 2.8. The 1 Hz ambiguity-fixed PPP diplacement and 100 Hz eimic diplacement are hown by red and black line, repectively. The tandard PPP float olution i alo hown for comparion with green line. The 900 period of eimic haking at 0183/AKT006 in the north, eat and up component are repectively hown in the Figure 2.8a, 2.8b and 2.8c. Peak urface diplacement at thi tation are about 1.0 m in the horizontal and 0.4 m in the vertical component. The comparion of PPP and eimic diplacement clearly how a high degree of reemblance, with aligned phae and very imilar amplitude of the dynamic component. The problem i that the permanent coeimic offet in the PPP and eimic waveform are very different. From the PPP waveform, the permanent coeimic offet of about 0.4 m, 0.5 m and few centimeter are repectively viible in Figure 2.8a, 2.8b and 2.8c. However, the correponding coeimic offet of eimic waveform are about 0.6, 1.0 and 0.2 m. Tilt and rotation of the eimic intrument lead to the baeline offet in the eimic recording, wherea the GPS receiver oberve diplacement directly and doe not uffer from drift, clipping or intrument tilting. Although the empirical baeline correction ha been applied to the eimic recording, the accuracy of the permanent coeimic offet derived from eimic waveform i till not comparable with that of the GPS-derived coeimic offet. The vertical GPS diplacement i the noiiet component due to the atellite contellation geometry and the high correlation between zenith tropopheric delay and the height component (Wright et al., 2012). The PPP and eimic diplacement waveform at GPS/eimic tation pair 0986/NGN017 for the Tohoku-Oki earthquake are alo hown in Figure 2.9. In general we found that the diplacement waveform, etimated from real-time ambiguity-fixed PPP and thoe provided by the accelerometer intrumentation are largely conitent

32 Figure 2.8: Comparion of the eimic and PPP diplacement waveform on the co-located AKT006 (eimic) and 0183 (GPS) tation during the 2011 Tohoku-Oki earthquake. The north, eat and up component are repectively hown in the ub-figure a, b, and c. The real-time ambiguity-fixed PPP waveform, etimated from GPS obervation, i hown by the red rectangle. The eimic diplacement waveform i drawn by the black triangle. The PPP float olution i hown with the green cycle

33 Figure 2.9: The eimic and PPP diplacement on the co-located NGN017 (eimic) and 0986 (GPS) tation during the Tohoku-Oki earthquake on March 11, The north, eat and up component are repectively hown in the ub-figure a, b, and c. The ambiguity-fixed PPP and eimic diplacement are repectively hown by the red and black line. The PPP float olution i drawn with the green line. The GPS velocity erie i alo compared with the velocity erie integrated from the collocated accelerometer. The 1 Hz GPS velocity waveform are derived from real-time ambiguity-fixed PPP. The 100 Hz eimic one are obtained through ingle integration of accelerometer data. The velocity reult at 0183/AKT006 and 0986/NGN017 are repectively

34 hown in Figure 2.10 and 2.11 a example where the velocity erie derived from PPP fixed olution are hown by the red line and the correponding eimic velocitie are hown by the black line. From the Figure 2.10a, b and 2.11a, b, the velocity erie in the horizontal component how a high degree of conitency with the correponding eimic reult. Figure 2.10c and 2.11c indicate that the vertical component i relatively noiy. A tatitical analyi indicate that the RMS of the difference between PPP and eimic velocitie are 2.5, 2.2 and 3.2 cm/ in north, eat, and vertical component, repectively. Figure 2.10: Comparion of the velocity erie derived from accelerometer and GPS on the colocated AKT006 (eimic) and 0183 (GPS) tation during the Tohoku-Oki earthquake on 11 March The north, eat and up component are repectively hown in the ub-figure a, b, and c. The red line how the velocity erie derived from the PPP fixed olution, and the black line how the correponding velocity erie integrated from accelerometer data

35 Figure 2.11: The velocity erie from the collocated 0986/NGN017 tation during the Tohoku-Oki earthquake on March 11, The north, eat and up component are hown in the ub-figure a, b, and c repectively. The PPP velocity erie are hown by the red line, while the eimic velocitie are hown by the black line Fault lip inverion To further validate the ambiguity-fixed PPP, we apply the PPP diplacement to fault lip inverion of the Tohoku-Oki earthquake. The inverion are carried out uing the code SDM written by Dr. R. Wang baed on the contrained leat-quare method, which ha been ued in a number of recent publication for analyzing GPS, InSAR and trong motion baed co- and pot-eimic deformation data (Diao et al., 2010; Wang et al., 2013; Li et al., 2013c). For

36 implicity of numerical analyi, the fault plane i repreented by a number of mall rectangular dilocation patche with uniform lip. The oberved diplacement data are related to the dicrete fault lip through Green function of the earth model, which are calculated uing linear elatic dilocation theory. For the dicrete lip to be an adequate repreentation of the true continuou lip ditribution, the patch ize mut be reaonably mall. In fact, if the available data do not include enough information for determining the lip ditribution with the deired reolution, the inverion ytem become underdetermined. To overcome the problem of nonuniquene and intability inherent in uch an underdetermined ytem, priori condition (fixed fault geometry and retricted variation range for the rake angle) and phyical contraint (mooth patial ditribution of lip or tre drop) are conidered. We derive the patial ditribution of fault lip uing the coeimic diplacement obtained from the real-time PPP float olution, real-time PPP fixed olution, and the pot-proceed ARIA olution, repectively. The pot-proceed ARIA olution provided by the ARIA team at JPL and Caltech (Simon et al., 2011) i depicted a reference. In the ame way a done by Wang et al. (2013), we employ a lightly curved fault plane, parallel to the aumed ubduction lab. The dip angle increae linearly from 10 on the top (ocean bottom) to 20 at about 80 km depth. To avoid any artificial bounding effect, a large enough potential rupture area of 650 km 300 km i ued. The upper edge of the fault i located along the trench eat of Japan, on the boundary between the Pacific plate and the North America plate. The patch ize i 10 km 10 km. The rake angle determining the lip direction at each fault patch i allowed to vary between 90 ± 20. Green function are calculated baed on the CRUST2.0 model (Bain et al., 2000) in the concerning area. In the inverion, the data i weighted twice a much for the two horizontal component a for the vertical component. The inverted fault lip ditribution are hown in Figure 2.12, and the comparion of oberved and ynthetic diplacement on horizontal and vertical component are hown in Figure The three inverion reult in calar eimic moment of , , Nm, equivalent to moment magnitude of Mw 8.82, 8.96, and 8.96, repectively. The maximum lip of the three inverion reult are 16.7, 21.2 and 21.1 m, repectively. The PPP float olution lead to underetimation of about 38% on the calar eimic moment and about 21% on maximum fault lip, which may lead to an underetimation on tunami cale. PPP fixed olution i quite conitent with pot-proceed ARIA olution, and i much better than PPP float olution. The PPP float olution how a circular rupture without obviou rupture propagation and direction, while the PPP fixed olution and pot-proceed ARIA olution how that the rupture mainly propagate along the fault up-dip direction and toward the ea bed. Integer ambiguity reolution bring the PPP moment magnitude into agreement with the pot-proceed value. The moment magnitude of the earthquake we etimated (Mw

37 8.96) in thi tudy i imilar to the moment olution of about Mw 9.0, etimated by the USGS, and lightly maller than Mw 9.1 of Global CMT. The inverion reult of real-time PPP fixed olution and the pot-proceed ARIA olution are quite imilar to each other not only in the moment magnitude, but alo in the lip ditribution pattern. Overall, the comparion of the three inverion reult how that integer ambiguity reolution in PPP i beneficial for fault lip inverion and the moment magnitude etimation. The PPP fixed olution can provide a reliable etimation of earthquake magnitude and even of the fault lip ditribution in real time. Figure 2.12: The inverted fault lip ditribution. (a) Inverion with permanent diplacement obtained from real-time PPP float olution; (b) Inverion with real-time PPP fixed olution; (c) Inverion with pot-proceed ARIA olution

38 Figure 2.13: The comparion of the oberved and ynthetic diplacement on horizontal component, and on vertical component, repectively. a) Inverion with permanent diplacement obtained from real-time PPP float olution; (b) Inverion with real-time PPP fixed olution; (c) Inverion with pot-proceed ARIA olution. 2.5 Application to the 2010 E1 Mayor-Cucapah earthquake GPS data and analyi The 2010 Mw 7.2 El Mayor-Cucapah earthquake (April 4, 2010, 22:40:42 UTC), truck Baja California approximately 65 km outh of the US Mexico border. Thi earthquake ruptured along the principal plate boundary between the North American and Pacific plate with a hallow focal depth of about 10 km. Surface rupture of thi earthquake extended for about 120 km from the northern tip of the Gulf of California northwetward nearly to the international

39 border, with breakage on a erie of fault occupying a general NW-SE zone. It caued ignificant ground motion at ditance up to everal hundred kilometer from the epicenter. Mot of the broadband eimometer cloe to the epicenter clipped in thi event, trong motion eimometer and high-rate GPS receiver are the two major candidate intrument to detect the urface diplacement. The UNAVCO Plate Boundary Obervatory (UNAVCO-PBO) of EarthScope i a geodetic obervatory deigned to characterize the three-dimenional train field acro the active boundary zone between the Pacific Plateand the wetern United State. The El Mayor Cucapah Earthquake wa well recorded not only by trong motion tation but alo by high-rate GPS receiver with a 5 Hz ampling rate at the PBO tation. Thi event i one of the bet example in California of a large earthquake for which abundant high-rate GPS and trong motion record are available (Allen and Ziv, 2011). With the real-time correction generated by the EPOS-RT oftware (the RMS of orbit error, clock error, and URE are about 4.3 cm, 5.6 cm, and 3.7 cm, repectively), we replay the 5 Hz GPS data collected by 30 nearfield UNAVCO-PBO tation during the El Mayor-Cucapah earthquake. Thee tation are ued for fault lip inverion and their ditribution i hown in Figure Figure 2.14: Location of the El Mayor Cucapah earthquake and the ditribution of the elected highrate GPS and trong motion tation. The epicenter of the El Mayor-Cucapah earthquake i marked by

40 the red tar. The blue circle repreent the GPS tation, and the gray triangle are trong motion tation. We calculated the RMS value of 2 hour (before the earthquake event) poition erie (after convergence) of the 30 GPS tation. The RMS value of PPP float olution are found to be 2.2, 4.1, and 7.6 cm repectively in north, eat and up component. PPP ambiguity reolution can improve the accuracy to 1.8, 1.9 and 3.9 cm in the correponding component. We calculated the RMS value of two hour (before the earthquake event) velocity erie for the 30 GPS tation. The RMS value are found to be 1.2, 0.7 and 4.0 cm/ repectively in the north, eat and up component Comparing GPS and eimic waveform Some of the GPS tation are co-located with eimic tation from the Southern California Seimic Network (SCSN) operated by the USGS (U.S. Geological Survey) and Caltech (Fig. 2.14). Almot all broadband velocity network intrument in California alo have an accelerometer in order to record large magnitude event when the velocity intrument are likely to clip. The accelerometer do not clip, and velocity and diplacement waveform can be obtained through ingle and double integration, repectively. The velocity and diplacement eimogram in thi tudy are provided by California Geological Survey (CGS/CSMIP, The baeline offet are removed by applying a high-pa filter at the price of low-frequency information lo, including the lo of permanent tation offet. The PPP and eimic diplacement waveform from P744 and 5028 for the El Mayor- Cucapah earthquake are exemplarily compared in Figure The 5 Hz ambiguity-fixed PPP diplacement and 200 Hz eimic diplacement are hown by the red and black line repectively. The tandard PPP float olution i alo hown for comparion with the green line. In the Figure 2.15a, we how the entire period of eimic haking at P744/5028 in the north component. The north component how very imilar amplitude of the dynamic component. From the PPP waveform, the permanent coeimic offet of about 0.1 m are repectively viible in Figure 2.15a, while permanent coeimic offet are lot in the eimic waveform. The Figure 2.15b diplay an excellent agreement of eimic and ambiguity-fixed PPP diplacement in the eat component within few centimeter. From the Figure 2.15c, the vertical component ha been evidently improved by PPP ambiguity reolution, but it i till the noiiet component

41 Figure 2.15: The eimic and PPP diplacement on the co-located 5028 (eimic) and P744 (GPS) tation during the El Mayor Cucapah earthquake on April 4, The north, eat and up component are repectively hown in the ub-figure a, b, and c. The ambiguity-fixed PPP and eimic diplacement are repectively hown by the red and black line. The tandard PPP float olution i alo drawn for comparion with the green line. The GPS velocity erie are alo compared with thoe, integrated from the collocated accelerometer. The 5 Hz GPS velocity waveform are derived from real-time ambiguity-fixed PPP. The 200 Hz eimic one are obtained through ingle integration of accelerometer data. The velocity reult at P744/5028 are hown in Figure The velocity erie derived from PPP fixed olution are hown by the red line, while the correponding eimic velocitie are

42 hown by the black line. From the Figure 2.16a and 2.16b, the velocity erie in the horizontal component how a high degree of conitency with the correponding eimic reult. The Figure 2.16c indicate that the vertical component i relatively noiy. A tatitical analyi indicate that the RMS of the difference between PPP and eimic velocitieare 2.1, 2.0 and 3.1 cm/ in north, eat, and vertical component, repectively. Figure 2.16: The velocity erie on the collocated P744/5028 tation during the El Mayor Cucapah earthquake on April 4, The north, eat and up component are hown in the ub-figure a, b and c repectively. The PPP velocity erie are hown by the red line, while the eimic velocitie are hown by the black line

43 2.5.3 Fault lip inverion We derive the patial ditribution of fault lip uing the permanent coeimic diplacement obtained from the real-time PPP float olution, real-time PPP fixed olution, and the potproceed daily olution (the difference between the day before the earthquake and the day after the earthquake), repectively. The fault geometric parameter (trike 313 /dip 88 ) are adopted from the global centroid moment tenor (GCMT) olution of the earthquake. The rake angle (lip direction relative to the trike) i allowed to vary ±20 around the GCMT olution of 186. The fault i given to be 130 km along the trike and 20 km wide down the dip, which i then divided into 26 4=104 ub-fault. To avoid unreaonable lip pattern, the moothing contraint i impoed. In the inverion, the data i weighted twice a much for the two horizontal component a for the vertical component. The inverted fault lip ditribution are hown in Figure 2.17, and the comparion of oberved and ynthetic diplacement on horizontal and vertical component are hown in Figure The three inverion reult in calar eimic moment of , and Nm, equivalent to moment magnitude of Mw 7.09, 7.19, and 7.19, repectively. The PPP float olution lead to an underetimation of about 30% of the calar eimic moment, and PPP fixed olution ignificantly improve it. The inverion reult of real-time PPP fixed olution and pot-proceed daily olution are quite imilar with each other not only in the moment magnitude, but alo in the lip ditribution pattern. The major lip area occurred at a very hallow depth (near the urface) at about 90 km along the trike direction on the fault plane. The rake variation how that there i a purely right lateral trike lip at the northwet of the fault, and a minor normal fault component occur at the outh eat of the fault. With the conideration of the hypocentral location, we can confirm that thi earthquake i an aymmetric bilateral rupture event: the rupture mainly propagate northwetward from the hypocenter during the ource proce

44 Figure 2.17: The inverted fault lip ditribution. (a) Inverion with permanent diplacement obtained from real-time PPP float olution; (b) Inverion with real-time PPP fixed olution; (c) Inverion with pot-proceed daily olution

45 Figure 2.18: The comparion of oberved and ynthetic diplacement on horizontal component, and on vertical component, repectively. a) Inverion with permanent diplacement obtained from real-time PPP float olution; (b) Inverion with real-time PPP fixed olution; (c) Inverion with potproceed daily olution. 2.6 Concluion Baed on the IGS real-time infratructure, everal IGS RTAC demontrated the capacity of the real-time global PPP ervice by providing precie orbit and clock product under the IGS RTPP framework. The tandard PPP ervice i recently ignificantly improved in both (re-) convergence time and poitioning accuracy by applying integer ambiguity reolution and uing raw obervation with ionophere delay a parameter with proper contraint. Thee recent improvement are implemented into the real-time PPP ervice, etablihed by GFZ a one of the IGS RTAC with integer ambiguity reolution for precie poitioning and geophyical application. In order to ae the preciion of the real-time PPP ervice, fifteen real-time GPS tation which are not ued for product generation are elected a uer tation. From the experimental reult, the long-term variation and hort-term fluctuation in the float PPP olution are ignificantly reduced by applying integer ambiguity reolution, epecially in eat component. On average, the poition RMS of the float olution in eat, north and up direction are reduced from about 3, 5 and 6 cm to that of the fixed olution of about 1, 1 and 3 cm, repectively. Thi improvement i alo demontrated by the comparion of the poition derived from float and fixed olution over the two hour period before the 2011 Tohoku-Oki and El Mayor-Cucapah earthquake. The 2011 Mw 9.0 Tohoku-Oki earthquake (March 11, 2011, 05:46:23 UTC) in Japan and the 2010 Mw 7.2 El Mayor-Cucapah earthquake (April 4, 2010, 22:40:42 UTC) in northern Baja California provide u with real event to evaluate the performance of real-time PPP derived coeimic diplacement. Both of thee two event were well recorded not only by trong motion tation but alo by high-rate GPS receiver. PPP diplacement are compared with the eimic diplacement at the collocated tation. The comparion how a high degree of reemblance between PPP and eimic diplacement, with aligned phae and very imilar amplitude of the dynamic component. The difference i that permanent coeimic offet are clearly viible in the PPP waveform, but accurate permanent coeimic offet are not available in the eimic waveform becaue of the baeline offet caued by tilt and rotation of the eimic intrument. In general the diplacement waveform, etimated from real-time

