Boston College The Graduate School of Arts and Sciences Department of Geology and Geophysics THE DEVELOPMENT OF A MOMENT-MAGNITUDE BASED EARTHQUAKE CATALOG FOR THE NORTHEASTERN UNITED STATES a thesis by ANASTASIA MACHERIDES Submitted in partial fulfillment of the requirements for the degree of Master of Science May 2003
copyright by ANASTASIA MACHERIDES 2003
The Development of a Moment-Magnitude Based Earthquake Catalog for the Northeastern United States Anastasia Macherides Dr. John E. Ebel Weston Observatory Boston College In this study a moment-magnitude (M) based earthquake catalog is developed for 425 northeastern United States earthquakes occurring between 1938 and 2002. Calculation of M for these earthquakes is accomplished using the Biswas and Aki (1984) approach, which uses the amplitudes of coda-waves to estimate seismic moment, and hence M. I have chosen events with known M o in order to calibrate the coda amplitude moment measurements. For these events, coda-wave amplitudes were measured at different lapse times, coda-wave amplitude decay was plotted as a function of lapse time, and average slope and intercept values were computed. Utilizing these results and the previously determined M o of the given events, a formula for computing M o is devised for use with the Weston Observatory broadband digital data. This formula is adjusted to be accurate for the older types of earthquake recordings from the U.S. National Seismic Network and from New England Seismic Network stations.
Acknowledgements I would like to thank my principal advisor, Prof. John E. Ebel, for all his guidance, and help throughout this endeavor. I appreciate his patience and quick reviews of this thesis. I would also like to acknowledge my co-advisor, Prof. Alan L. Kafka, for his helpful suggestions. Weston Observatory of Boston College provided a pleasant and positive environment for my research. I thank Tracy Downing, Ned Johnson, Father James W. Skehan, S.J., and Pat Tassia for their friendship and advice. Special thanks go to my father, Theodore, my mother, Evangelia, my sister, Tammy, and my grandmother, Stamatina Berlis, for their love and encouragement. Without their examples of perseverance, I would not have been able to accomplish the great task of finishing this thesis. Above all, I would like to thank my husband, Anestis Moulis, for his constant love, support, and understanding, for being my best friend, and for making life so wonderful. i
Table of Contents Page Number List of Tables..... iv List of Figures.v Chapter 1. Introduction.....1 2. Coda Wave Formation Models... 4 3. The New England Seismic Network... 7 3.1 The An 1 and An 2 Seismic Systems..7 3.2 The An 3 Seismic System....8 3.3 The Ds 1 Seismic System....8 3.4 The Ds MIM Seismic System.. 9 3.5 The Ds 2 Seismic System....10 4. Background... 11 4.1 M N Scale 11 4.2 M c Scale.....12 4.3 M Scale.. 13 5. Research Methods. 15 6. Data Analysis.... 18 6.1 The Measurement of Coda Waves.....18 ii
6.2 An 1 and An 2 System Data Analysis... 19 6.3 An 3 System Data Analysis. 19 6.4 Ds 1 System Data Analysis. 21 6.5 Ds MIM and Ds 2 System Data Analysis...22 7. Results....24 7.1 Determination of X for Each System..... 24 7.2 Scattering Theory...25 7.3 Uncertainty in M Determinations..27 7.4 Comparison of M with M N and M c for Analog Data.....29 7.5 Comparison of M with M N and M c for Digital Data...31 7.6 Interstation Consistency. 32 8. Conclusions...34 Tables.36 Figures....63 References.. 76 Appendix A NESN Station Gains at 0.977 Hz. 79 Appendix B Plot of An 3 Average Amplitude Response to Ground Displacement...80 Appendix C Ds 1 Measured Displacement Amplitude Response..81 iii
List of Tables Table Page Number 1. Instrumentation History of Weston Observatory s Seismic Network.....36 2. Weston Observatory s Seismic Network Station Locations 1974-1993..37 3. Location Details of Stations Operating 1994-2000..38 4. Recent Station Additions to the Ds 2 Network......38 5. Details of the Events With Known Seismic Moments.. 39 6. Calculated Constants for Each Weston Observatory Recording System..40 7. M formulas for the Northeastern United States.... 41 8. Examples of Data Analysis From Each Recording System...42 9. Moment-Magnitude Based Earthquake Catalog for the Northeastern U.S....45 10. Standard Deviation of M values for Northeastern U.S. Events........61 11. Calculated Moment Magnitudes for Events During 1987.... 62 12. Interstation Variability in the M Determination of an Event....62 iv