46 ambiguity-fixed PPP and thoe provided by the accelerometer intrumentation are largely conitent in the dynamic component within few centimeter. The reult alo indicate that integer ambiguity reolution improve the accuracy of real-time PPP diplacement ignificantly. We derive the patial ditribution of fault lip for the 2011 Tohoku-Oki earthquake and the 2010 El Mayor-Cucapah earthquake uing the coeimic diplacement obtained from the realtime PPP float olution, real-time PPP fixed olution, and pot-proceed olution, repectively. In the cae of the 2010 El Mayor-Cucapah earthquake, the three inverion reult in calar eimic moment of Nm, Nm, Nm, equivalent to moment magnitude of Mw 7.09, Mw 7.19, and Mw 7.19, repectively. The PPP float olution lead to an underetimation of about 30% of the calar eimic moment, and PPP fixed olution ignificantly improve it. For the 2011 Tohoku-Oki earthquake, the three inverion reult in calar eimic moment of Nm, Nm, Nm, equivalent to moment magnitude of Mw 8.82, Mw 8.96, and Mw 8.96, repectively. The PPP float olution lead to an underetimation of about 38% of the calar eimic moment, integer ambiguity reolution bring the PPP moment magnitude into agreement with the pot-proceed value. The PPP fixed olution can provide a reliable etimation of earthquake magnitude and even of the fault lip ditribution in real time and become complementary to exiting eimic EEW methodologie. The real-time ambiguity-fixed PPP module can be embedded into high-rate GPS receiver firmware and be incorporated into EEW ytem epecially for region at threat from large magnitude earthquake and tunami

47

48 3 Augmented PPP for eimological application uing dene GNSS network 3.1 Introduction Appropriate and precie GPS real-time data analyi i crucial for the ue of the network data for hazard monitoring. Currently, the relative baeline/network poitioning technique i predominantly ued for thi purpoe. For moderate-to-hort baeline, integer ambiguity reolution can be achieved within a few econd and ometime with only one obervational epoch to achieve a high poitioning accuracy of a few cm. For the relative poitioning technique, GPS data from a network i analyzed imultaneouly to etimate tation poition. Thi i a ignificant limitation for the challenging imultaneou and precie real-time analyi of GPS data from hundred or thouand of ground tation. Furthermore, intermittent tation dropout complicate the network-baed relative poitioning. Relative poitioning alo require a local reference tation, which might itelf be diplaced during a large eimic event, reulting in mileading GPS analyi reult. The reference tation hould be ufficiently far from the focal region, but mut alo be part of a ub-network that ha relatively hort baeline. Alternatively, precie point poitioning (PPP) can provide abolute diplacement with repect to a global reference frame (defined by the atellite orbit and clock) uing a ingle GPS receiver. It i more flexible than the relative poitioning technique and i widely ued for hazard monitoring. However, the PPP method require a long convergence period of about 20 minute after receiver activation or after eriou and/or long ignal interruption for mot of the GPS atellite. The wort cae cenario for the GPS component of an earthquake/tunami monitoring ytem would be a power failure during the diater, which would reduce the uefulne of the PPP baed diplacement olution becaue of the time required for reconvergence. To avoid thi major diadvantage, the PPP regional augmentation (Li et al., 2011) ha been developed by making ue of atmopheric correction from a regional reference network to achieve nearly intantaneou ambiguity reolution. But the regional monitoring tation could alo be diplaced by the earthquake. Therefore the current PPP regional augmentation, in which the reference tation are aumed being in tatic mode and even with known coordinate for generating atmopheric correction (Li et al., 2011) or pre-fit undifferenced obervation reidual (Ge et al., 2012), could not be ued for earthquake monitoring

49 Thi i our motivation to propoe here a novel method for fat or even intantaneou poitioning, making full ue of the currently available global PPP ervice and regional GPS monitoring network. We etimate coordinate of all monitoring tation in kinematic mode to avoid the effect of the earthquake induced-diplacement on atmopheric correction. The derived atmopheric correction at the tation with fixed ambiguitie then can be provided to other monitoring tation for intantaneou ambiguity reolution, o that precie diplacement can alway be achieved within a few econd. The erie of diplacement, derived uing the propoed method, will be uninterrupted even in cae of a break in tracking (lo of ignal lock, cycle lip, or data gap) due to a power outage or imilar diruption. Thi i a coniderable advantage for hazard monitoring application. The new method doe not depend on a pecific reference tation and therefore the analyi reult will not be affected by imultaneou haking of any particular tation. It alo ha better flexibility and efficiency compared to complicated network/ubnetwork analyi. We demontrate the advantage of the novel augmented PPP approach uing 1 Hz GEONET data, collected during the Tohoku-Oki earthquake (Mw 9.0, 11 March, 2011) in Japan. 3.2 Augmented PPP approach Succeful reolution of integer-cycle carrier-phae ambiguitie i a prerequiite to achieve the mot precie poition etimate with GPS by tranforming precie but ambiguou phae range meaurement into precie unambiguou meaurement (Blewitt, 1989; Dong and Bock, 1989). For relative poitioning, the uncalibrated phae delay (UPD) are removed by the application of the double-difference (DD) technique and thu the phae ambiguity can be fixed to integer (Dong and Bock, 1989). The atmopheric delay are alo motly eliminated in cae of moderate-to-hort baeline, o that integer-cycle phae ambiguitie can be fixed within few econd. Recent tudie how that the UPD can be etimated with high accuracy and reliability from a global reference network and tranferred to the GPS monitoring tation to allow reolution of the ambiguitie without differencing (Li et al., 2013; Ge et al., 2008). Several international GNSS ervice (IGS) analyi center provide GPS orbit, clock, and UPD data product to allow real-time PPP ue enabling ambiguity reolution anywhere in the world (Dow et al., 2009; Ge et al., 2012; Loyer et al., 2012). However, PPP till need a comparatively long (re)convergence time of approximate 20 minute to achieve reliable integer ambiguity reolution becaue precie atmopheric delay model cannot be derived from uch a pare global reference network (Li et al., 2013). An increaing number of regional GPS monitoring network are intalled around the world for precie navigation and geophyical application, epecially in eimically active region (e.g. Japan, Wetern North America, Greece, and Chile). One poible olution for achieving

50 fat ambiguity reolution in PPP i to retrieve the atmopheric delay a correction from data of thee dene regional network. By applying the UPD correction, the integer un-differenced ambiguitie on the L1 and L2 frequencie can be fixed in PPP mode at all regional monitoring tation. The atmopheric correction of the ionopheric lant and tropopheric zenith wet delay then can be derived from the PPP fixed olution a I m Z u r l t t ( b b ) N (3.1) r, j r r r r, j r j r, j j j r, j r, j I m Z u r p t t c( d d ) e (3.2) r, j r r r r, j r r, j j r, j Where, l r, j, p, r j denote phae and code obervation minu computation (OMC) from atellite to receiver r at frequency j ; u i the unit direction vector from ite to atellite; r denote the increment of the receiver poition; r Z r denote the tropopheric zenith wet delay; m r i the wet mapping function; t and tr are the clock error; j i the wavelength; br, ji the receiver-dependent uncalibrated phae delay; b j i the atellite- dependent UPD; dr, jand d j are the code biae; I r, j i the ionopheric delay; N r, ji the integer phae ambiguity; e r, j and, r j are the meaurement noie term of the peudo-range and carrier phae. Thi procedure i very flexible and computational efficient to be applied even for monitoring network with a large number of tation a the atmopheric correction are derived for each tation individually. Becaue regional monitoring tation themelve could be diplaced by the earthquake, the coordinate are etimated in kinematic mode to avoid the effect of earthquake induced-diplacement on the atmopheric correction that are generated. The contraint impoed on the kinematic coordinate of adjacent epoch are fine-tuned by uing an adaptive filter (Yang et al., 2001) in real-time to trengthen the olution. Uually atmopheric delay i rather table over hort period and can be repreented by a contant or a linear function. Therefore, even in period of trong haking, tation poition and atmophere are ditinguihable in parameter etimation becaue of the ignificant difference in their temporal character. A polynomial model can be ued to repreent the derived atmopheric correction on mall regional cale. Here three or more nearby monitoring tation are elected a augmenting tation for each monitoring tation, and the atmopheric correction of the elected augmenting tation are interpolated by a Linear Combination Method (LCM) (Han, 1997) a n n n ˆ ˆ 2 i 1, i( m i) 0, i i1 i1 i1 X X Min (3.3)

51 vˆ n vˆ (3.4) m i i i1 Where, n i the number of elected augmenting tation; m and i are indice for the monitoring and the elected augmenting tation, repectively; i denote the interpolation coefficient; Xˆ m and X ˆ i are the tation coordinate in the local horizontal plane ytem; X im and Yim are the plane coordinate difference between the monitoring and augmenting tation; v ˆi i the ionopheric or tropopheric delay; v ˆm i the interpolated ionopheric or tropopheric delay at the monitoring tation. For regional reference network with moderate-to-hort baeline (few ten of kilometer inter-tation ditance) cm-level accuracy can be achieved for the interpolated atmopheric delay correction. The precie interpolated atmopheric correction are impoed a a trong contraint on the related parameter of the monitoring tation, while the coordinate are etimated in kinematic mode. Auming that r 1 to r n are elected a augmenting tation for interpolating correction for the monitoring tation r m. The ionopheric lant delay parameter for an individual atellite i i contrained to the interpolated correction a i i 2 I I w w N (3.5),, ~ (0, ) r r r r I I w m 1 2 n I And the contraint for the zenith wet delay parameter i 2 Z Z w w N (3.6) Where I i rm,, ~ (0, ) r r r r T T w m 1 2 n T denote the lant ionopheric delay from tation r m to atellite i ; interpolated ionopheric correction; Z r1, r2 rn Zr m i the interpolated correction. w I and I i r1, r2rn i the denote the zenith wet delay for tation r m, and w T are the biae between the true and the interpolated atmopheric correction. The tatitical procee of w I and w T are zero mean white procee with variance of 2 2 w and I w T for the ionopheric and tropopheric delay, repectively. By adding thi precie atmopheric delay model to the orbit, clock and UPD product ued in global PPP ambiguity reolution, intantaneou ambiguity reolution i achievable at the monitoring tation, o that the augmented PPP can have ambiguity reolution performance equivalent to relative poitioning. It hould be mentioned that the election of augmenting tation i critical, a atmopheric correction can only be derived from augmenting tation at which the ambiguity reolution i uccefully achieved

52 3.3 Application of augmented PPP approach and reult The 2011 Mw 9.0 Tohoku-Oki earthquake (11 March 2011, 05:46:23 UTC) in Japan i one of the bet GPS recorded large earthquake, a Japan ha one of the denet GPS network in the world. The Geopatial Information Authority of Japan (GSI) operate more than 1,200 continuouly oberving GPS tation (collectively called the GPS Earth Obervation Network Sytem) all over Japan. The geographical ditribution of the tation i indicated in Figure 3.1. The ue of the GEONET data provide an excellent opportunity to evaluate the performance of our novel PPP analyi method. We replayed all the 1 Hz GPS data collected by the GEONET tation during the 2011 Tohoku-Oki earthquake uing the augmented PPP method in imulated real-time mode. Figure 3.1: Location of the 2011 Tohoku-Oki earthquake epicenter and the ditribution of the high-rate GPS ite. The epicenter i marked by the red tar. The brown circle repreent GPS ite. The black diamond repreent the reference ite of relative poitioning analyi. The purple rectangle repreent the ite of the time erie example. Thi figure i drawn uing GMT oftware

53 Firt we proce 1 Hz GPS ground tracking data of about 80~90 globally ditributed realtime IGS tation uing the GFZ EPOS-RT oftware in imulated real-time mode for providing GPS orbit, clock and uncalibrated phae delay (UPD) (Li et al., 2013) correction at a 5 ampling interval. Uing the orbit, clock and UPD data, the integer ambiguitie are fixed in PPP mode for all of the GEONET tation and atmopheric correction are derived on an individual tation bai. For each GEONET tation, three nearby GPS tation are elected a augmenting tation. In addition to the orbit, clock and UPD data product from the global PPP ervice, the atmopheric correction of the augmenting tation are interpolated and impoed a a contraint on related parameter. Then intantaneou ambiguity fixing i performed independently at each epoch. The diplacement waveform, derived from augmented PPP olution, at tation 0176 are hown in the Figure 3.2a, to illutrate typical behavior. The north, eat and up component are repectively hown by the blue, red and black curve

54 Figure 3.2: The diplacement waveform derived from the augmented PPP olution. The north, eat and up component are hown by the blue, red and black curve, repectively. a): The diplacement waveform at tation 0176; b): The diplacement waveform at the reference tation

55 Figure 3.3: Comparion of the diplacement waveform derived from augmented PPP, global PPP and relative poitioning olution. The north, eat and up component are hown by the blue, red and black curve, repectively. a) The diplacement derived from augmented PPP olution at tation 0175, which ha a data gap of about 2 min during the eimic haking; b) The diplacement derived from the global PPP olution at tation 0175; c) The diplacement derived from relative poitioning at tation 0175, with 0065 a reference tation

56 It i found that there are ignificant GPS data gap or cycle lip during the eimic haking at ome GEONET ite (e.g., 0175, 0588, etc). There i for example a data gap of about 2 min at tation 0175, which tart at epoch 05:47:21 and end 05:49:27 (GPS time, GPST). The diplacement from the augmented PPP olution for tation 0175 are hown in Figure 3.3a. Station 0172, 0914 and 0918 are elected a the augmenting tation for The etimated ionopheric correction during eimic haking at the augmenting tation are illutrated in Figure 3.4a and Figure 3.5a. The etimated zenith wet delay during the 600 eimic haking period are repectively 5.4±0.1 cm, 6.5±0.1 cm and 6.4±0.1 cm at three augmenting tation. With the atmopheric correction, retrieved from the augmenting tation, the atmopheric delay for 0175 are interpolated uing the linear combination method. The reulting interpolation are compared with the etimated value at 0175 in order to ae the accuracy of the interpolation. Figure 3.4b and Figure 3.5b how the ionopheric difference between interpolated and etimated value. The difference are found to be maller than 5 cm. The tropopheric interpolation error i about 0.26 cm. We found that the interpolated atmopheric correction are accurate enough for rapid ambiguity reolution

57 Figure 3.4: Ionopheric correction at augmenting tation and ionopheric interpolation error. a) The etimated ionopheric correction for GPS atellite PRN 15 at the augmenting tation 0172, 0914 and 0918 during eimic haking; b) Ionopheric interpolation error of PRN 15 for the tation

58 Figure 3.5: Ionopheric correction for the augmenting tation and the ionopheric interpolation error. a) The etimated ionopheric correction for GPS atellite PRN 28 for the augmenting tation of 0172, 0914 and 0918 during eimic haking; b) Ionopheric interpolation error of PRN 28 for the tation

59 Figure 3.6: Comparion of diplacement waveform derived from augmented PPP, global PPP and RP olution. The north, eat and up component are hown by the blue, red and black curve, repectively. a) The diplacement derived from augmented PPP olution at tation 0588, which ha a

60 data gap of about 2 min during the eimic haking; b) The diplacement derived from global PPP olution at tation 0588; c) The diplacement derived from relative poitioning at tation 0588, with 0065 a the reference tation. We alo derive diplacement waveform of all GEONET tation from the relative poitioning (RP) and global PPP olution, and compare them with the augmented PPP olution. The global PPP diplacement for tation 0175 are hown in Figure 3.3b. In the global PPP olution, the diplacement erie how a large diturbance after the data gap that i caued by the convergence equence for fixing the PPP ambiguitie (about 20 min). Thi untable behavior i an unavoidable problem for a real-time PPP ue a the pare global reference network employed cannot provide accurate atmophere delay for fat ambiguity reolution. The relative poitioning olution for the tation 0175 i alo hown in Figure 3.3c. For the relative poitioning analyi, we adopt the ame reference tation 0065 a Ohta et al (2012). It can be een that there are ome fluctuation in the diplacement erie derived from the relative poitioning olution, which are caued by the ground haking at the reference tation location. The Figure 3.2b how the ground diplacement at the 0065 reference tation. Peak urface diplacement of up to half a meter were recorded at thi tation during the earthquake even though it i about 700 km away from the epicenter. The diplacement waveform for the tation 0588 derived from augmented PPP (0217, 0590 and 0965 are elected a augmenting tation), global PPP and RP olution are alo compared in Figure 3.6. The permanent coeimic diplacement of ninety evenly-ditributed tation derived from pot-proceed ARIA olution (5 min olution), real-time augmented PPP, global PPP, and RP olution are hown in Figure 3.7a, 3.7b, 3.7c, and 3.7d, repectively, by the red arrow. The pot-proceed ARIA olution i provided by the ARIA team at JPL (Jet Propulion Laboratory) and Caltech (California Intitute of Technology). It can be found that the permanent coeimic diplacement, derived from the real-time augmented PPP olution, are quite conitent with thoe of pot-proceed ARIA olution in both horizontal and vertical component. The root mean quared error (RMS) of the difference between the two olution are 1.4, 1.1, and 1.7 cm in north, eat, and vertical component, repectively. Figure 3.7c how ome ignificant difference between global PPP and ARIA diplacement at ome tation, which are caued by the data interruption at thee tation. The correponding RMS value of the difference are 4.3, 22.7, and 9.0 cm in north, eat, and vertical component. Figure 3.7d how, that the RP diplacement have obviou diagreement with the ARIA reult at nearly all tation due to problem of the earthquake haking of the reference tation. The RMS value of the difference are 10.1, 14.1, and 5.7 cm in north, eat, and vertical component. Figure

61 how the diplacement difference between the ARIA olution and the other three olution. Thee comparion how that the augmented PPP method can ignificantly improve the reliability and accuracy of earthquake-induced coeimic diplacement in real-time cenario

62 - 53 -

63 Figure 3.7: The comparion of oberved and ynthetic diplacement in horizontal component, and in vertical component, repectively. (a) Inverion with the pot-proceed ARIA olution; (b) Inverion with coeimic diplacement obtained from real-time augmented PPP olution; (c) Inverion with realtime global PPP olution; (d) Inverion with real-time RP olution. Thi figure i drawn uing GMT oftware

64 Figure 3.8: The reidual diplacement from the ARIA olution. (a) Reidual difference between augmented PPP and ARIA vector; (b) Reidual difference between global PPP and ARIA vector; (c) Reidual difference between RP and ARIA vector. Thi figure i drawn uing GMT oftware. We derived four fault lip ditribution baed on the four different GPS analyi technique introduced above. Identical finite fault parameter are ued for the four inverion. Identically a done by Wang et al. (2013), we employ a lightly curved fault plane, parallel to the aumed ubduction lab. The dip angle increae linearly from 10 on the top (ocean bottom) to 20 at about 80 km depth. To avoid any artificial boundary effect, a large enough potential rupture area of 650 km 300 km i ued. The upper edge of the fault i located along the trench eat of Japan, on the boundary between the Pacific plate and the North American plate. The patch ize i about 10 km 10 km. The rake angle determining the lip direction at each fault patch i allowed to vary between 90 ± 20. Green function are calculated baed on a local CRUST2.0 model by uing the oftware code from Wang et al. (2003). The comparion of ynthetic and oberved diplacement on horizontal and vertical component are hown in Figure 3.7, and the inverted fault lip ditribution are hown in Figure 3.9. Although the four reult how imilar lip ditribution, the inverion from realtime augmented PPP olution i the mot conitent with pot-proceed ARIA olution not only for the lip ditribution, but alo for the diplacement fitting. Suppoing that the potproceed ARIA reult i the mot reliable and can be taken a a reference for other three reult, the inverion of global PPP ha the wort lip ditribution, and the inverion of RP olution ha the wort diplacement fitting. Figure 3.10 how the fault lip difference between the ARIA olution and the other three olution. Overall, the comparion of the inverion how that the augmented PPP method i beneficial for fault lip inverion in realtime cenario. It provide a more accurate and robut etimation of the fault lip ditribution and diplacement fitting than the global PPP olution and RP olution. By contrat, the global PPP and RP olution reult in relatively poor lip ditribution not only in peak lip, but alo in the extenion of the lip area (Figure 3.10)

65 Figure 3.9: The inverted fault lip ditribution. (a) Inverion with pot-proceed ARIA olution; (b) Inverion with coeimic diplacement obtained from real-time augmented PPP olution; (c) Inverion with real-time global PPP olution; (d) Inverion with real-time RP olution. The tar denote the epicenter. Thi figure i drawn uing GMT oftware

66 Figure 3.10: The reidual lip ditribution from the ARIA olution. (a) Reidual difference between augmented PPP and ARIA inverion; (b) Reidual difference between global PPP and ARIA inverion; (c) Reidual difference between RP and ARIA inverion. The tar denote the epicenter. Thi figure i drawn uing GMT oftware. 3.4 Concluion We propoed a new GPS analyi method for hazard (e.g. earthquake and tunami) monitoring. The new augmented PPP method can overcome the limitation of current relative poitioning and global PPP approache for thi application. The performance of the new approach i evaluated by GPS ground network data, oberved during the 2011 Tohoku-Oki earthquake in Japan. The atmopheric correction retrieved from the nearby monitoring tation can be interpolated with accuracy better than 5 cm. Thi mean that the interpolated atmopheric correction are accurate enough for rapid ambiguity reolution, which i a prerequiite to achieve the mot precie diplacement. The diplacement waveform, derived uing the augmented PPP approach are immune to the convergence problem caued by data gap and cycle lip and the problem of the earthquake haking the reference tation compared to the waveform baed on RP and global PPP analyi. Thi make augmented PPP potentially appropriate for the application in operational earthquake/tunami monitoring and warning ytem. The reliability and accuracy of permanent coeimic diplacement are alo ignificantly improved. The RMS accuracy of about 1.4, 1.1, and 1.7 cm are achieved in the north, eat, and vertical component, repectively. The inverion reult indicate that the augmented PPP olution i the mot conitent with pot-proceed ARIA olution both in the fault lip ditribution and diplacement fitting

67

68 4 Temporal point poitioning approach for GNSS eimology uing a ingle receiver 4.1 Introduction High-rate GNSS (e.g., 1 Hz or higher frequency) meaure diplacement directly and can provide reliable etimate of broadband diplacement, including tatic offet and dynamic motion of arbitrarily large magnitude (Laron et al., 2003; Bock et al., 2004). GNSS-derived diplacement can be ued to quickly etimate earthquake magnitude, model finite fault lip, and alo play an important role in earthquake/tunami early warning (Blewitt et al., 2006; Wright et al., 2012; Hoechner et al., 2013;). There are two primary trategie for real-time GNSS proceing: relative baeline/network poitioning and precie point poitioning (PPP) (Zumberge et al., 1997). The diadvantage of relative poitioning (RP) i that the olution are influenced by movement of the reference tation (Ohta et al., 2012). Additionally the computational load increae very quickly a the network get larger (Crowell et al., 2009). In contrat, PPP can provide abolute eimic diplacement related to a global reference frame defined by the atellite orbit and clock with a ingle GNSS receiver (Kouba 2003; Wright et al., 2012; Li et al., 2013a). However, real-time PPP require precie atellite orbit and clock correction and alo need a long (re)convergence period, of about thirty minute, to achieve centimeter-level accuracy (Collin et al., 2009). Coloimo et al. (2011) propoed a variometric approach to overcome the difficultie of the two aforementioned, preently adopted, approache for GNSS eimology. Thi approach i baed upon the time ingle-difference of the carrier phae obervation recorded by a ingle GNSS receiver at a given ground tation. The time erie of the tation velocitie are etimated, and thee velocitie are integrated to provide coeimic diplacement. However, eventual biae of the etimated velocitie accumulate over time and diplay a a drift in the coeimic diplacement. The aumption of a linear drift limit the integration interval to few minute

69 (Branzanti et al., 2013). If the entire period of eimic haking lat longer than few minute in the cae of large earthquake, the drift value could be large and can not be fully removed by a linear de-trending. In thi Chapter, we propoe a new approach for etimating coeimic diplacement with a ingle receiver in real-time. The approach overcome not only the diadvantage of the PPP and RP technique, but alo decreae the decribed drift in the diplacement derived from the variometric approach. The coeimic diplacement could be etimated with few centimeter accuracy uing GNSS data around the earthquake period. Meanwhile, we preent and compare the obervation model and proceing trategie of the current exiting ingle-receiver method for real-time GNSS eimology. Furthermore, we propoe everal refinement to the variometric approach in order to eliminate the drift trend in the integrated coeimic diplacement. The mathematical relationhip between thee method i dicued in detail and their equivalence i alo proved. The impact of error component uch a atellite ephemeri, ionopheric delay, tropopheric delay, and geometry change on the retrieved diplacement are carefully analyzed and invetigated. Finally, the performance of thee ingle-receiver approache for real-time GNSS eimology i validated uing 1 Hz GPS data collected during the Tohoku-Oki earthquake (Mw 9.0, March 11, 2011) in Japan. 4.2 Temporal point poitioning approach The linearized equation for carrier phae and code obervation can be expreed a follow, l u xt t B I T (4.1) r, j r r r, j r, j r r, j r j r j p u xt t I T e (4.2) r, j r r r, j r r, j Where, l,, p, denote oberved minu computed phae and code obervation from atellite to receiver r at frequency j ( j 1, 2 ); u r i unit direction vector from receiver to atellite; x denote receiver poition increment; T r, Ir, jdenote tropopheric and ionopheric

70 delay; t, t r are clock error of atellite and receiver; Br, ji phae ambiguity; e r, j,, meaurement noie of carrier phae and code. In order to achieve the mot precie poition etimate with GNSS, the phae center offet and variation, and tation diplacement by tidal loading mut be conidered. Phae wind-up and relativitic delay mut alo be corrected according to the exiting model (Kouba and Héroux, 2001), although they are not included in the equation. The ionopheric delay can be etimated a unknown parameter or eliminated by uing dual-frequency phae and code data. The tropopheric delay i corrected with an a priori model, and the reidual part i decribed a a random walk proce (Boehm et al., 2006). The receiver clock i etimated epoch-wie a white noie. Furthermore, real-time precie atellite orbit and clock product are now available online via the International GNSS Service (IGS) real-time pilot project (RTPP) (Caiy et al., 2012; Dow et al., 2009). For real-time PPP proceing, the phae ambiguitie are etimated together with the receiver poition, receiver clock, and reidual tropopheric delay. The ambiguitie need ome time to converge (e.g. thirty minute) to the correct value, until enough obervable are ued in the filter. There will be a big diturbance in the diplacement equence during the convergence period (ee Figure 4.1). In the variometric approach, ambiguitie are eliminated uing the time difference of phae obervation and thu the convergence proce i not required. Although the velocitie can be etimated with a high accuracy, the integration proce from velocitie to diplacement may lead to accumulated drift if longer than few minute (ee reult in Coloimo et al and/or Figure 4.2). In fact, for the eimological application, we are mainly intereted in the poition variation relative to the poition before the earthquake. Generally, the receiver poition before the earthquake i well known. Auming that the receiver poition at the epoch t 0 (before the r j are earthquake) i x( t 0), the ambiguitie B( t0) can be etimated along with the receiver clockt ( t 0) and tropopheric delay Tt ( 0) (fixed to a priori model) parameter at thi epoch a, r Bt ( ) t( t) Tt ( ) lt ( ) ut ( ) xt ( ) t( t) ( t) (4.3) 0 r

71 In our proceing, all the error component are carefully conidered following the PPP model. When the receiver poition x( t 0) i well known, the ambiguitie B( t 0) with a certain accuracy can be expected. Then we hold the etimated ambiguitie B( t 0) fixed in the ubequent epoch. At the epocht n, the poition x( t n) can be etimated a, ut ( ) xt ( ) t( t) Tt ( ) lt ( ) t( t) Bt ( ) ( t) (4.4) n n r n n n n 0 n A the ambiguitie are held to fixed value intead of being etimated a unknown parameter, the convergence proce will not be required. Furthermore, the poition x( t n) are etimated directly and thu the integration proce i alo avoided. We ubtitute the equation (4.3) into the equation (4.4) and have, ut ( ) xt ( ) t( t, t) Tt (, t) ut ( ) xt ( ) lt (, t) t( t, t) ( t, t) n n r 0 n 0 n n 0 n 0 n (4.5) It can be found that the accuracy of the poition etimate x( t n) i mainly affected by the variation of the tropopheric delay from the epoch t 0 to t n. Generally, the variation of the tropopheric delay i at centimeter level for few ten of minute. Therefore, the poition etimate are reaonably preumed to be with a good accuracy at centimeter level. We can ee that equation (4.5) i in the ame form a the time-differenced equation of phae obervation between the epoch t 0 and t n. Thi i equivalent to calculating the poition at epoch t n relative to the well-known poition at epocht 0. Thi method i baed on obervation from a ingle receiver. Therefore, we refer to it a the temporal point poitioning (TPP) method in the following ection. In our approach, an accurate initial poition at epoch t 0 (i.e. the receiver poition before the earthquake) i important for achieving high-accuracy diplacement. Figure 4.3 how the diplacement reult uing initial poition with different accuracie

72 Figure 4.1: PPP diplacement during convergence period in north, eat and up component, repectively. Twenty minute interval of 00:00-00:20 (GPST) on 11 March 2011, at GPS tation 0177 (GEONET). The north, eat, and up component are repectively hown by blue, red, and black line. North Diplacement (m) Potproce PPP Variometric-POPC Variometric-BOBC Eat Diplacement (m) Up Diplacement (m) Second of the week () Figure 4.2: Comparion of the coeimic diplacement waveform derived from the variometric approach and pot-proceed PPP olution. The red line how the pot-proceed PPP waveform a

73 reference. The blue line are the waveform derived from the variometric approach uing precie atellite orbit and clock (POPC olution), while the black line indicate the reult uing broadcat orbit and clock (BOBC olution). Twenty minute interval around the entire period of eimic haking on 11 March 2011, at GPS tation 0986 (GEONET). From top to bottom are the reult in north, eat, and up component, repectively. Figure 4.3: Diplacement derived from real-time TPP olution in eat component. The blue line how the reult uing initial poition with cm-level accuracy, the red line i the reult uing initial poition with 0.5m error, and the black line i the reult uing initial poition with 2m error. Twenty minute interval of 00:00-00:20 (GPST) on 11 March 2011, at GPS tation 0986 (GEONET). 4.3 Application of TPP approach and reult The 2011 Mw 9.0 Tohoku-Oki earthquake (11 March 2011, 05:46:23 UTC) in Japan i one of the bet recorded large-magnitude earthquake in hitory, by GNSS, a Japan ha one of the mot dene GNSS ground network in the world. Thi network i operated by the Geopatial Information Authority of Japan (GSI) and conit of more than 1,200 continuouly oberving

74 GNSS tation (the GNSS Earth Obervation Network Sytem, GEONET) all over Japan ( Firtly, the 1 Hz GEONET GPS data (dual frequency) before the earthquake wa proceed to evaluate the accuracy of the propoed TPP method. Twenty minute of diplacement from 00:00-00:20 (GPST) on 11 March 2011, at GNSS tation 0986, are hown in Figure 4.4. We compare the diplacement, derived from the real-time TPP olution uing different orbit and clock product. The black line how the reult uing broadcat orbit and clock (BOBC olution), which i routinely available from the GNSS receiver itelf in real-time. The red line are the reult uing precie atellite orbit and clock olution (POPC olution). The atellite orbit i generally predicted for real-time application a it dynamic tability. Here the ultrarapid orbit, updated every three hour and provided by GFZ, i applied. The clock correction have to be etimated and updated much more frequently (Zhang et al. 2011) due to their hortterm fluctuation. We proce 1 Hz data from globally ditributed real-time IGS tation uing the GFZ EPOS-RT oftware (Ge et al., 2011) in imulated real-time mode (a trictly forward filter) for generating precie GNSS clock correction at a 5 ampling interval. Real-time orbit and clock correction are reliant on an internet connection for tranmiion to monitoring tation, but the reality i that the internet connection and communication infratructure could be detroyed during large earthquake. In thee cae, atellite clock correction have to be extrapolated, although predicted ultra-rapid atellite orbit from the IGS or GFZ can be downloaded in advance. Here we alo evaluate how our product would be degraded during large earthquake, when the real-time tream would be unavailable. The reult uing the precie predicted orbit and extrapolated clock (POEC olution) are hown by the blue line. From Figure 4.4, we can ee that there i no obviou drift for even a twenty minute period in the horizontal component of TPP derived diplacement when precie orbit and clock correction are applied. In the vertical component, there i only a mall drift of a few centimeter. When only broadcat orbit and clock product are available, the drift in the diplacement erie are clearly viible, epecially in the vertical component. The drift value for twenty minute are everal centimeter in the horizontal component, and a few decimeter

75 in the vertical component. If we compare thi reult (TPP with BOBC) and Figure 4.2 reult (variometric approach with BOBC), we can ee that the two approache diplay imilar accuracy level. In the cenario that we can only ue extrapolated atellite clock due to failure of the internet connection, the drift value are everal centimeter in the horizontal component, and about one decimeter in the vertical component. Thi i everal centimeter wore than the precie clock reult, but much better than the broadcat orbit and clock reult, particularly in the vertical component. Obviouly, the accuracy of orbit and clock play a crucial role, and the difference between POPC, POEC and BOBC are reduced to few centimeter if only the firt 3-4 minute are conidered. We calculated the root mean quare (RMS) of the drift error at twenty minute of eighty evenly-ditributed GEONET tation. The reult for the different orbit and clock product are ummarized in Table 4.1. The drift of the BOBC olution can reach up to 9.1, 7.8, and 28.2 cm in north, eat and up direction repectively. The precie orbit and clock correction can remarkably improve the accuracy to 2.9, 2.3 and 5.8 cm in the correponding direction. It i even comparable to the accuracy of PPP after convergence period. With the extrapolated atellite clock, accuracie of 5.3, 4.7, 11.3 cm can be achieved in three component, repectively. Although thee accuracie are degraded compared to the POPC olution, it ignificantly improve the BOBC olution. From thee reult, we alo found that the vertical component i the mot enitive to the quality of the orbit and clock product. Table 4.1: Root mean quare of the drift value at eighty evenly-ditributed GEONET tation RMS North (cm) Eat (cm) Up (cm) BOBC olution POPC olution POEC olution We reproceed the 1 Hz GPS data (dual frequency) collected by GEONET tation during the 2011 Tohoku-Oki earthquake uing the TPP method in real-time mode. The coeimic diplacement waveform, for the twenty minute period around the entire eimic haking at GNSS tation 0986, are hown in Figure 4.5. The TPP waveform uing precie atellite orbit and clock are hown by the blue line. The pot-proceed PPP waveform, which have an

76 accuracy of few centimeter (Kouba 2003; Wright et al., 2012), can be regarded a a reference, and are hown by the red line. The comparion between them how that the TPP waveform are quite conitent with the PPP reult at a few centimeter accuracy during the entire haking period. When only broadcat orbit and clock are applied to the proceing, the performance of the TPP method i degraded to about one decimeter in the horizontal component and about two decimeter in the vertical component, a indicated by the black line. For comparion, we alo proce all the data uing the variometric approach. All the error component are carefully corrected following the PPP and/or TPP model. The cumulative diplacement at GNSS tation 0986 are hown in Figure 4.2, illutrating typical behavior. Although precie orbit and clock are applied, there are drift up to few decimeter in the cumulative diplacement. Compared to Figure 4.5, one can ee that the TPP method can improve the diplacement accuracy for POPC olution if the duration i longer than few minute Diplacement (m) North Eat Up POPC POEC BOBC Second of the week() Figure 4.4: Diplacement derived from real-time TPP olution. The red line how the reult uing precie atellite orbit and clock (POPC olution), the blue line i the reult uing precie orbit and extrapolated clock (POEC olution), and the black line i the reult uing broadcat orbit and clock

77 (BOBC olution). Twenty minute interval of 00:00-00:20 (GPST) on 11 March 2011, at GNSS tation 0986 (GEONET). From top to bottom are the reult in north, eat, and up component, repectively. North Diplacement (m) Potproce PPP TPP-POPC TPP-BOBC Eat Diplacement (m) Up Diplacement (m) Second of the week () Figure 4.5:Comparion of the coeimic diplacement waveform derived from real-time TPP olution and pot-proceed PPP olution. The red line how the pot-proceed PPP reult a a reference for TPP reult, the blue line i the TPP reult uing precie atellite orbit and clock (POPC olution), and the black line i the reult uing broadcat orbit and clock (BOBC olution). A twenty minute interval around the entire period of eimic haking on 11 March 2011, at GNSS tation 0986 (GEONET) i hown. From top to bottom are the reult in north, eat, and up component, repectively. The permanent coeimic offet i the important information for magnitude etimation and fault lip inverion. In Figure 4.6, we compare the permanent coeimic offet of eighty evenly-ditributed tation derived from the TPP olution and the pot-proceed PPP olution. The pot-proceed PPP reult, TPP reult uing precie atellite orbit and clock, and TPP reult uing broadcat orbit and clock are hown repectively by the red, green and purple