List of Figures Figure Page Number 1. Seismogram of Lisbon, NH Earthquake on MIM (z)...63 2. Map of Recent Seismicity of the Northeastern United States.....64 3. Map of Weston Observatory NESN Stations 1974-1993.........65 4. Map of Weston Observatory NESN Stations 2002... 66 5. Spectrum of Continuous 1 Hz Pulse at BRY (z)... 67 6. Spectrum of Signal-to-Noise Ration of Lisbon, NH event on MIM (z)...68 7a. Plot of Amplitude vs. Lapse Time for Events Recorded on the An 1 System...69 7b. Plot of Amplitude vs. Lapse Time for Events Recorded on the An 2 System...69 7c. Plot of Amplitude vs. Lapse Time for Events Recorded on the An 3 System...69 7d. Plot of Amplitude vs. Lapse Time for Events Recorded on the Ds 1 System....69 7e. Plot of Amplitude vs. Lapse Time for Events Recorded on the Ds MIM System...69 7f. Plot of Amplitude vs. Lapse Time for Events Recorded on the Ds 2 System....69 8. Seismograms of Waterville, ME Earthquake Recorded on the Ds 2 System.70 9. Plots of Coda-Wave Amplitude Decay Characteristics vs. Lapse Time for each of Weston Observatory s Ds 2 Stations.......71 10. Coda Amplitude Decay for Events of Varying Lapse Times......73 11. Short Lapse Times vs. Long Lapse Times for a Single Event...73 12a. Correlation Plots Between M and M N for Weston Observatory Instruments..74 12b. Correlation Plots Between M and M c for Weston Observatory Instruments...75 v
1. Introduction The investigation of national and regional earthquake hazard in the United States has become increasingly important for determining the proper seismic design levels for each part of the country. It is essential that progress be made in our understanding of seismic hazard so that seismic ground motions can be accurately computed at any probability of occurrence. When ground motions from earthquakes with different probabilities of occurrence can be determined, possible damage at various distances from the sources can be estimated. For the estimation of earthquake hazard it is important to understand the properties of earthquake sources, the effect the earth as a medium has on the seismic waves generated by earthquakes, and the variation of ground motion amplitudes at different distances from earthquake sources (Pulli, 1984). Many uncertainties still exist in the area of earthquake source properties. The accurate determination of the magnitudes of known earthquakes is an answer to diminishing one area of source uncertainty. In order to calculate accurate ground motions, accurate earthquake magnitudes are required. In the analyses of seismic hazard, the moment-magnitude scale is the scale of choice for describing the size of an earthquake because moment-magnitude is directly related the physical processes of the earthquake source. For the northeastern United States (NEUS), however, the currently available catalogs of earthquakes include a variety of magnitude scales, including M N and M c, and thus do not contain a uniform measure of earthquake size. In this thesis, I develop a moment-magnitude formula for the NEUS, called M in this thesis, which uses the earthquake s source characteristics to represent 1
M w, where M w = 2 / 3 logm o - 10.7 (Hanks and Kanamori, 1979). M o, seismic moment, is a measure of a physical strength of the source and is therefore the best measure of event size, for it represents the actual energy released by an earthquake and directly relates to the rupture parameters of an event (Aki and Chouet, 1975). Unlike the M magnitude scale, no other magnitude scale is truly proportional to seismic moment, and therefore moment magnitude. Moment magnitude is the one magnitude scale that is independent of the region where the earthquake occurred, and therefore earthquake size can be compared on a global basis. Measurements of event size made with other magnitude scales are dependent on such variables as the focal depth of the earthquake and its radiation pattern. In the case of other magnitude scales, corrections for ground-motion attenuation with distance is dependent on regional properties (such as surface geology and the seismic structure of the upper crust), focal depth, ray path, and wave frequency. Moment magnitude, on the other hand, is not dependent on these properties. Because the ideal frequency at which to measure total event energy is zero, the moment magnitude M scale is the most accurate of scales to measure and characterize total event energy since it parameterizes the source radiation at the smallest measureable frequencies. Furthermore, for the eastern United States, Atkinson and Boore (1987), Atkinson and Boore (1995), and Toro et al. (1997) have developed ground-motion attenuation relations for ground motions from eastern North American earthquakes employing the M scale. To best utilize the eastern United States ground-motion relations, one would like to have an earthquake catalog with moment magnitude as one of the parameters reported for each event in the catalog. 2
At the present time, the catalog for the northeastern United States contains a number of magnitudes, namely m blg, m b, M c, and M N. In this study a catalog that includes the moment magnitudes of 425 events, occurring between 1938 and 2002, is developed for the northeastern United States, where the moment magnitude is based on measurements of amplitudes of coda waves using a methodology that was developed by Biswas and Aki (1984). With the development of the new earthquake catalog, moment magnitudes for all future recorded earthquakes can be routinely calculated and added to the catalog, and the source strength of northeastern United States events can be directly compared to other events of different regions. 3
2. Coda Wave Formation Models Coda waves are identified as the energy composing the tail part of the seismogram of a local earthquake, following the direct arrivals of the P, S, and surface waves, as seen in Figure 1. The coda consists of backscattered waves generated when the primary S waves encounter velocity and structural heterogeneities in the crust and upper mantle (Pulli, 1984). Coda-wave generation models have been developed to explain theoretically the formation of coda waves. The single scattering model describes a process where the propagating primary S wave encounters randomly distributed heterogeneities in the earth s crust, producing secondary waves which are recorded as the coda. It assumes that the coda-envelope shape of decaying amplitude with time on a seismogram is controlled by single-scattered S waves. This model is valid when the size of the scatterer is larger than the wavelength of the coda wave. Gao et al. (1983) showed that the attenuation mechanisms, and resulting Q values, for coda waves and S waves are similar to each other in the upper lithosphere and that they exhibit the same site effects. This observation provides evidence that the coda is produced by scattering of the direct S wave. It was suggested by Aki (1969) that because the scatterers are randomly distributed in the earth s crust and the fact that the later arriving coda waves have sampled a greater variety of heterogeneities than the earlier coda, the coda can be analyzed using statistical methods. Frankel and Wennerberg (1987) stated that the single scattering model does not properly describe the gradual coda amplitude decay but rather overestimates it; instead of 4
gradually decaying they argued that coda amplitude rapidly decays for scattering attenuation Q 150. Pulli (1984) measured seismic-wave attenuation in New England and concluded that for short and long lapse times the coda-wave Q is equal to 400-1300 and 660-1500, respectively, which is consistent with a weak scattering process. Because New England Q values are much higher than 150, Pulli (1984) concluded that codaamplitude decay is in fact gradual and can be modeled by the single scattering theory. Gao et al. (1983) agreed that the single scattering model can be used to describe coda waves at short lapse times. They proposed that at longer lapse times the coda waves scatter twice or three times before reaching the receiver. Gao et al. (1983) tested this idea using a curve-fitting technique in a simulation in 2-D and 3-D random media. They used the multiple scattering model to explain coda waves appearing at long lapse times, where the dominant period of the coda waves lengthens. This model suggests that coda-wave amplitude measurements taken at short lapse times will have a different rate of amplitude decay than the coda-wave amplitude measurements taken at long lapse times. The diffusion model proposed by Wesley (1965) describes the seismograms of an event within 1000 km of a seismic source. Wesley (1965) proposed that pulses radiating from a source encounter interfaces where many ray paths are created by reflections and refractions, and the process can be characterized as diffusive. Very strong scattering is required for diffusion to take place and such a mechanism has been invoked to describe lunar seismograms (Dainty and Toksöz, 1981). The Moon has strong velocity gradients, causing the strong scattering to occur, while the Earth lacks such strong scattering. Because of the lack of such strong scattering the model of diffusion does not characterize 5