78 arrow. It i found that the permanent TPP coeimic offet agree with PPP one very well in both horizontal and vertical component when precie orbit and clock correction are applied. The RMS value of the difference between the two olution are 3.0, 2.1, and 5.6 cm in north, eat and vertical component repectively. The TPP reult uing broadcat orbit and clock how ome diagreement with the PPP reult; the RMS value of the difference between them are found to be 8.2, 7.0, and 22.9 cm in north, eat, and vertical component. The reult how that the TPP method can provide reliable permanent offet, epecially if precie orbit and clock correction are available. We derive the patial ditribution of the fault lip uing the coeimic diplacement obtained from the real-time TPP olution with broadcat orbit/clock, TPP with precie orbit/clock, and pot-proceed PPP olution, repectively. In the ame way a done by Wang et al. (2013), we employ a lightly curved fault plane, parallel to the aumed ubduction lab. The dip angle increae linearly from 10 on the top (ocean bottom) to 20 at about 80 km depth. To avoid any artificial bounding effect, a large potential rupture area of km i ued. The upper edge of the fault i located along the trench eat of Japan, on the boundary between the Pacific plate and the Euraian plate. The patch ize i km. The rake angle determining the lip direction at each fault patch i allowed to vary between 90 ± 20. Green function are calculated baed on the CRUST2.0 model (Bain et al., 2000) in the relevant area. The three inverion reult in moment magnitude of Mw 8.90, 8.96, and 8.97, repectively. The maximum lip of the three inverion reult are 21.0, 23.0 and 23.3 m, repectively. The inverted fault lip ditribution are hown in Figure 4.7. The pot-proceed PPP reult i conidered to be the mot reliable and i taken a the reference. The inverion reult of realtime TPP with precie orbit/clock and the pot-proceed PPP olution are quite conitent with each other not only in the moment magnitude, but alo in the lip ditribution pattern. TPP uing broadcat orbit/clock lead to an underetimation of the moment magnitude and fault lip value to an extent. The comparion of the three inverion reult how that the TPP method can provide a reliable etimation of earthquake magnitude and of the fault lip ditribution, epecially when precie atellite orbit and clock correction are ued

79 Figure 4.6: A comparion of the permanent coeimic offet derived from real-time TPP olution and pot-proceed PPP olution on horizontal component and on vertical component, repectively. The red arrow denote the pot-proceed PPP reult a a reference for TPP reult, the green arrow denote the TPP reult uing precie atellite orbit and clock, and the purple arrow i the reult uing broadcat orbit and clock

80 Figure 4.7: Comparion of the inverted fault lip ditribution derived from real-time TPP olution and pot-proceed PPP olution. From left to right are the inverion reult derived from potproceed PPP, real-time TPP uing precie orbit/clock, and real-time TPP uing broadcat orbit/clock, repectively. 4.4 Single-receiver approache for real-time GNSS eimology Comparion of analyi method The linearized equation for undifferenced (UD) carrier phae and peudorange obervation can be repectively expreed a following, l u xt o t I T ( N b b ) (4.6) r, j r r r, j r j r, j r, j j r, j p u xt o t I T c( d d ) e (4.7) r, j r r r, j r r, j j r, j where l, and p, r j r j denote oberved minu computed phae and peudorange obervable from atellite to receiver r at the frequency j ; u r i the unit vector of the direction from the receiver to the atellite; x denote the vector of receiver poition increment relative to a priori poition x 0, which i ued for linearization; o denote atellite orbit error; t and t r are clock error of atellite and receiver repectively; I r, ji the ionopheric delay on the path at the j frequency; Tr denote the tropopheric delay along the path; j i the wavelength; N r, ji the integer phae ambiguity; b, r j and bj are receiver- and atellitedependent uncalibrated phae delay (UPD); d r, j and d j are code biae of receiver and atellite; e r, j denote peudorange meaurement noie and multipath; r, j denote meaurement noie of carrier phae and multipath. In real-time PPP proceing, the phae center offet and variation and tation diplacement by tidal loading mut be conidered. Phae wind-up and relativitic delay mut alo be corrected according to the exiting model (Kouba and Héroux, 2001), although they are not included in the equation. With the available real-time precie atellite orbit and clock product from the International GNSS Service (IGS) real-time pilot project (RTPP) (Caiy et al., 2012; Dow et al., 2009), the error of atellite orbit and clock are greatly reduced to a few

81 centimeter and can be neglected here. The ionopheric delay can be eliminated by the ionophere-free linear combination (Kouba and Héroux, 2001) or can be proceed by etimating the lant ionopheric delay in raw obervation a unknown parameter (Li et al., 2013c). The tropopheric delay i corrected with an a priori model, and the reidual part i etimated a a random walk proce (Boehm et al., 2006). If UPD correction are available, the UD ambiguitie will have integer feature and can be fixed to integer value. Otherwie, the UD ambiguitie are etimated a float value. A modified idereal filtering propoed by Choi et al. (2004) could be ued to mitigate the multipath error, but it i neglected here at preent. The etimated parameter are, X x t T I ) N ) (4.8) T T r r r,1 r, j A equential leat quare or Kalman filter can be employed to etimate the unknown parameter for real-time proceing. The increment of the receiver poition x are etimated epoch by epoch without any contraint between epoch for retrieving rapid tation movement. The receiver clock i etimated epoch-wie a white noie. The ionopheric delay are taken a etimated parameter for each atellite and at each epoch by uing dual-frequency carrier phae and peudorange obervation. The reidual tropopheric delayt r i decribed a T a random walk proce with noie of about 2-5 mm / hour. The carrier-phae ambiguitie N r, j are etimated a contant over time until ucceful ambiguity fixing or convergence. Coloimo et al. (2011) propoed a variometric approach for real-time GNSS eimology. Thi approach i baed upon the time ingle-difference (SD) of the carrier phae obervation recorded by a ingle GNSS receiver. The model of variometric approach can be derived from the time ingle-difference of UD obervation equation (4.6) and (4.7) between two conecutive epoch ( t, t 1 ) on the aumption that the obervation data i continuou a follow, n n

82 l ( t, t ) u ( t ) x( t ) u ( t ) x( t ) t ( t, t ) r, j n n1 r n1 n1 r n n r n n1 o ( t, t ) t ( t, t ) I ( t, t ) T ( t, t ) ( t, t ) n n1 n n1 r, j n n1 r n n1 r, j n n1 (4.9) p ( t, t ) u ( t ) x( t ) u ( t ) x( t ) t ( t, t ) r, j n n1 r n1 n1 r n n r n n1 o ( t, t ) t ( t, t ) I ( t, t ) T ( t, t ) e ( t, t ) n n1 n n1 r, j n n1 r n n1 r, j n n1 (4.10) where l, ( t, t 1) i time ingle-difference phae obervation l, ( t 1 ) l, ( t ) ; r j n n r j n r j n pr, j( tn, tn 1) i time ingle-difference peudorange obervation; u ( t ) and u ( 1) are the r n r tn unit direction vector from receiver to atellite at epoch t n and tn 1 ; x( t n) and x( tn 1) are the receiver poition increment at epoch t n and tn 1 ; Other item repreent the variation of the correponding error component between epoch ( t, t 1), for example, n n Ir, j( tn, tn 1), Tr tn tn 1 (, ) repreent range variation caued by tropopheric and ionopheric refraction delay. Compared with the equation (4.6) and (4.7), it can be een that phae ambiguitie ( N, ), phae delay ( b,, b ) and code biae ( d,, d ) can be eliminated r j r j j through the time difference operation, a they can be regarded a contant for at leat ten of minute. The accuracy of phae obervation i much higher (about 100 time) than the peudorange obervation, thu the time-differenced poition i mainly determined by phae obervation. We will hereafter focu on phae obervation; the equation (4.9) can be reformulated a, l ( t, t ) u ( t ) ( xt ( ) xt ( )) ( u ( t ) u ( t)) xt ( ) t( t, t ) err ( t, t ) r, j n n1 r n1 n1 n r n1 r n n r n n1 r, j n n1 u ( t ) x( t, t ) ( u ( t ) u ( t )) x( t ) t ( t, t ) err ( t, t ) r n1 n n1 r n1 r n n r n n1 r, j n n1 r j j (4.11) err ( t, t ) o ( t, t ) t ( t, t ) I ( t, t ) r, j n n1 n n1 n n1 r, j n n1 T ( t, t ) ( t, t ) r n n1 r, j n n1 (4.12) x( t, ) i the change in the receiver poition increment for the time interval ( t, t 1), n tn 1 which i the quantity of greatet interet; t ( t, 1) i the change in the receiver clock r n tn n n

83 error; err, ( t, t 1) repreent the um of change in all other error component; r j n n ( u ( t ) u ( t )) x( t ) account for the change in the relative atellite/receiver geometry r n 1 r n n due to the line-of-ight vector change it orientation. The etimated parameter are, X x( t, t ) t ( t, t ) T (4.13) T n n1 r n n1 which can be eaily etimated by uing the leat quare method when at leat four atellite are being tracked imultaneouly. In the variometric approach, the velocitie can be etimated with a high accuracy on the order of mm/ uing a high-rate tand-alone receiver. A dicrete integration of etimated velocitie i then employed to recontruct the coeimic diplacement. Well known i that thi dicrete integration i very enitive to etimation biae due to a poible mimodeling of different intervening effect that accumulate over time and diplay their ignature a a trend in coeimic diplacement. The trend can be aumed to be linear if the integration interval wa limited up to few minute (Branzanti et al., 2013). Furthermore, the variometric approach i effective even when uing a implified model with broadcat orbit and clock and ingle frequency receiver, where the effect due to the ionophere, tropophere, phae center variation, relativity, and phae wind-up are neglected (Coloimo et al. 2011). In order to eliminate or ignificantly decreae the drift trend in the integrated diplacement and alo avoid the linear de-trending proce, we propoe everal refinement to the variometric approach: 1) Variation in atellite orbit error o ( t, t 1) and clock bia t ( t, t ) are corrected by uing real-time precie atellite orbit and clock product which n n 1 are now available online via the IGS RTPP (Caiy et al., 2012). 2) All of the other error component are carefully corrected following the PPP model. Ionopheric delay change are compenated uing dual frequency meaurement. The change in tropopheric delay i motly mitigated by a priori tropopheric model (Saatamoinen, 1972), the reidual part i at centimeter level for few ten of minute. The change in the phae center offet and variation, tidal loading, phae wind-up and relativitic delay can be corrected according to the exiting model. 3) Special attention i given to the geometry correction ( u ( t 1) u ( t )) x( t ), n n r n r n n which account for change in the relative atellite/receiver geometry. Uually, the geometry error item i ignored or an approximate receiver poition etimated from tandard point poitioning (SPP) i ued to calculate and correct it. However, the geometry error could be large if the integration duration i longer than few minute (the line- of-ight vector change u ( t 1) u ( t0) will be large) or the approximate SPP poition i not r n r

84 accurate enough (the error of x( t n) will be large). In eimological application, we are mainly intereted in the diplacement relative to the receiver poition before the earthquake and the poition before the earthquake i generally well known. Thi accurate receiver poition can be ued to fully correct the geometry error. Auming that the receiver poition before the earthquake x( t 0) i accurately known, it can be ued to correct the geometry error ( ( ) ( )) ( ) ur t1 u r t0 x t0 in x t0 t1 (, ) etimation. Then we can have, x( t ) x( t ) x( t, t ) (4.14) By analogy, the integrated x( t 1) can be ued to correct the geometry error ( u ( t ) u ( t )) x( t ) in x( t1, t2) etimation, and o on. The integrated x( t n) i ued to r 2 r 1 1 correct the geometry error ( u ( t 1) u ( t )) x( t ) in x( tn, tn 1) etimation. r n r n n After all of error ource are carefully conidered, the integrated diplacement from the refined variometric approach are reaonably preumed to be with a good accuracy at centimeter level without the need of de-trending. The accuracy mainly depend on the variation of reidual tropopheric delay, which i at centimeter level for few ten of minute. We recently propoed an innovative TPP approach to ingle point, ingle epoch, GNSS poitioning at few centimeter preciion level over a period up to about 20 minute (Li et al., 2013b), which i typically required for coeimic diplacement determination after major earthquake. Baed on the fact that: 1) the poition change (relative to the poition before the earthquake) i the quantity of greatet interet in eimological application; 2) the receiver poition before the earthquake i generally well known. The model of TPP approach can be derived from UD obervation equation (4.6) and (4.7) a follow (phae obervation i concentrated here a it much higher preciion), Bt ( ) t( t) T ( t) l ( t) u ( t) xt ( ) o( t) t( t) I ( t) ( t) 0 r 0 r 0 r, j 0 r r, j 0 r, j 0 0 j r, j r, j j (4.15) B( t ) ( N b b ) (4.16) The receiver poition at the epoch t 0 (before the earthquake) i aumed to be preciely known a x( t 0). All the error component including atellite orbit and clock error, ionopheric and tropopheric delay, phae center offet and variation, tidal loading, phae wind-up and relativitic delay are carefully conidered following the PPP model. The realvalued ambiguitie B( t0) can be etimated along with the receiver clock t ( t 0) and tropopheric delay Tt ( 0) (tightly contrained or fixed to a priori model) parameter at thi r

85 epoch. Then we hold the etimated ambiguitie B( t 0) fixed in the ubequent epoch. At the epocht n, the poition x( t n) can be etimated a, u ( t ) x( t ) t ( t ) T ( t ) l ( t ) t ( t ) o ( t ) B( t ) I ( t ) ( t ) (4.17) r n n r n r n r, j n n n 0 r, j n r, j n A the ambiguitie are held to fixed value intead of being etimated a unknown parameter, the convergence proce will not be required. Furthermore, the poition x( t n) are etimated directly and thu the integration proce i alo avoided. When the receiver poition x( t 0) i preciely known and all of error ource are carefully conidered, the ambiguitie B( t 0) with a certain accuracy can be expected. The accuracy of the poition etimate x( t n) will be mainly affected by the variation of reidual tropopheric delay from the epoch t 0 to t n. Generally, the variation of the tropopheric delay i at centimeter level for few ten of minute. Therefore, the poition etimate are reaonably preumed to be with a good accuracy at centimeter level without de-trending proce. In TPP approach, an accurate initial poition at epoch t 0 (i.e. the receiver poition before the earthquake) i important for achieving high-accuracy diplacement. The influence of initial poition accuracy on the TPP diplacement can be found in the ection 4.2. For real-time PPP proceing, the phae ambiguitie are etimated together with the receiver poition, receiver clock, and reidual tropopheric delay. The ambiguitie need ome time to converge (e.g. thirty minute) to the correct value, until enough obervable are ued in the filter. There will be a big diturbance in the diplacement equence during the (re)convergence period. Once the ambiguitie are uccefully fixed to correct integer value or converged to accurate real value, diplacement accuracy of few centimeter can be achieved. In order to avoid the convergence problem, the TPP method make full ue of two critical feature in eimological application: the receiver poition before the earthquake i generally well known and the ambiguity i contant on the aumption that the obervation data i continuou. The TPP method i equivalent to PPP with the real phae ambiguitie fixed at value determined from the known poition at the epoch, preceding the earthquake and uing an a priori tropopheric delay. Thi new TPP method can provide about the ame, a cm level preciion, a the converged PPP, which require up to 30 min data prior the earthquake for a PPP olution convergence. It can be found that the TPP and the converged PPP have imilar mathematical model, the difference between them i that TPP ue the known poition at initial

86 epoch to calculate accurate phae ambiguity, while PPP ue a period of obervation data for phae ambiguity convergence. In the model of TPP approach, we ubtitute the equation (4.15) into the equation (4.17) and then have, u ( t ) x( t ) t ( t, t ) u ( t ) x( t ) l ( t, t ) err ( t, t ) (4.18) r n n r 0 n r 0 0 r, j 0 n r, j 0 n err ( t, t ) o ( t, t ) t ( t, t ) I ( t, t ) r, j 0 n 0 n 0 n r, j 0 n T ( t, t ) ( t, t ) r 0 n r, j 0 n (4.19) Meanwhile, the equation (4.11) of variometric approach can be reformulated a, u ( t ) x( t ) t ( t, t ) u ( t ) x( t ) l ( t, t ) err ( t, t ) (4.20) r n1 n1 r n n1 r n n r, j n n1 r, j n n1 We can ee that equation (4.18) derived from TPP model i in the ame form a the timedifferenced equation (4.20) in the refined variometric model. The difference i that the TPP method i equivalent to calculating the diplacement at epoch t n relative to the well-known poition at epocht 0, while the variometric approach ue time-differenced phae obervation between two adjacent epoch t n and tn 1 to calculate velocitie. In the variometric approach, ambiguitie are eliminated by uing time difference operation, and thu the convergence proce i alo not required. But an integration proce i needed to recontruct diplacement from velocitie. For the time erie from epoch t 0 tot n, the equation (4.20) can be expreed a, u ( t ) x( t ) t ( t, t ) u ( t ) x( t ) l ( t, t ) err ( t, t ) u r 1 1 r 0 1 r 0 0 r, j 0 1 r, j 0 1 r t2 x t2 tr t1 t2 ur t1 x t1 lr, j t1 t2 errr, j t1 t2 ( ) ( ) (, ) ( ) ( ) (, ) (, ) u ( t ) x( t ) t ( t, t ) u ( t ) x( t ) l ( t, t ) err ( t, t ) r n n r n1 n r n1 n1 r, j n1 n r, j n1 n (4.21) The cumulative um of equation (4.21) i, u ( t ) x( t ) t ( t, t ) u ( t ) x( t ) l ( t, t ) err ( t, t ) (4.22) r n n r 0 n r 0 0 r, j 0 n r, j 0 n The accumulated equation (4.22) i the ame a the equation (4.18) derived from TPP. It mean that the TPP and refined variometric approache can be equivalent after all of error ource, epecially orbit, clock and geometry error, are carefully conidered