seismograms from the Earth and thus cannot describe the nature of coda decay in New England. For this thesis, I use the Biswas and Aki (1984) method of calculating the seismic moment of an earthquake. This method is based on the single scattering model, which Pulli (1984) showed to be consistent with the coda waves recorded for northeastern United States earthquakes. After discussing how the measurements of coda waves from northeastern United States events are analyzed in this study, I demonstrate in Chapter 7 that my data are consistent with the single scattering model. 6
3. The New England Seismic Network The seismic activity in New England is monitored by Weston Observatory of Boston College. The recorded earthquakes are widely dispersed throughout the northeastern North America, as seen in Figure 2, and probably are a result of intraplate tectonics in which stress released is due to the reactivation of ancient fault zones (Taylor and Toksöz, 1979; Ebel and Kafka, 1991). The earthquakes analyzed in this coda wave study were recorded at stations distributed throughout the northeastern United States and operated by the Weston Observatory. Several times over the years the New England Seismic Network has upgraded its network system with newer instruments and better technology, often while increasing the number of its seismic stations. Details of the different stages of the network evolution are listed in Table 1. 3.1 The An 1 and An 2 Seismic Systems The earliest recorded earthquakes analyzed in this research occurred in 1938 and were recorded on Weston Observatory s single seismic station at that time. This threecomponent continuously recording seismic station, located in Weston, Massachusetts at the Weston Observatory, proceeded to record events on photographic paper until 1962. This station was an analog system, which I have named An 1. In 1963 this system was replaced by a new analog system called here An 2. The An 2 station consisted of instrumentation that was continuously recording three-components of both short-period and long-period seismic signals. This single station was part of the WWSSN system and is also located at Weston Observatory. The An 2 system recorded on photographic paper until 1988, when the photographic paper recorders were replaced by heat sensitive paper 7
recorders; An 2 is presently operating and is maintained by Weston Observatory of Boston College. 3.2 The An 3 Seismic System The An 3 NESN network was established in 1974 with two stations, WES and BNH, and increased to ten stations in 1975 (Ebel, 1985). By 1979 the network consisted of thirty-six seismographic stations, as shown in Figure 3, sited throughout New England (Ebel, 1985). The opening date and location details of the thirty-six stations are listed in Table 2. In August of 1982 the six Dickey stations in Maine (D1A, D2A, D3A, D4A, D5A, and D6A) were closed. The An 3 system initially used one-second period Benioff geophones and recorded three components of ground motion. All ground motion analog data were continually transmitted to Weston Observatory by telephone telemetry (Ebel, 1985), and recorded on 16 mm Develocorder film with a galvanometer of 16 Hz natural frequency. By 1976 the An 3 stations were changed to vertical-component, one-second period HS-10 seismometers, and the analog seismic data were sent by FM telephone telemetry, except for PQ0 and PQ1, for which analog seismic data were sent by radio to a relay station where the data were converted to telephone telemetry (Ebel, 1985). The station gains and the average amplitude response curve for the An 3 system are given in Appendix A and Appendix B respectively. 3.3 The Ds 1 Seismic System In 1986 and 1987 the thirty stations in the An 3 seismographic system were incorporated into a digital recording system. This digital system, which overlapped in 8
time with and eventually replaced the An 3 system, is named here Ds 1. The station locations of the Ds 1 system are shown in Figure 3, although the Dickey stations in Figure 3 had been removed before Ds 1 became operational. The Ds 1 system replaced the analog An 3 develocorders with a microcomputer for recording the data. The seismic data acquisition software, analysis system, and hardware were designed by Edward Johnson of Weston Observatory. TECMAR computers were in operation with the Ds 1 system, digitizing at 50 Hz with an antialias corner frequency at 12.5 Hz. The digital seismic data had maximum amplitude of + or - 2,048 counts. The Ds 1 station gains are listed in Appendix A and the amplitude response of the system is shown in Appendix C. 3.4 The Ds MIM Seismic System The Ds 1 system was accompanied in its last year of operation in 1994 by an improved on-line digital recording station named Ds MIM in Milo, Maine. The Ds MIM station location details are listed in Table 3. The Ds MIM station was equipped with a 1 Hz HS-10 seismometer (Edward Johnson, personal communication). The digital data acquisition, analysis software, and RD3 digitizer (100 Hz) were provided by Nanometrics, Inc. In 1999 the HS-10 seismometer was replaced with a Guralp CMG-40T seismometer. In 2000 the station was closed. 9
3.5 The Ds 2 Seismic System In 1994 the regional Ds 1 system s stations were dismantled, and Weston Observatory began the installation of a more modernized on-line digital network called here Ds 2. The Ds 2 network is currently the system in use for regional monitoring of earthquake activity by Weston Observatory. The station location details of the Ds 2 network are listed in Table 3. The station location details of the two stations recently added to the Ds 2 network since the start of this thesis are listed in Table 4. The Ds 2 network station locations are shown in Figure 4. Each Ds 2 station is supplied with a broadband Guralp CMG-40T seismometer, a Nanometrics RD3 digitizer (100Hz), and Nanometrics data acquisition and analysis software. All stations in the Ds 2 network record with the same gain setting. 10
4. Background The magnitudes of small local and small regional events occurring in the northeastern United States, recorded on the Weston Observatory regional seismic network in New England (NESN), have already been routinely measured by employing amplitude measurements of the Lg wave and/or the duration of the coda waves. These magnitude scales are summarized in the following sections. 4.1 M N Scale The first magnitude scale used when the An 3 seismic network opened in 1974 was the m blg Nuttli (1973) magnitude scale, applied in the northeastern United States by measuring the largest Lg wave and dividing it by the period of the signal for waves of period between 0.04 seconds and 1.0 seconds. Ebel (1987) produced a report assigning Nuttli (1973) M N and Rosario (1979) M c values to events recorded from 1938 1975. The m Lg (f) magnitude scale of Herrmann and Kijko (1983) was adjusted for use with northeastern North American events by Ebel (1994) and has been used to obtain magnitudes for the Ds 2 system since 1994. Both the m blg and m Lg (f) scales use the largest amplitude of the Lg wave in their respective formula and are assigned an M N designation in the Weston Observatory earthquake catalogs. Because the An 3 system had dynamic range limitations, the Lg amplitudes of very large events with small epicentral distances were clipped, thus not allowing an M N determination. Another shortcoming of the M N magnitude determinations of Weston Observatory is that they do not correlate very well to the Canadian Geological Survey M N values 11
(Ebel, 1994). Even though the Ebel (1994) magnitude scale was calibrated to m b and corrects for the Lg attenuation of the local area, it is not necessarily representative of M. The M N scale tends to be measured at high frequencies (2-10 Hz), so it may not be representative of the low frequency seismic moment for many events. 4.2 M c Scale The M c magnitude scale, developed for the NESN by Rosario (1979), is also one of the standard magnitude scales used for northeastern United States events. It is a scale which is based on the total duration of the earthquake coda waves on a seismogram. The M c scale can be used to determine event size by measuring the total duration of an event, the time from the origin of the event to the time when the coda ends, even when other seismic wave phases such as the Lg wave are clipped on the seismic trace. It is often easier to make measurements of coda duration on quiet days because background noise and/or aftershocks can make it difficult or even impossible to estimate accurately the coda duration of an event, thus leading to inaccurate M c measurements. In several cases, signals of aftershocks appear during a previous event s seismic signal. Because of this, the end of the prior event s coda was hidden by the aftershock s seismic signal, so a proper coda-magnitude determination could not be made. Another limitation to using this magnitude scale for the Ds 1 system was that background noise on this digital system typically had an amplitude of 2-3 bits. This distorted the background noise but was done to enhance the dynamic range of the earthquake signals. The problem with this type of recording is that at the end of the coda, the coda amplitudes, like the background 12