87 In PPP approach, once ambiguitie are fixed or converged to correct value, it alo ha the ame obervation model a TPP method for ubequent epoch and the ame equation a (4.18) can alo be derived from PPP model. The only difference i that PPP can ue a better tropopheric delay etimated from convergence proce, while TPP and variometric approache ue a priori tropopheric delay model. Fortunately, the variation of the tropopheric delay i low, at centimeter level for few ten of minute, which i of greatet interet in eimological application. From the above analyi on the ingle-receiver approache for real-time GNSS eimology, we can conclude that the TPP, converged PPP and refined variometric approache have equivalent mathematical model and hould provide about the ame diplacement preciion Error analyi and preciion validation Numerou tudie how that PPP i a powerful technique for eimological application, and PPP-derived diplacement accuracy i comparable to relative poitioning method if undifferenced ambiguitie are uccefully fixed (Li et al., 2013a; Geng et al., 2013). Compared with PPP approach, there i till little reearch on detailed error analyi and preciion validation of variometric and TPP approache for coeimic diplacement retrieving. In thi ection, we carefully analyze the impact of error component on variometric and TPPderived diplacement. The preciion of thee ingle-receiver approache i alo evaluated and compared by uing 1 Hz GEONET (the GNSS Earth Obervation Network Sytem) data collected during the 2011 Mw 9.0 Tohoku-Oki earthquake in Japan. Thi network i operated by the Geopatial Information Authority of Japan (GSI) and conit of more than 1,200 continuouly oberving GNSS tation all over Japan ( Table 4.2: Four different cheme for the variometric approach Scheme 1 (BOBC L1) Scheme 2 (BOBC LC) Scheme 3 (POPC) Scheme 4 (POPC geometry) Satellite ephemeri broadcat ephemeri broadcat ephemeri precie orbit and clock precie orbit and clock * LC: Ionophere-Free Combination ionopheric delay L1 obervation LC obervation* LC obervation LC obervation geometry error an approximate poition an approximate poition an approximate poition an accurate poition

88 The variometric approach firtly compute the delta poition of one tation between two adjacent epoch, and then the diplacement waveform i recontructed through the dicrete integration method. Well known i that thi (dicrete) integration i very enitive to etimation biae due to the poible mimodeling of different intervening effect (uch a orbit and clock error, atmopheric error and geometry error) that accumulate over time and diplay their ignature a a trend in the coeimic diplacement. We deign four cheme a lited in Table 1 to evaluate the impact of thee error on cumulative diplacement. All of the other error component (e.g. phae center offet and variation, tidal loading, phae wind-up and relativitic delay) are carefully corrected according to the exiting model a PPP (Kouba and Héroux, 2001). Ionopheric effect The cumulative diplacement from 00:00-00:20 (GPST, before the earthquake) on 11 March 2011 for tation 0177 are exemplarily hown in Figure 4.8. The reult uing broadcat orbit, broadcat clock and L1 carrier phae obervation (BOBC L1, ionopheric delay i not compenated) are depicted by the blue line, and the reult in which ionopheric delay i eliminated by uing ionophere-free combination obervation (BOBC LC) are hown by the red line. To clearly diplay the impact of ionopheric delay on the cumulative diplacement, the diplacement difference between BOBC L1 and BOBC LC reult are hown in the blue line in Figure 4.9. A drift trend can be clearly een in all three component. The linear fitting of diplacement difference i alo depicted in Figure 4.9 with the red line. Beide linear trend, the diplacement difference alo contain ome hort-term fluctuation becaue of the ionopheric diturbance. For 20 minute integration interval, the diplacement difference of tation 0177 due to ionopheric delay could reach about 17 cm, 58 cm, and 83 cm in the north, eat, and up component, repectively

89 Time (UT) 00: :05 00:10 00:15 00: North 0.00 Cumulative Diplacement (m) Eat Up BOBC LC BOBC L Second of the week () Figure 4.8: Cumulative diplacement uing the variometric approach: impact of ionopheric delay. Reult of tation 0177 (GEONET) for 20 minute interval 00:00:00-00:20:00 (GPST) on March Time (UT) 00: :05 00:10 00:15 00: Ionopheric effect Linear fitting Diplacement (m) North Eat Up Second of the week () Figure 4.9: The diplacement difference of tation 0177 due to ionopheric delay for the 20 minute interval 00:00:00-00:20:00 (GPST) on March

90 The diplacement error of BOBC L1 and BOBC LC olution of about twenty tation for 20 minute interval are hown in Figure The diplacement error of other tation are imilar to the reult of tation The diplacement error of BOBC L1 olution are obviouly larger than the BOBC LC olution, epecially in up component North BOBC LC BOBC L Diplacement Bia (m) Eat Up Figure 4.10: Comparion of the diplacement error of BOBC L1 and BOBC LC olution of about twenty tation for the 20 minute interval 00:00:00-00:20:00 (GPST) on March The diplacement error of north, eat and up component are hown in the top, middle and bottom ubfigure. The BOBC L1 olution are in red and the BOBC LC one in blue. The effect of atellite ephemeri Currently, two type of orbit and clock product are available in real time. One i broadcat orbit and clock, which i routinely available from the GNSS receiver itelf with an accuracy of about decimeter to meter level. The other one i precie atellite orbit and clock product from the International GNSS Service (IGS) real-time pilot project (RTPP) with an accuracy of few centimeter (Caiy et al., 2012; Dow et al., 2009). Here the ultra-rapid orbit, updated every three hour and provided by GFZ, i applied. The clock correction have to be etimated and updated much more frequently (Zhang et al. 2011) due to their hort-term fluctuation. We proce 1 Hz data from globally ditributed real-time IGS tation uing the GFZ

91 EPOS-RT oftware (Ge et al., 2011) in imulated real-time mode (a trictly forward filter) for generating precie GNSS clock correction at a 5 ampling interval. The cumulative diplacement of tation 0177 for 20 minute interval are hown in Figure The reult uing broadcat orbit, broadcat clock and LC obervation (BOBC) are depicted by blue line, and the reult uing precie orbit, precie clock and LC obervation (POPC) are hown by red line. Compared with POPC reult, BOBC reult how a complicated drift character with more fluctuation. Take the up component for intance, the BOBC cumulative diplacement ha a drift up to about 30 cm. The diplacement error of POPC and BOBC olution of about twenty tation for 20 minute interval are hown in Figure The difference of the cumulative diplacement between the two olution denote the effect of atellite ephemeri on diplacement, and diplacement difference of the tation 0177 could reach about 10 cm in horizontal component and about 50 cm in up component for 20 minute integration interval. It can be found that the diplacement error of POPC olution are generally maller than BOBC olution. In addition, the diplacement difference are not linearly proportional to the integration interval. Taking the up component for intance, the difference between POPC and BOBC olution on average are about 44.6 cm for 20 minute interval, 14.9 cm for 10 minute interval and 13.8 cm for 5 minute interval. It i concluded that atellite ephemeri ha important influence on accumulative diplacement, and the diplacement error caued by broadcat orbit and clock i not a imple linear trend. Time (UT) 00: :05 00:10 00:15 00: North 0.00 Cumulative Diplacement (m) Eat Up POPC BOBC Second of the week ()

92 Figure 4.11: Cumulative diplacement uing the variometric approach: impact of atellite orbit and clock. The red line how the reult uing precie atellite orbit and clock, while the blue line i the reult uing broadcat clock and orbit. Reult of tation 0177 (GEONET) for the 20 minute interval 00:00:00-00:20:00 (GPST) on March North POPC BOBC Diplacement Bia (m) Eat Up Figure 4.12: Comparion of the diplacement error of POPC and BOBC olution of about twenty tation for 20 minute interval 00:00:00-00:20:00 (GPST) on March The diplacement error in north, eat and up component are hown in the top, middle and bottom ub-figure. The BOBC olution are in red and the POPC one in blue. The geometry error effect The different cumulative diplacement waveform, devoted to the effect of geometry error for tation 0177, are exemplarily hown in Figure The reult without compenating the geometry error by uing precie ephemeri and LC obervation (POPC) i depicted by the blue line, and the reult in which geometry error i carefully corrected (POPC geometry) i hown by the red line. The difference between the two accumulative diplacement indicate the

93 effect of geometry error on the diplacement. After 20 minute, the diplacement difference between POPC geometry reult and POPC (no geometry correction) reult could reach 13.3 cm, cm, and 18.2 cm in the north, eat, and up component, repectively. The POPC geometry olution, conidered to be the mot accurate etimation in four trategie, can achieve an accuracy of about few centimeter, which could be caued by the reidual tropopheric delay. The diplacement error of POPC geometry and POPC (no geometry correction) olution of about twenty tation for 20 minute interval are hown in Figure It i obviou that the geometry error ha very ignificant impact on accumulative diplacement, it hould be carefully conidered to retrieve precie coeimic diplacement. The diplacement error caued by geometry item can reach up few decimeter for 20 minute interval. 00:00 00:05 00:10 00:15 00: North Time (UT) Cumulative Diplacement (m) Eat POPC geometry POPC Up Second of the week () Figure 4.13: Cumulative diplacement waveform uing the integrated velocitie: impact of the geometry error with (red line) and without (blue line) conideration. Reult of 0177 (GEONET) in the 20 minute interval 00:00:00-00:20:00 (GPST) on March

94 North POPC geometry POPC Diplacement Bia (m) Eat Up Figure 4.14: Comparion of the diplacement error from POPC geometry and POPC olution of about twenty tation for 20 minute interval 00:00:00-00:20:00 (GPST) on March The diplacement error in north, eat and up component are hown in the top, middle and bottom ubfigure. The POPC olution are in red and the POPC geometry one in blue. To further reflect the pectral characteritic of different diplacement waveform, the power pectral denitie (PSD) at tation 0177 for each cheme are hown in Figure Four diplacement reult are repectively depicted by different color line: (1) POPC geometry reult in red line; (2) POPC reult in blue line; (3) BOBC reult in black line; and (4) BOBC L1 reult in cyan line. On the whole, the POPC geometry PSD curve perform more or le flat, epecially at high frequency band between 0.05 Hz and 0.5 Hz, but other three curve have many fluctuation mainly caued by their diplacement waveform with a nearly linear trend. At the low frequency band le than 0.05 Hz, the POPC geometry PSD value are obviouly the mallet in all three component, which indicate the POPC geometry diplacement have few biae off the truth. Converely, the BOBC L1 PSD value are the bigget, and the correponding diplacement contain large biae. The POPC and the BOBC PSD curve are between the above two reult, and the BOBC PSD value are lightly larger than the POPC PSD value due to the low preciion of broadcat ephemeri

95 Power pectral denity (m 2 /Hz) POPC geometry POPC BOBC BOBC L Frequency (mhz) Figure 4.15: Power pectral denity comparion of the diplacement waveform at tation 0177 for each cheme: upper panel for the eat component; middle panel for the north component; and lower panel for the vertical component. A ionopheric delay can be compenated by uing dual-frequency obervation and TPP method doe not uffer from geometry error, we mainly concentrate on the impact of orbit and clock error on the TPP diplacement. To invetigate the effect of the atellite orbit and clock product on the TPP method, we proce the 1 Hz GEONET data uing different orbit and clock product. The TPP diplacement of tation 0177 for 20 minute interval are hown in Figure The reult uing precie orbit and clock (POPC) i the cloet to the zero line without a drift trend at an accuracy of few centimeter. The reult uing precie clock and broadcat orbit (PCBO) i the econd cloet to the zero line, but it gradually diverge from the zero value, epecially in the up component. Compared with the POPC/PCBO reult, the reult uing broadcat clock (both POBC and BOBC olution) have an evident drift error up to few decimeter. The TPP diplacement error of POPC, PCBO, POBC and BOBC olution of about fifteen tation for 20 minute interval are hown in Figure It i clearly hown that the diplacement error for PCBO, POBC and BOBC olution increae evidently up to few decimeter along with the extenion of proceing period, while the error of POPC olution i only few centimeter in all three component. In addition, the diplacement uing precie atellite clock are much better than the one uing broadcat clock, both of the POBC and BOBC error exceed one decimeter even when the integration interval i 5 minute, while the

96 POPC and PCBO error are maller than five centimeter. It can be concluded that the atellite clock error ha more influence on the TPP reult than atellite orbit error. The precie atellite clock product i accurate enough a a reference value, thu the difference between the broadcat and the precie clock product can be conidered a error of broadcat atellite clock product. Figure 4.18 how the broadcat clock error for atellite PRN 09 (ee Figure S8 in auxiliary material for atellite PRN 10). We can find that the variation of clock error could reach few decimeter for 20 minute. The correponding reidual error after a linear trend removal are alo hown in bottom ub-figure. Time (UT) 00: :05 00:10 00:15 00: North 0.00 Diplacement (m) Eat Up POPC PCBO POBC BOBC Second of the week () Figure 4.16: Diplacement uing the TPP method: impact of atellite orbit and clock. Reult of 0177 (GEONET) for 20 minute interval 00:00:00-00:20:00 (GPST) on March

97 North POPC PCBO POBC BOBC Diplacement Bia (m) Eat Up Figure 4.17: Comparion of diplacement error from POPC, PCBO, POBC and BOBC olution of about fifteen tation for 20 minute interval 00:00:00-00:20:00 (GPST) on March The diplacement error in north, eat and up component are hown in the top, middle and bottom ubfigure, repectively. Satellite clock bia (m) Reidual (m) Time (UT) 00: :05 00:10 00:15 00:20 G09 Linear fitting y = * x Second of the week () Figure 4.18: The broadcat atellite clock error of PRN 09 for 20 minute interval. The linear fitting reult for the clock error and the reidual after a linear trend removal are alo hown in red line

98 4.4.3 Application to the 2011 Tohoku-Oki earthquake We reproceed the 1 Hz GPS data (dual frequency) collected by GEONET tation during the 2011 Mw 9.0 Tohoku-Oki earthquake (11 March, 2011, 05:46:24 UTC; GPS Time-UTC=15) uing ingle-receiver approache (PPP, variometric and TPP) in real-time mode. For the PPP method, we proceed thee data uing precie atellite orbit and clock product. For the variometric and TPP method, we proceed thee data uing precie and broadcat orbit/clock product, repectively. The coeimic diplacement waveform, for the twenty minute period around the entire eimic haking at two GNSS tation (0183, 0986), are hown a example from Figure 4.19 to Figure The earthquake ignature can be clearly oberved in the 3D diplacement waveform. Figure 4.19 how a comparion of diplacement erie between PPP and variometric method for tation 0183 (about 250 km away from the epicenter). The converged PPP (ambiguity fixed olution) waveform, which have an accuracy of few centimeter (Li et al., 2013a) and can be regarded a a reference, are hown by the red line. The variometricbaed diplacement uing broadcat ephemeri (Variometric-BOBC) ha a viible drift from the converged PPP reult. Although precie orbit and clock are applied, Variometric-POPC olution till drift up to few decimeter in the cumulative diplacement. After the geometry error correction, the variometric-baed diplacement (Variometric-POPC geometry) agree quite well with the converged PPP reult. Figure 4.20 how a comparion between diplacement waveform derived from PPP and TPP method. The comparion between them how that the TPP waveform are quite conitent with the PPP reult at few centimeter accuracy during the entire haking period. The difference between the PPP (the red line) and TPP-POPC olution (the blue line) i within 3.0 cm in horizontal component and within 5.0 cm in up component. When only broadcat orbit and clock are applied to the proceing, the performance of the TPP method i degraded to about one decimeter in the horizontal component and about two decimeter in the vertical component, a indicated by the black line. Figure 4.21 and Figure 4.22 are the diplacement waveform of tation 0986 (about 485 km away from the epicenter). In view of the reult of tation 0986, we come to a imilar concluion like tation When real-time precie orbit and clock correction are available, TPP-POPC and Variometric-POPC geometry derive the diplacement waveform, which are both at a comparable level with the converged PPP waveform at an accuracy of few centimeter during the entire haking period, even for a period of twenty minute

99 North Diplacement (m) Eat Diplacement (m) Up Diplacement (m) 05:40 05:45 05:50 05:55 06: Converged PPP Variometric-POPC geometry Variometric-POPC Variometric-BOBC Time (UT) Second of the week () Figure 4.19: Comparion of the diplacement waveform uing variometric method and converged PPP olution for tation 0183 in the 20 minute interval from 05:40:00 to 06:00:00 (GPST) on 11 March,

100 North Diplacement (m) Eat Diplacement (m) 05:40 05:45 05:50 05:55 06: Converged PPP TPP-POPC TPP-BOBC Time (UT) Up Diplacement (m) Second of the week () Figure 4.20: Comparion of the diplacement waveform uing TPP method and converged PPP olution for tation 0183 in the 20 minute interval from 05:40:00 to 06:00:00 (GPST) on 11 March, North Diplacement (m) Time (UT) 05:40 05:45 05:50 05:55 06: Converged PPP Variometric-POPC geometry Variometric-POPC Variometric-BOBC Eat Diplacement (m) Up Diplacement (m) Second of the week ()

101 Figure 4.21: Comparion of the diplacement waveform uing variometric method and converged PPP olution for tation 0986 in the 20 minute interval from 05:40:00 to 06:00:00 (GPST) on 11 March, North Diplacement (m) Time (UT) 05:40 05:45 05:50 05:55 06: Converged PPP TPP-POPC TPP-BOBC Eat Diplacement (m) Up Diplacement (m) Second of the week () Figure 4.22: Comparion of the diplacement waveform uing TPP method and converged PPP olution for tation 0986 in the 20 minute interval from 05:40:00 to 06:00:00 (GPST) on 11 March, The permanent coeimic diplacement of ninety evenly-ditributed tation derived from the PPP, TPP and variometric approach are hown in Figure The PPP olution, which ha been validated by numerou tudie, i depicted a a reference here. In all the cheme, the TPP-POPC and variometric-popc geometry olution can achieve the mot accurate coeimic diplacement of about few centimeter (with a centralized direction to the earthquake ource centroid), which agree quite well with the PPP reult. The RMS of the difference between TPP-POPC and PPP olution i about 3.0 cm, 1.8 cm and 6.0 cm in north, eat and up component, repectively. The correponding RMS of the difference between variometric-popc-geometry and PPP olution i 3.1 cm, 1.9 cm and 6.0 cm. The variometric- POPC reult are the econd conitent to the PPP reult, the difference between them are about 1 decimeter in horizontal component and 2 decimeter in vertical component. The variometric-bobc and TPP-BOBC olution how a relatively large uncertainty, although the horizontal diplacement value are motly conitent within 25% with PPP diplacement

102 value, the diplacement vector direction do not agree very well with the PPP reult accompanied by everal degree biae

103 Figure 4.23: The comparion of the oberved and ynthetic coeimic diplacement on horizontal component, and on vertical component, repectively. a) Inverion with permanent diplacement obtained from converged PPP olution; (b) Inverion with TPP-POPC olution; (c) Inverion with TPP- BOBC olution; (d) Inverion with variometric-popc geometry olution; (e) Inverion with variometric-popc olution; (f) Inverion with variometric-bobc olution

104 Figure 4.24: Fault lip ditribution for the 2011 Tohoku earthquake inverted from different permanent coeimic diplacement obtained by different trategie: (a) converged PPP; (b) TPP-POPC; (c) TPP-BOBC; (d) variometric-popc geometry; (e) variometric-popc; (f) variometric-bobc. We derived ix fault lip ditribution uing the coeimic diplacement obtained from the converged PPP olution, TPP-POPC olution, TPP-BOBC olution, variometric-popc geometry olution, variometric-popc olution, and variometric-bobc olution, repectively. The inverion are carried out uing a FORTRAN code SDM baed on the contrained leat quare method (Wang et al., 2011). A priori condition and phyical contraint are choen a the ame a Wang et al. (2013). The total rupture area i aumed to be 650 km along the trike direction and 300 km along the dip direction, which i then divided into 1950 ub-fault with length and width of 10 km and 10 km, repectively. The dip angle linearly increae from 10 on the top (ocean bottom) to 20 at about 80 km depth. The rake angle (lip direction relative to the trike) i allowed to vary ±20 around 90. Green function are calculated baed on the CRUST2.0 model (Bain et al., 2000) in the concerning area

105 The comparion of ynthetic and oberved diplacement on horizontal and vertical component are hown in Figure 4.23, and the inverted fault lip ditribution are hown in Figure The bet reolved lip model i aumed to be that derived from the converged PPP dataet. Thi model indicate that the peak coeimic lip of the earthquake nearly reached 23 m which i in agreement with previou reult obtained by Wang et al. (2013) with onhore GPS data. The moment magnitude of the earthquake i etimated to be Mw 8.97, which i imilar to the moment olution of about Mw 9.0, etimated by the USGS. Both the inverion reult derived from TPP-POPC and variometric-popc geometry dataet are quite conitent with the PPP lip model not only in the lip ditribution pattern and moment magnitude, (Mw 8.96 for both), but alo in the diplacement fitting. For other three inverion of TPP-BOBC, variometric-popc and variometric-bobc (about Mw 8.90), there are obviou difference not only for the lip ditribution pattern, but alo for the diplacement fitting. The peak lip value for the TPP-BOBC and variometric-popc model are le than 21 m. Overall, the comparion of the ix inverion reult how that the TPP-POPC and the variometric- POPC geometry olution can derive reliable fault lip ditribution, having conitent performance with the reult inverted from converged PPP olution. 4.5 Concluion A new approach for real-time GNSS eimology uing a ingle receiver wa preented. The performance of the propoed TPP approach i validated uing 1 Hz GEONET data collected during the 2011, Mw 9.0 Tohoku-Oki earthquake. When real-time precie orbit and clock correction are available, the diplacement waveform, derived from TPP, are conitent with the pot-proceed PPP waveform at an accuracy of few centimeter during the entire haking period, even for a period of twenty minute. The TPP permanent coeimic offet agree with PPP one very well with RMS value of 3.0, 2.1, and 5.6 cm in north, eat, and vertical component, repectively. The reult of the fault lip inverion alo indicate that the TPP method can provide a reliable etimation of moment magnitude and even of the fault lip ditribution. If jut the broadcat orbit and clock are available, the diplacement accuracy will be degraded to ome extent and thi lead to underetimation of the moment magnitude and fault lip value. In the dicuion of 4.2, we conider the GNSS obervation to be free from cycle lip during the earthquake period. In practice, everal method of cycle-lip fixing (e.g., Zhang and Li, 2012; Geng et al., 2010; Li et al., 2013b) can be ued to correct the phae obervation when cycle lip occur. Furthermore, a joint proceing of multi-gnss (e.g., GPS, GLONASS, Galileo and BeiDou) data will ignificantly increae the number of available atellite and thu enhance the reliability of our approach

106 In Section 4.4, we alo compared the technical detail of current ingle-receiver GNSS eimology approache. Furthermore, everal refinement are propoed to the variometric approach in order to eliminate the drift trend in the integrated coeimic diplacement. We dicued the mathematical relationhip among the PPP, TPP and refined variometric approache and verified their equivalence baed on two condition: one i that all the error component in the TPP and variometric approache are carefully conidered following the PPP model; the other i that both TPP and variometric approache ue accurate known coordinate at the initial epoch (before the earthquake) to eliminate the geometry error. We carefully analyzed the impact of error component uch a atellite ephemeri, ionopheric delay, and geometry change on the diplacement retrieved from the TPP and variometric approache. The ionopheric delay ha very ignificant impact on accumulative diplacement and the drift value can reach up to everal decimeter in horizontal component and about 1 meter in up component for 20 minute integration interval. The atellite ephemeri, epecially the atellite clock error, ha critical influence on diplacement which i depicted a complicated drift character with more fluctuation when broadcat orbit and clock i adopted. The geometry error alo ha a ignificant impact on accumulative diplacement and the diplacement error caued by geometry item can reach up few decimeter for 20 minute interval. We validated the performance of thee ingle-receiver proceing trategie (PPP, TPP and refined variometric approache) uing 1 Hz GPS data collected during the Tohoku-Oki earthquake (Mw 9.0, March 11, 2011) in Japan. After careful correction of all error component, the diplacement waveform derived from TPP and refined variometric approach are conitent with converged PPP at an accuracy of few centimeter. The reult of the fault lip inverion alo indicate that the TPP and the refined variometric approach can provide a reliable etimation of moment magnitude and fault lip value a the converged PPP. From the above analyi and reult on the ingle-receiver approache for real-time GNSS eimology, we can conclude that the TPP, refined variometric approache have equivalent mathematical model and can provide the ame diplacement preciion with the converged PPP method. Moreover, thee two approache overcome the convergence problem of PPP, making them more uitable for eimological application

107

108 5 Tightly-integrated proceing of raw GNSS and accelerometer data 5.1 Introduction The problem with GPS diplacement i that it noie level i much higher than that from mot eimic enor. In GPS diplacement, thi noie i baically white acro the whole eimic frequency band. Seimic enor meaure acceleration with a very high preciion and ampling rate and the eimic diplacement can be obtained by double integration of the oberved accelerometer ignal. However, the acceleration i accompanied by unphyical drift due to enor rotation and tilt (Trifunac and Todorovka, 2001; Lee and Trifunac, 2009), hyterei (Shakal and Peteren, 2001), and impreciion in the numerical integration proce (Boore et al., 2002; Smyth and Wu, 2006). It noie level, viewed in term of diplacement, will rie with decreaing frequency: at ome frequency thi noie level will exceed that of GPS. Therefore, GPS and eimic intrument can be mutually beneficial for eimological application becaue weaknee of one obervation technique are offet by trength in the other. In order to take full ue of the complementary of GPS and eimic enor, we propoe an approach of integrating the accelerometer data into the precie point poitioning (PPP, Zumberge et al., 1997) proceing. Intead of combing the GPS-derived diplacement with the accelerometer data (Emore et al., 2007; Bock et al., 2011), a tightly-integrated filter i developed to etimate eimic diplacement from GPS phae and range and accelerometer obervation. We apply the tightly-coupled integration to analyze collocated GPS and eimic data collected during the 2011 Tohoku-Oki (Japan) and the 2010 El Mayor-Cucapah (Mexico) earthquake. Time and frequency domain analyi how that the integrated diplacement and velocity waveform are more accurate than GPS-only or eimic-only reult. The integrated diplacement waveform can capture both tranient phenomena (wave) and permanent or tatic deformation. From the integrated reult, we detect the P-wave arrival, locate the epicenter, and extract the permanent offet for tatic lip inverion and magnitude etimation. 5.2 Overview of combining GPS and accelerometer data GPS relative kinematic poitioning i uually adopted to etimate eimic diplacement a double-differenced ambiguitie can be fixed to integer for guaranteeing high accuracy (Laron et al., 2003; Blewitt et al., 2006; Crowell et al., 2012; Melgar et al., 2012; Ohta et al., 2012). In relative poitioning, data from a network i analyzed imultaneouly to etimate

109 tation poition with repect to at leat one reference tation which could alo be diplaced. PPP can provide abolute eimic diplacement related to a global reference frame defined by the atellite orbit and clock with a ingle GPS receiver (Kouba 2003; Wright et al., 2012). Epecially, PPP integer ambiguity reolution, developed in recent year (Ge et al., 2008; Geng et al., 2012; Li and Zhang, 2012; Loyer et al., 2012), enable it to achieve comparable accuracy a relative poitioning. Li et al. (2013a) demontrated the performance of real-time PPP with ambiguity reolution uing 5 Hz GPS data collected during El Mayor-Cucapah earthquake (Mw 7.2, 4 April, 2010) in Mexico. Emore et al. (2007) etimated GPS diplacement baed on relative network analyi uing the GPS analyi oftware GIPSY, developed by JPL (Jet Propulion Laboratory) with orbit held fixed to precie IGS (International GNSS Service) final product. A contrained inverion technique wa then ued to combine GPS diplacement and accelerometer data from the 2003 Mw 8.3 Tokachi-oki earthquake to etimate diplacement and tep function offet in accelerometer record, after correcting for poible miorientation of the accelerometer. A multirate Kalman filter wa propoed by Smyth and Wu (2006) for fuing raw accelerometer with collocated GPS diplacement data and wa ued for bridge monitoring (Kogan et al., 2008) and tructural engineering application (Chan et al., 2006). Bock et al. (2011) applied the multirate Kalman filter to etimate broadband diplacement for the 2010 Mw 7.2 El Mayor Cucapah earthquake by combining 1 Hz GPS diplacement and 100 Hz data of collocated trong motion enor in outhern California. Hereby the 1 Hz GPS diplacement wa etimated uing intantaneou GPS poitioning in relative poitioning mode (Bock et al., 2000). Geng et al. (2013) propoed a eimogeodetic approach and applied it to GPS and accelerometer obervation of the 2012 Brawley eimic warm. Melgar et al. (2013) demontrated the Kalman filter performance for the Tohoku-oki event and analyzed the pectral difference between GPS, Kalman and accelerometer data in detail. Wang et al. (2013) dicued the potential for an automated baeline correction cheme for accelerometer data that doe not rely on GPS data. In thee combination procedure, the long-period tability of GPS derived poition i employed to contrain the eimic data. A i well known, in kinematic poitioning, precie dynamical information will give rather tight contraint on coordinate of adjacent epoch to trengthen the olution for more reliable ambiguity fixing and better diplacement accuracy. The precie dynamical information of the movement provided by eimic enor cannot be properly utilized to enhance GPS olution if etimated coordinate are ued. Therefore, integration on the obervation level i required in order to have the advantage of both enor and offet their weakne. In thi tudy, the accelerometer data are integrated into the ambiguity-fixed PPP proceing on the raw obervation level

110 5.3 The tightly-integrated algorithm Fixing ambiguitie to integer can ignificantly improve the GPS poitioning quality, epecially for the eat component (e.g., Blewitt 1989; Dong and Bock 1989). Due to the exitence of uncalibrated phae delay (UPD) originating at receiver and atellite (Blewitt 1989), for a long time only double-differenced ambiguitie between atellite and receiver can be fixed. In the recent year, it wa demontrated that atellite UPD could be etimated from a reference network and applied to other tation for fixing integer ambiguity in PPP mode (Ge et al. 2008; Collin 2008; Laurichee et al. 2008; Li et al., 2013b). Thu, PPP with integer ambiguity fixing require not only precie atellite orbit and high-rate atellite clock correction but alo UPD product. There are everal IGS real-time analyi center providing UPD product for PPP ambiguity fixing (Ge et al., 2012; Loyer et al., 2012). With the correction of GPS atellite orbit, clock and UPD, the correponding biae in the obervation can be removed. The receiver-dependent UPD can be aimilated into receiver clock parameter. Hence, the linearized equation for raw carrier phae and peudo-range obervation then can be implified a (Teunien and Kleuberg 1996), l u rm Z t I N (5.1) j j j j j p u r m Z t I e (5.2) j j j where, l j, p j denote oberved minu computed phae and code obervable from atellite to receiver at frequency j ; u i the unit direction vector from receiver to atellite; r denote the vector of the receiver poition increment; Z denote tropopheric zenith wet delay; m i the wet part of global mapping function; t are the receiver clock error; j i the wavelength of the j frequency; N j I j i ionopheric delay on the path at the j frequency; i the integer phae ambiguity; e j i the peudo-range meaurement noie; j i meaurement noie of carrier phae. Other error component uch a the dry tropopheric delay, phae center offet and variation, phae wind-up, relativitic effect and tide loading could be corrected with exiting model (Kouba and Héroux, 2001). Uually the ionophere-free linear combination i employed in PPP to eliminate the effect of ionopheric delay. In order to uppre the meaurement noie, intead of uch linear combination we ue in thi contribution raw carrier-phae and peudo-range obervation at L1 and L2 frequencie (Schaffrin and Bock, 1988). The lant ionopheric delay are etimated a unknown parameter and a temporal contraint i introduced to trengthen the olution

111 Auming that n atellite are oberved by the receiver at the epoch k, the obervational equation for all the atellite at thi epoch can be expreed a, Y A X, ~ N(0, Q ) (5.3) k k k Yk Y Y T T T ( L1, L2 ) 1 n T 1 n T Y, Lj lj,, lj, Pj pj,, pj (5.4) T T T ( P1, P2 ) The deign matrix and unknown parameter are: j j 2 2 A A', jn, Jn, Jn j2 j2 02 (5.5) 1 1 u m 1 0 A',, u m (5.6) 0 2 / n n 1 2 X r r Z t I ) N ) N ), 1,, n) (5.7), T T T T T where r denote the vector of the receiver velocity; J n i an identity matrix of n dimenion; jn denote a column vector of n dimenion in which all of the element are unity; i the Kronecker product; QY i the variance-covariance matrix of Y ; i the coefficient of ionopheric delay. The tate equation can be decribed by: X 1X 1 1a 1, ~ N(0, Q ) (5.8) k k k k k S k1 S S J J 3 3 J J n J 2n, 2 J3 2 J3 0 1*3 0 1*3 0n*3 0 2 n*3 (5.9)

112 3 2 qa qa qa qa 2 Q qz q t qi 0 2n, (5.10) where, i the ytem dynamic matrix; a i the ytem input vector (raw accelerometer obervation from the eimic enor); i the input matrix; i the accelerometer ampling interval; QS i the variance-covariance matrix of S ; q a i the acceleration variance (1,000 time the pre-event noie of 60 in thi paper); q z, q t and q i are the variance for the zenith wet delay (about 2-5 mm / hour ), receiver clock (i et to white noie with a very large value) and ionopheric delay (generally a few millimeter for the 5 Hz data ampling) repectively. With the GPS obervational equation of (5.3) and the tate equation of (5.8), the real-time Kalman filter can be employed to etimate the unknown parameter, X Xˆ a (5.11) k k1 k1 k1 k1 T Qk k 1Qk1k1 QSk (5.12) 1 ˆ T 1 X X Q A Q ( Y A X ) (5.13) k k k k Y k k k k Q ( Q A Q A ) (5.14) 1 T 1 1 k k k Yk k The time update of (5.11) and (5.12) i performed at every accelerometer ampling, while the meaurement update of (5.13) and (5.14) i applied at every GPS epoch. The time and particularly the frequency domain performance of the filter can alo be improved in potproceing with a moother and in near real-time with a fixed lag moother (Bock et al. 2011; Melgar et al., 2013). The integer ambiguity reolution i attempted at every GPS epoch, L1 and L2 ambiguitie are fixed imultaneouly uing the LAMBDA method by Teunien (1995). With the predicted ionopheric delay from previou ambiguity-fixed epoch, reliable ambiguity reolution i achievable within few econd for re-convergence (e.g., Geng et al., 2010; Zhang and Li, 2012; Li et al., 2013b), although a convergence period of about 20 min for ambiguity fixing i till required

113 Another critical iue i the validation of the fixed integer ambiguitie. There are everal approache to ae the reolved integer ambiguitie, uch a R-ratio, W-ratio a well a the Integer Aperture-baed R-ratio, and W-ratio method (Li and Wang, 2012). In thi tudy, the well-known R-ratio tet wa ued to validate the ambiguity reolution. The R-ratio i defined a the proportion of the econd minimum and the minimum quadratic ditance between the integer and the real-valued ambiguitie. It i ued to dicriminate between the econd et of optimum integer candidate and the optimum one uually with a critical criterion of three (Han 1997). 5.4 Reult The 2011 Mw 9.0 Tohoku-Oki earthquake (11 March, 2011, 05:46:24 UTC) in Japan and the 2010 Mw 7.2 El Mayor-Cucapah earthquake (4 April, 2010, 22:40:42 UTC) in Mexico were well recorded not only by trong motion tation but alo by high-rate GPS receiver. They are good example to evaluate the performance of integrated diplacement for which abundant high-rate GPS and trong motion record are available. We firtly proceed 1 Hz data of about 90 globally ditributed real-time IGS tation uing the EPOS-RT oftware of GFZ in imulated real-time mode for providing GPS orbit, clock and UPD correction at 5 ampling interval. Baed on thee correction, we replay the GPS and trong motion data collected at about thirty collocated tation during the Tohoku-Oki and El Mayor-Cucapah earthquake. A PPP can be performed with a ingle GPS receiver, the integrated diplacement are etimated on a pair-by-pair bai for each collocated GPS and trong motion pair Comparion of GPS, eimic and integrated waveform The 2010 Mw 7.2 El Mayor-Cucapah earthquake (4 April, 2010, 22:40:42 UTC) in northern Baja California, Mexico, provide u with a real event to evaluate the performance of the propoed tightly-integrated approach. GPS data i collected from the California Real-Time Network (CRTN, Genrich and Bock, 2006) and Plate Boundary Obervatory (PBO, Jackon, 2003). 200 Hz accelerometer data i collected from trong motion tation of the Southern California Seimic Network (SCSN) operated by the USGS (U.S. Geological Survey) and Caltech. Table 5.1 ummarize the tation name, location, ditance to epicenter and eparation for four collocated tation analyzed. Table 5.1: Collocated high-rate GPS and trong motion (SM) tation

114 Station Latitude Longitude( Dit to epic Separation(km (GPS/SM) (ºN) ºE) (km) ) P NP P NP P NP P NP Diplacement waveform are etimated for each collocated pair of GPS and trong motion enor uing the preented tightly-integrated filter, in a imulated real-time mode. We compare the integrated diplacement with GPS-only diplacement derived from real-time ambiguity-fixed PPP and eimic-only diplacement obtained through double integration of eimic acceleration. The eimic-only diplacement in thi tudy are provided by California Geological Survey (CGS/CSMIP, The baeline offet are already corrected by applying a high-pa filter. The GPS tation P496, which i located about 60 km from the epicenter, i collocated with SCSN eimic tation 5058 (about 140 m ditance). Comparion of the GPS-only, eimic-only and tightly integrated diplacement in all three component for thi pair (5058/P496) i exemplarily hown in Figure 5.1 by black, blue and red line, repectively

115 Figure 5.1: Comparion of GPS-only, eimic-only and tightly-integrated diplacement on the collocated 5058 (eimic) and P496 (GPS) tation during the El Mayor-Cucapah earthquake on 4 April The ub-figure (a), (b), (c) how the entire period of eimic haking in north, eat and up component repectively. The 5 Hz GPS-only, 200 Hz eimic-only, and 200 Hz tightly-integrated diplacement are repectively hown by the black, blue and red line. In Figure 5.1a, we how the entire period of eimic haking in the north component. The GPS-only and eimic-only diplacement how a high degree of imilarity of the dynamic component. The tandard deviation (STD) value of the difference between GPS-only and eimic-only diplacement are found to be 1.1, 1.0 and 2.1 cm repectively in north, eat and vertical component. The obviou difference i that a permanent coeimic offet of 0.2 m i viible in the GPS-only diplacement. Tilt and rotation of the eimic intrument reult in

116 ditortion and baeline offet. Although thee effect are largely removed by high-pa filter, low-frequency information i lot, including the lo of permanent coeimic offet in the eimic-only diplacement (Allen and Ziv, 2011). In the tightly integrated diplacement, the 0.2 m permanent offet in the north component i clearly een a the eimic data i contrained by the long-period tability of GPS meaurement and the baeline-hift problem in eimic data can be overcome. The 5 Hz GPS-only diplacement are with lower ampling rate and higher noie compared to the 200 Hz eimic-only diplacement. The root mean quare (RMS) value of GPS-only olution (10 min pre-event diplacement erie) are found to be 1.1, 1.1 and 3.0 cm repectively in north, eat and vertical component. The vertical component (Figure 5.1c) i the noiiet a expected, due to the atellite contellation configuration and the high correlation between zenith tropopheric delay and the vertical component. With the aid of the accelerometer data, the tightly-integrated filter i capable of producing a more precie waveform. The mall-amplitude eimic ignal can be detected from the tightly integrated olution (e.g. from 20 to 35 in Figure 5.1c and Figure 5.2c) in pite of the diminihed preciion of the GPS vertical component. Thi i a ignificant improvement compared to the GPS-only olution where earthquake ignal i detected only for trong event with ignificant haking

117 Figure 5.2: The blowup of the firt 45 of the coeimic diplacement in all three component on the collocated 5058 (eimic) and P496 (GPS) tation during the El Mayor Cucapah earthquake on 4 April The north, eat and up component are hown in the ub-figure a, b, and c, repectively. For clarity, the blowup of the diplacement erie in all three component for it firt 45 i hown in Figure 5.2. We can ee that the tightly-integrated diplacement are in good agreement with GPS-only olution in term of peak diplacement and long-period tability. Meanwhile, the diplacement preciion i alo improved by precie dynamical information provided by eimic enor. The mall-amplitude detail of the movement (e.g., mall hake around 47 in Figure 5.2a, 5.2b, and 5.2c), which are often covered by meaurement noie in GPS-only olution, can be clearly oberved from the tightly-integrated waveform. In Figure 5.3, we how the difference between tightly-integrated filter and GPSonly/eimic-only diplacement for the 5058/P496 pair. The reult for north, eat and up

118 component are repectively hown in Figure 5.3a, 5.3b and 5.3c. One can ee that the difference between GPS-only and filter diplacement how a high frequency noie due to the diminihed preciion of the GPS. The difference are more catter during the trong haking period. It may be caued by the eparation between enor (not trictly collocated) and/or an overweighting of the accelerometer data in the filter. The difference between eimic-only and filter diplacement how a low-frequency trend becaue of the baeline-hift problem of eimic data. The differenced time erie for the 5028/P744, 5054/P500, and 5060/P499 pair are hown in Figure 5.4, 5.5, and 5.6, repectively. Similar performance i alo achieved at thee pair, the reult confirm that the tight integration of high-rate GPS and very high-rate eimic meaurement can take their individual advantage and offet their weakne and improve the diplacement ignificantly. 0.3 GPS-filter Seimic-filter difference North (m) (a) Second after 22:40:50 (GPST) 0.2 GPS-filter Seimic-filter difference Eat (m) (b) Second after 22:40:50 (GPST)

119 0.2 GPS-filter Seimic-filter 0.1 difference Up (m) (c) Second after 22:40:50 (GPST) Figure 5.3: Difference between the diplacement erie from tightly-integrated filter and each of the two input (GPS and eimic diplacement) for 5058/P496 pair. The difference between GPS-only and filter diplacement are hown by the black line, while the difference between eimic-only and filter diplacement are hown by the red line. The difference in north, eat and up component are repectively hown in the ub-figure a, b, and c. 0.2 GPS-filter Seimic-filter difference North (m) (a) Second after 22:40:50 (GPST)

120 0.1 GPS-filter Seimic-filter difference Eat (m) (b) Second after 22:40:50 (GPST) 0.1 GPS-filter Seimic-filter difference Up (m) (c) Second after 22:40:50 (GPST) Figure 5.4: Difference between the diplacement erie from tightly-integrated filter and each of the two input (GPS and eimic diplacement) for 5028/ P744 pair. The difference between GPS-only and filter diplacement are hown by the black line, while the difference between eimic-only and filter diplacement are hown by the red line. The difference in north, eat and up component are repectively hown in the ub-figure a, b, and c

121 0.2 GPS-filter Seimic-filter difference North (m) (a) Second after 22:40:50 (GPST) 0.2 GPS-filter Seimic-filter difference Eat (m) (b) Second after 22:40:50 (GPST) 0.2 GPS-filter Seimic-filter 0.1 difference Up (m) (c) Second after 22:40:50 (GPST) Figure 5.5: Difference between the diplacement erie from tightly-integrated filter and each of the two input (GPS and eimic diplacement) for 5054/ P500 pair. The difference between GPS-only and filter diplacement are hown by the black line, while the difference between eimic-only and

122 filter diplacement are hown by the red line. The difference in north, eat and up component are repectively hown in the ub-figure a, b, and c. 0.2 GPS-filter Seimic-filter difference North (m) (a) Second after 22:40:50 (GPST) 0.2 GPS-filter Seimic-filter difference Eat (m) (b) Second after 22:40:50 (GPST) 0.2 GPS-filter Seimic-filter 0.1 difference Up (m) (c) Second after 22:40:50 (GPST)

123 Figure 5.6: Difference between the diplacement erie from tightly-integrated filter and each of the two input (GPS and eimic diplacement) for 5060/ P499 pair. The difference between GPS-only and filter diplacement are hown by the black line, while the difference between eimic-only and filter diplacement are hown by the red line. The difference in north, eat and up component are repectively hown in the ub-figure a, b, and c. Power pectral denitie for filter diplacement at P496/5058 are alo hown in Figure 5.7a to quantify the frequency content of the ignal. Similar to Bock et al (2011), a aw tooth pattern in the waveform aociated with the multi-rate apect of the filter wa hown to have an impact in the power pectra (the blue line). However, it i a minor problem for real-time eimological application a the increae in noie introduced by the peak i mall compared with the ignal. Furthermore, the puriou peak can be removed by a 5-econd lag moother, which i alo hown by the red line (Bock et al., 2011; Meglar et al., 2013). The power pectral denitie of the 3 kind of diplacement (5 Hz GPS, 200 Hz eimic, and 200 Hz tightlyintegrated filter with a 5-econd lag moother) are alo compared in Figure 5.7b. The frequency domain analyi of thee waveform decribe what frequency band each data type i reliable in: GPS perform better at the lower frequencie and accelerometer i better at the higher frequencie. The power pectral denitie of filter diplacement follow the GPS-only pectrum at the low frequencie and the accelerometer-only pectrum at the high frequencie. From the power pectral denity analyi, we can alo infer that the filter waveform i more precie and accurate than the (5 Hz) GPS-only or (200 Hz) eimic-only waveform, i.e. an accurate broadband waveform ha been achieved no mooth with mooth PSD (m 2 /Hz) (a) Frequency (Hz)

124 10 0 filter Seimic GPS PSD (m 2 /Hz) (b) Frequency (Hz) Figure 5.7: Power pectral denitie. (a) Power pectral denity for tightly-integrated diplacement waveform at P496/5058. The blue line denote the reult without a moother, while the red line denote the reult with a 5-econd lag moother. (b) Power pectral denity for 5 Hz GPS diplacement at P496 (the black line), 200 Hz high-pa filtered eimic diplacement at 5058 (the blue line), and 200 Hz tightly-integrated diplacement (with a 5-econd lag moother) at P496/5058 (the red line). Fixing ambiguitie i a prerequiite to achieve high accuracy poitioning reult in GNSS application. The ratio of the econd minimum to the minimum quadratic form of reidual (Rratio) i ued here to decide the correctne and confidence level of integer ambiguity candidate. The ratio value can be conidered a an index to denote the reliability of ambiguity reolution. Thu, larger ratio value denote more reliable ambiguity reolution. The ratio value of tightly-integrated and GPS-only olution for 5058/P496 and 5028/P744 pair are repectively hown in Figure 5.8a and 5.8b. The ratio value of tightly-integrated olution are hown by the red line, while the ratio value of GPS-only olution are hown by the black line. A hown in Figure 5.8, the ratio value of GPS-only olution are generally rather mall and below 5 uually. With the aid of the accelerometer data, the ratio value are increaed remarkably compared to that of GPS-only. The averaged ratio i increaed from 4.5 and 3.8 of GPS-only for 5058/P496 and 5028/P744 pair to 11.6 and 6.4 of the tightly-integrated olution, repectively. The reult indicate that the propoed algorithm can ignificantly improve the ability of reolving integer-cycle phae ambiguitie, which i very critical for promoting the contribution of GPS phae obervation. The comparion of ratio value for 5054/P500 and 5060/P499 pair are alo repectively hown in Figure 5.9a and 5.9b. The average value of

125 GPS-only ratio value for thee two pair are improved from about 3.6 and 4.8 to 8.0 and 10.1, repectively. Figure 5.8: Comparion of the ratio value for tightly-integrated and GPS-only olution. (a) for the collocated 5058 (eimic) and P496 (GPS) pair; (b) for the collocated 5028 (eimic) and P744 (GPS) pair. The ratio value of tightly-integrated and GPS-only olution are hown by the red and black line, repectively

126 Figure 5.9: Comparion of the ratio value for tightly-integrated and GPS-only olution. (a), for the collocated 5054 (eimic) and P500 (GPS) pair; (b), for the collocated 5060 (eimic) and P499 (GPS) pair. The ratio value of tightly-integrated and GPS-only olution are hown by the red and black line repectively. For the 2011 Tohoku-Oki earthquake, the 1 Hz GPS data i collected at the GEONET (the GPS Earth Obervation Network Sytem) tation operated by the Geopatial Information Authority (GSI) of Japan. 100 Hz accelerometer data i collected from trong motion tation of the K-Net and Hi-Net. We compare the integrated diplacement with eimic-only waveform obtained from double integration of raw acceleration data. The reult of two collocated pair AKT006/0183 and NGN017/0986 are hown in Figure 5.10 a an example. The left ub-figure how the entire period of the eimic haking in north/eat/up component at AKT006/0183 and the right one how the eimic haking at NGN017/0986 in the ame three component. The GPS tation 0183 ( N, E), which i located 251 km from the epicenter of Tohoku-Oki earthquake, i collocated with K-Net eimic tation AKT006 (about 20 m away from GPS tation), and the other pair NGN017 and 0986 tation within 5 km ditance, where the ditance to the epicenter i about 480 km. The uncorrected eimic diplacement are traditionally oberved from zero-order corrected with only conideration removing the pre-event mean bia. Although the dynamic motion can

127 be determined, a linear or parabolic drift i apparent in the latter part of each diplacement time erie, and the permanent coeimic offet i lot in a eimic-only olution. The corrected eimic diplacement are derived from the baeline-corrected trong motion recording which are proceed uing the automatic empirical baeline correction cheme propoed by Wang (2000). Although the corrected eimic diplacement have a high degree of imilarity of the dynamic component with the integrated reult, they till maintain everal decimeter difference in permanent coeimic offet due to the effect of the reidual baeline bia error. From the integrated diplacement waveform, there are obviou permanent coeimic offet which are about 0.47 m, 0.51 m, and 0.03 m in the north, eat, and up component at tation AKT006/0183, while the permanent offet of tation NGN017/0986 are relatively mall, about 0.04 m in the north, 0.12m in the eat, and 0.01m in the up component. Eat (m) North (m) uncorrected Accelerometer corrected Accelerometer Integrated AKT006 / 0183 NGN017 / Up (m) Time after origin time () Time after origin time () Figure 5.10: Comparion of uncorrected eimic-only and corrected eimic-only and integrated diplacement on the collocated AKT006 (eimic) and 0183 (GPS) pair and NGN017 (eimic) and 0986 (GPS) pair during the Tohoku-Oki earthquake on 11 March All ub-figure how the entire period of eimic haking. The 100 Hz integrated diplacement i hown by the red line. The 100 Hz eimic-only diplacement without baeline correction and with baeline correction are repectively hown by the blue line and the black line, repectively

128 In Figure 5.11 and Figure 5.12, we compare the tightly-integrated diplacement (the red line) and GPS-only diplacement (the black cro ymbol). The reult of the AKT006/0183 and NGN017/0986 pair are repectively hown in the left and right ide of Figure 5.11, and the imilar reult of the 5058/P496 and 5028/P744 pair are alo hown in Figure The GPS tation P496, which i located about 60 km from the epicenter of 2010 El Mayor- Cucapah earthquake, i collocated with SCSN eimic tation 5058 (about 70 m eparation). The other pair P744 and 5028 tation are within 140 m of each other, and the ditance from them to the epicenter i about 65 km. All ub-figure from top to bottom depict the entire period of eimic haking in north, eat and up component. We can ee that the integrated diplacement are in good agreement with GPS-only olution in term of peak diplacement, permanent offet and long-period tability. However, it i clearly hown that the GPS-only diplacement are with lower ampling rate and higher noie compared to the integrated diplacement (Detail can alo be een in Figure 5.14 and Figure 4.15). The root mean quare (RMS) value of GPS-only olution (10 min pre-event diplacement erie) are 1.1, 1.1 and 3.0 cm repectively in north, eat and vertical component. The preciion of integrated diplacement i ignificantly improved by precie dynamical information provided by eimic enor. 0.0 AKT006 NGN North (m) GPS Integrated GPS Integrated 0.6 Eat (m) Up (m) Time after origin time () Time after origin time () Figure 5.11: Comparion of GPS-only and tightly-integrated diplacement on the collocated AKT006 (eimic) and 0183 (GPS) pair and NGN017 (eimic) and 0986 (GPS) pair during the Tohoku-oki earthquake on 11 March The ub-figure how from top to bottom the entire period of eimic haking in north, eat and up component repectively. The 1 Hz GPS-only and 100 Hz tightly-integrated diplacement are hown repectively by the black croe and the red line

129 North (m) GPS GPS+Accelerometer GPS GPS+Accelerometer -0.2 Eat (m) Up (m) Time after origin time () Time after origin time () -0.1 Figure 5.12: Comparion of GPS-only and tightly-integrated diplacement on the collocated 5058 (eimic) and P496 (GPS) pair and 5028 (eimic) and P744 (GPS) pair during the El Mayor Cucapah earthquake on 4 April The ub-figure from top to bottom how the entire period of eimic haking in north, eat and up component repectively. The 5 Hz GPS-only and 200 Hz tightlyintegrated diplacement are hown repectively by the black cro ymbol and red line. The power pectral denitie of the three kind of diplacement (GPS-only, eimic-only, and integrated diplacement) at AKT006/0183 and P744/5028 pair are alo compared in Figure 5.13 to quantify the frequency content of the ignal. The frequency domain analyi of thee waveform how in which frequency band each data type i reliable. GPS perform better at lower frequencie and eimic enor i better at higher frequencie. We can ee that the power pectral denitie of integrated diplacement follow the GPS-only pectrum at the low frequencie and the eimic-only pectrum at the high frequencie. From the power pectral denity analyi, we can alo infer that the integrated waveform i more precie and accurate than the GPS-only or eimic-only waveform. An accurate broadband waveform, which ha the advantage of both enor, ha been achieved

130 10 0 Seimic Integrated GPS PSD (m 2 /Hz) (a) Frequency (Hz) 10 0 Seimic Integrated GPS PSD (m 2 /Hz) (b) Frequency (Hz) Figure 5.13: Power pectral denitie. (a) Power pectral denity for 1 Hz GPS diplacement at tation 0183 (the black line), 100 Hz eimic diplacement at AKT006 (the blue), and 100 Hz tightlyintegrated diplacement waveform at AKT006/0183 (the red line). (b) Power pectral denity for 5 Hz GPS diplacement at P744 (the black line), 200 Hz eimic diplacement at 5028 (the blue line), and 200 Hz tightly-integrated diplacement at P744/5028 (the red line) Detection of P-wave arrival Earthquake monitoring and early warning ytem not only depend on the accurate etimation of permanent diplacement, but alo rely on the capability of the ene of P-wave arrival which i employed to predict the arrival and intenity of detructive S and urface wave. Figure 5.11 and Figure 5.12 have hown that the integrated reult could get accurate permanent offet. The following ection mainly focu on another iue. The enlarged view of

131 the firt 20 econd of the integrated and GPS-only reult for tation 5028/P744 i hown in Figure 5.14, and the imilar enlarged view for tation AKT006/0183 i hown in Figure From coeimic diplacement and velocity waveform, we can oberve that the GPS-only olution i noiy and ha a preciion limited to everal millimeter in diplacement and few centimeter per econd in velocity. The vertical component i much noiier a expected, due to the atellite contellation configuration and the high correlation between zenith tropopheric delay and the height component. The preciion of vertical diplacement i of the order of few centimeter, and vertical velocity preciion i around everal centimeter per econd, which i not enough to detect P-wave accurately. With the aid of the eimic data, the tightly-integrated filter i capable of producing a precie integrated diplacement and velocity waveform, epecially in the up component. We can oberve the mall-amplitude P-wave in the recording which are often covered by meaurement noie in GPS-only olution, can be clearly oberved from the integrated waveform, and detect P-wave arrival from the integrated olution in pite of the diminihed preciion of the GPS vertical component. Thi i a ignificant improvement over the GPS-only olution where earthquake ignal i detected only after the S-wave arrival, which i generally a few econd later than the P-wave arrival for near-field tation. The bottom ub-figure in figure 5.14 and 5.15 are STA/LTA ratio value baed on tightlyintegrated reult for north/eat/up component, which are ued to pick up the earthquake P- wave arrival. The hort-term average (STA) through long-term average (LTA) picker i the mot broadly ued automatic algorithm in eimology (Allen, 1978). It continuouly calculate the average value of the abolute amplitude of a eimic ignal in two conecutive movingtime window. The hort time window (STA) i enitive to eimic event while the long time window (LTA) provide information about the temporal amplitude of eimic noie at the ite (Trnkoczy et al., 2002). When the ratio of both exceed a pre-et threhold mean the arrival of P-wave. The STA/LTA picker parameter etting are alway a tradeoff between everal eimological and intrumental conideration. For thee two earthquake event in thi paper, the STA window duration i 0.2 ec, the LTA window duration i 2 ec, and the pre-et threhold i et to 10. We can clearly identify P-wave arrival in the STA/LTA ratio time erie. It i noted that the P-wave appear in vertical component firt and in the horizontal component a few milliecond later. The detected earthquake P-wave arrival time of tation AKT006/0183 i compared with the USGS reference value calculated by TauP Toolkit (Crotwell et al., 1999), and the P-wave arrival time of tation 5028/P744 i compared with the reference value It i demontrated that the integrated reult could be ued to pick up an accurate P-wave arrival time. However, it i difficult for the GPS-only olution to be accurately identified P-wave becaue of the ignificantly le preciion. Thu, the integrated reult improve on both eimic-only and GPS-only method, by providing the

132 full pectrum of eimic motion from the detection of P-wave arrival to the etimation of permanent offet. Diplacement (m) North Eat Up Integrated GPS Velocity (m/) STA/LTA ratio Time after origin time () Figure 5.14: An enlarged view of the firt 20 of the coeimic diplacement and velocitie in all three component on the collocated 5028 (eimic) and P744 (GPS) pair during the El Mayor Cucapah earthquake. The 5 Hz GPS-only and 200 Hz tightly-integrated diplacement and velocitie are repectively hown by the blue dotted line and red line. The bottom ub-figure are STA/LTA ratio reult baed on tightly-integrated reult, which how the firt arrival time of eimic wave. The ubfigure how, from left to right, the north, eat and up component

133 Diplacement (m) North Eat Up Integrated GPS Velocity (m/) STA/LTA ratio Time after origin time () Figure 5.15: An enlarged view of the firt 20 of the coeimic diplacement and velocitie in all three component on the collocated AKT006 (eimic) and 0183 (GPS) tation during the Tohoku-oki earthquake on 11 March The 1 Hz GPS-only and 100 Hz tightly-integrated diplacement and velocitie are repectively hown by the blue dotted line and red line. The bottom ub-figure are STA/LTA ratio reult baed on tightly-integrated reult, which how the firt arrival time of eimic wave. The ub-figure how, from left to right, the north, eat and up component. When P-wave i detected at four or more near-field GPS/trong motion pair, the epicenter, the velocity of earthquake wave and the origin time can be determined by uing a leat quare method a follow, x1x0 x2 x0 y1 y0 y2 y0 0 0 ( ) dx ( ) dy ( t t2) v ( d1 d2) 0 d1 d2 d1 d2 x1x0 x3 x0 y1 y0 y3 y0 0 0 ( ) dx ( ) dy ( t t3) v ( d1 d3) 0 d1 d3 d1 d3 x1 x0 xn x0 y1 y0 yn y0 0 0 ( ) dx ( ) dy ( t tn) v ( d1 dn) 0 d1 dn d1 dn n di ( ti ) i1 v t0 n (5.15)

134 x Where, 0, y0 denote the approximate coordinate of the epicenter; xi, yi( i 1, n) 0 denote the coordinate of the i th tation; di approximate coordinate of epicenter; denote the ditance from the i th tation to the dx, dy denote the increment of epicenter; v denote t velocity of earthquake wave; i denote the arrival time of earthquake wave at the i th tation; di denote the ditance from the i t th tation to the epicenter; 0 denote the origin time. Several iteration are required to avoid the linearization error. In order to tet thi technique, the five GPS/trong motion pair where P-wave i detected earliet during the El Mayor Cucapah earthquake are ued. The detected earthquake P-wave arrival time i 0.09, 0.15, 0.11, 0.10, and 0.13 later than the USGS reference value of P- wave arrival time at the five pair. The epicenter etimate i roughly 2.5 km away from the U.S. Geological Survey (USGS) epicenter etimate. The origin time etimate i 0.12 later than the USGS reference value of 22:40:57 (GPS time). The accurate detection of P-wave arrival i critical for earthquake early warning, a it allow for prediction of the arrival of the detructive S-wave. The P-wave-baed earthquake parameter uch a epicenter and origin time can be releaed before the S-wave arrival Extraction of permanent offet and fault lip inverion In addition to P-wave arrival time, the important information, provided by the integrated poition erie, i the permanent offet. We ue the real-time algorithm propoed by Allen and Ziv (2011) to remove dynamic ocillation and extract thee offet. The permanent offet derived from integrated olution (about 1 minute after the arrival of the earthquake wave) are compared with the one from the pot-proceed daily olution in Figure The RMS of the difference between them i about 3.7 mm

135 Figure 5.16: Comparion of the permanent (tatic) offet from the tightly-integrated olution and the pot-proceed daily olution. The blue rectangle how tatic offet derived from the tatic PPP olution with daily obervation (the difference between daily olution of the day before the earthquake and the day after the earthquake). The red rectangle how the tatic offet derived from the real-time tightly-integrated olution. We derived the patial ditribution of the fault lip uing the coeimic diplacement obtained from both the real-time tightly-integrated olution and the pot-proceed daily olution. In the ame way a done by Li et al. (2014), the fault geometric parameter (trike 312 /dip 88 ) are adopted from the Global Centroid Moment Tenor (GCMT) olution of the earthquake. The rake angle (lip direction relative to the trike) i allowed to vary ±20 around the GCMT olution of 186. The fault ize i given to be 130 km along the trike and 20 km

136 along the dip, which i then divided into 26 4=104 ub-fault. In the inverion, the data i weighted twice a much for the two horizontal component a for the vertical component. The inverion reult are hown in Figure The two inverion reult in calar eimic moment of Nm and Nm repectively, equivalent to moment magnitude of Mw7.18 for both. Although there are ome difference exiting on the maximum lip value which may be caued by the inconitency in the vertical component between the two dataet, the two inverion reult are quite imilar not only in the moment magnitude, but alo in the lip ditribution pattern. The major lip area occurred at a very hallow depth (near the urface) at about 90 km along the trike direction on the fault plane. The rake variation how that there i a purely right lateral trike lip at the northwet of the fault, and a minor normal fault component occur at the outh eat of the fault. Conidering the hypocentral location, we can confirm that thi earthquake i an aymmetric bilateral rupture event: the rupture mainly propagate northwetward from the hypocenter during the ource proce. Overall, the comparion of the two inverion reult how that the integrated olution can provide a reliable etimation of earthquake magnitude and even of the fault lip ditribution in real time. Figure 5.17: Fault lip inverion. (a) Inverion with permanent coeimic diplacement obtained from real-time tightly-integrated olution; (b) Inverion with pot-proceed daily olution. From top to bottom are the inverted fault lip ditribution, comparion between the oberved and the ynthetic diplacement on the horizontal component, and on the vertical component, repectively

137 5.5 Concluion We preented an approach for tightly combining GPS and eimic enor data where the accelerometer data are integrated into the ambiguity-fixed PPP proceing on the obervation level. The performance of the propoed tightly-integrated approach wa validated uing the collocated high-rate GPS and trong motion data collected during the 2010, Mw 7.2 El Mayor- Cucapah earthquake and the 2011 Tohoku-Oki (Japan) earthquake. For tightly-integrated diplacement, the peak diplacement and long-period tability are in agreement with GPSonly olution. A a typical example, the permanent coeimic offet which i uually underetimated in the eimic-only olution can be now obtained exactly in the integrated olution. Some mall-amplitude eimic detail, which are not detectable in the GPS-only approach, can be detected from the tightly integrated diplacement. The integrated waveform take the advantage of both enor and i more precie and accurate than the GPS-only or eimic-only waveform. A power pectral denity analyi alo demontrate that an accurate broadband diplacement waveform can be derived from the tightly-integrated filter. The power pectral denitie of integrated diplacement follow the GPS-only pectrum at the low frequencie and the eimic-only pectrum at the high frequencie. Furthermore, the ambiguity-fixing ratio value of the tightly-integrated olution are ignificantly improved from about 4 of the GPS-only olution to 10 on average. The integrated diplacement can provide the full pectrum of the eimic motion allowing the detection of P-wave arrival and the etimation of permanent offet. Small-cale feature including P wave are viible in the integrated diplacement and velocity waveform. The P- wave arrival can be picked up accurately and ued for reliable determination of epicenter and origin time. Permanent offet can alo be extracted with high accuracy and ued for reliable fault lip inverion and magnitude etimation. Thee earthquake parameter are critical for earthquake/tunami monitoring and early warning ytem

138 6 Concluion and outlook The main contribution of thi thei can be ummarized a follow: The PPP technique can provide abolute coeimic diplacement with repect to a global reference frame with a tand-alone GPS receiver. In thi paper, we preent an approach of uing real-time ambiguity-fixed PPP for earthquake early warning. The 2010 El Mayor- Cucapah earthquake and the 2011 Tohoku-Oki earthquake were ued to evaluate our approach for poible ue in EEW. Comparion of the diplacement, etimated from PPP and accelerometer, diplayed a high agreement within few centimeter. Integer ambiguity fixing can improve the accuracy of real-time PPP diplacement ignificantly, epecially in the eat component. The ue of original carrier-phae and peudo-range can alo uppre the noie and improve the preciion of real-time PPP. The reult of the fault lip inverion indicate that the real-time ambiguity-fixed PPP can improve fault lip inverion and the moment magnitude etimation and become complementary to exiting eimic EEW methodologie. The real-time ambiguity-fixed PPP module can be embedded into high-rate GPS receiver firmware and be incorporated into EEW ytem epecially for region at threat from large magnitude earthquake and tunami. We propoed a new GPS analyi method for hazard (e.g. earthquake and tunami) monitoring. The new augmented PPP method can overcome the limitation of current relative poitioning and global PPP approache for thi application. The performance of the new approach i evaluated by GPS ground network data, oberved during the 2011 Tohoku-Oki earthquake in Japan. The atmopheric correction retrieved from the nearby monitoring tation can be interpolated with accuracy better than 5 cm. Thi mean that the interpolated atmopheric correction are accurate enough for rapid ambiguity reolution, which i a prerequiite to achieve the mot precie diplacement. The diplacement waveform, derived uing the augmented PPP approach are immune to the convergence problem caued by data gap and cycle lip and the problem of the earthquake haking the reference tation compared to the waveform baed on RP and global PPP analyi. Thi make augmented PPP potentially appropriate for the application in operational earthquake/tunami monitoring and warning ytem. The reliability and accuracy of permanent coeimic diplacement are alo ignificantly improved. The RMS accuracy of about 1.4, 1.1, and 1.7 cm are achieved in the north, eat, and vertical component, repectively. The inverion reult indicate that the augmented PPP olution i the mot conitent with pot-proceed ARIA olution both in the fault lip ditribution and diplacement fitting

139 A new approach for real-time GNSS eimology uing a ingle receiver wa preented. The performance of the propoed TPP approach i validated uing 1 Hz GEONET data collected during the 2011, Mw 9.0 Tohoku-Oki earthquake. When real-time precie orbit and clock correction are available, the diplacement waveform, derived from TPP, are conitent with the pot-proceed PPP waveform at an accuracy of few centimeter during the entire haking period, even for a period of twenty minute. The TPP permanent coeimic offet agree with PPP one very well with RMS value of 3.0, 2.1, and 5.6 cm in north, eat, and vertical component, repectively. The reult of the fault lip inverion alo indicate that the TPP method can provide a reliable etimation of moment magnitude and even of the fault lip ditribution. If jut the broadcat orbit and clock are available, the diplacement accuracy will be degraded to ome extent and thi lead to underetimation of the moment magnitude and fault lip value. We compared the technical detail of current ingle-receiver GNSS eimology approache. Furthermore, everal refinement are propoed to the variometric approach in order to eliminate the drift trend in the integrated coeimic diplacement. After careful correction of all error component, the diplacement waveform derived from TPP and refined variometric approach are conitent with converged PPP at an accuracy of few centimeter. The reult of the fault lip inverion alo indicate that the TPP and the refined variometric approach can provide a reliable etimation of moment magnitude and fault lip value a the converged PPP. From the above analyi and reult on the ingle-receiver approache for real-time GNSS eimology, we can conclude that the TPP, refined variometric approache have equivalent mathematical model and can provide the ame diplacement preciion with the converged PPP method. Moreover, thee two approache overcome the convergence problem of PPP, making them more uitable for eimological application. We preented an approach for tightly combing GPS and eimic enor data where the accelerometer data are integrated into the ambiguity-fixed PPP proceing on the obervation level. The performance of the propoed tightly-integrated approach wa validated uing the collocated high-rate GPS and trong motion data collected during the 2010, Mw 7.2 El Mayor- Cucapah earthquake and the 2011 Tohoku-Oki (Japan) earthquake. For tightly-integrated diplacement, the peak diplacement and long-period tability are in agreement with GPSonly olution. A a typical example, the permanent coeimic offet which i uually underetimated in the eimic-only olution can be now obtained exactly in the integrated olution. Some mall-amplitude eimic detail, which are not detectable in the GPS-only approach, can be detected from the tightly integrated diplacement. A power pectral denity analyi alo demontrate that an accurate broadband diplacement waveform can be derived from the tightly-integrated filter. Furthermore, the ratio value of the tightly-integrated olution are ignificantly improved from about 4 of the GPS-only olution to 10 on average

140 The integrated diplacement can provide the full pectrum of the eimic motion allowing the detection of P-wave arrival and the etimation of permanent offet. Small-cale feature including P wave are viible in the integrated diplacement and velocity waveform. The P- wave arrival can be picked up accurately and ued for reliable determination of epicenter and origin time. Permanent offet can alo be extracted with high accuracy and ued for reliable fault lip inverion and magnitude etimation. Thee earthquake parameter are critical for earthquake/tunami monitoring and early warning ytem. Up to now, 74 atellite are already in view and tranmitting data compared to pat year with 32 GPS only. Once all four ytem are fully deployed, about 120 navigation atellite will be available for GNSS uer. Undoubtedly, the rapid development of multi-contellation GNSS could enable a wider range of more precie and reliable application, e.g. for poitioning, navigation, timing, and geophyical application. In the near future, a joint proceing of multi-gnss (e.g., GPS, GLONASS, Galileo and BeiDou) data for better eimological application will be invetigated

141

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148 Acknowledgment The completion of thi thei would not have been poible without the upport of many people and organization. Firt of all I would like to expre my profound repect and gratitude to my upervior, Prof. Harald Schuh at TU Berlin and GFZ, Dr. Maorong Ge, and Prof. Ur Hugentobler, for uperviing thi thei, for their continuou upport, guidance and encouragement of my tudie and reearch. They were alway willing to hare their inight with me and were patient with every quetion. I am grateful to Prof. Dr. Harald Schuh, director of GFZ Department 1 for hi kindly help, organization of my work and improvement of my publication. I alo would like to thank Dr. Jen Wickert for hi helpful uggetion for my publication and Phd work. I owe a pecial thank to my upervior Dr. Maorong Ge, whom I thank o much for hi continuou and extenive upport throughout the lat year. Hi elfle help, detailed guidance and dicuion are the ource of my forward momentum. I would alo like to thank my GFZ colleague Dr. Dick Galina, Dr. Mathia Fritche, Dr. Florian Zu, Dr. Rongjiang Wang, Dr. Yong Zhang, Dr. Jurgen Klotz, Dr. Tong Ning, Dr. Tobia Nilon, Dr. Robert Heinkelmann, Dr. Jan Doua, Dr. Zhiguo Deng, Dr. Michal Bender, Dr. Gerd Gendt, Dr. Marku Ramatchi, Dr. Faqi Diao, Mr. Maik Uhlemann, Mr. Marku Bradke, Mr. Andre Brandt, Mr. Thoma Nichan, Dr. Junping Chen, Dr. Ming Shangguan, Dr. Rui Tu, Xiaolei Dai, Hua Chen, Kaifei He, Kejie Chen, and other, for their kindly help and dicuion. I appreciate their kindly help, cooperation and dicuion. I have enjoyed working with all of my colleague. I am indebted to my hot intitute GFZ where I wa doing my reearch from 2010 to TU Berlin i alo thanked for my tudy during thi period. The International GNSS Service (IGS) are thanked for providing GNSS data and product. Finally, I would like to expre my gratitude to my parent for their endle upport and undertanding. The peron I wih to thank mot i my wife and daughter, who fill my heart with confidence, courage, and love all the time