noise, are distorted. This combination produces an artificially low signal-to-noise ratio, and a good measure of where the coda ended is difficult to obtain. 4.3 M Scale The method of moment-magnitude determination used in this thesis is a method based on an estimate of M o. High frequency waves attenuate faster with distance traveled than low frequency waves, and because the predominant period of coda waves naturally increases with lapse time, the coda waves act as a low-pass filtered version of the seismic radiation, especially the late coda waves. This property of coda waves makes them a favorable method for M determinations. Previous seismic moment determinations for large earthquakes in northeastern North America have been determined using the amplitudes of body and surface waves recorded on available seismograms (e.g., Ebel et al., 1986). Ebel et al. (1986) compared their amplitude measurements to those of synthetic seismograms computed with known source parameters in order to determine a seismic moment. This technique employs surface and body waves at teleseismic distances; therefore the Ebel et al. (1986) method for finding seismic moment can only be applied to the rare, large (M 5.0) earthquakes in the region. The moment-magnitude determination method made from coda amplitude measurements described in this thesis can be applied to small earthquakes, is rapid and accurate, and can give a robust determination of the moment magnitudes. The other advantage to using the proposed technique to determine moment magnitude is the fact that the low-frequency coda waves, detected long after the S/Lg wave train, are easily 13
measured on the paper and film records, where the analog data are not digitized, as well as on digital seismograms. Therefore, the method of moment-magnitude determination implemented in this thesis can be applied to the entire variety of instrument types that have been used for earthquake monitoring by Weston Observatory. The coda amplitude measurements of small events, which are taken long after the S/Lg wave train, must have longer periods than the event corner period. As long as coda measurements are taken at a lower frequency than the source corner frequency, then in theory the seismic moment of an earthquake can be determined. Boatwright (1994) published information on the source parameters of a number of northeastern United States earthquakes where he listed the corner frequencies of those events. From the list of Boatwright (1994) it is clear that the majority of events analyzed in this thesis had corner frequencies higher than 3 Hz, i.e. higher than the frequencies of the coda waves measured in this study. The coda waves are recorded at frequencies smaller than the event corner frequency, meaning that moment magnitudes for events of all sizes can be properly determined. 14
5. Research Methods In this study I compute a moment-magnitude M based earthquake catalog for the northeastern United States. Calculation of M for the 425 northeastern United States earthquakes in this study is accomplished using the Biswas and Aki (1984) approach. Biswas and Aki (1984) made measurements of coda waves amplitudes from Alaskan events with known M o values to develop a formula to calculate seismic moments of all small events occurring in Alaska. In this research, I use the same method as that of Biswas and Aki (1984), but I modify their moment formula for application in the northeastern United States. One or more events with a known seismic moment are needed to calibrate the Biswas and Aki (1984) method. The more events used, the more robust the calibration. Biswas and Aki (1984) made measurements of peak-to-peak coda amplitude as a function of lapse time on vertical-component seismograms for two events with known seismic moments which occurred in Alaska. With these data, they developed the following formula for the Alaska network: log 10 (M o ) = log 10 (A) + 3.85 log 10 (t) + 12.0 (1) with M o = seismic moment (dyne-cm), A = peak-to-peak coda wave amplitude (mm) from the Alaskan station, and t = lapse time of about 100 < t < 1000 sec after the origin time of the event. The Biswas and Aki (1984) formula can be broken down in order to isolate the controlling variables to be altered for application to a different region: log (M o ) = log (A) + X log (t) + C (2) log (A) = log (M o ) X log (t) C (3) 15
log (A) = -X log (t) + K (4) where K = y-intercept of the coda amplitude decay line on a log-log plot of amplitude versus time, X = slope of the coda amplitude decay line on a log-log plot of amplitude versus time, and C = log (M o ) K (5) In order to apply the Biswas and Aki (1984) method to the northeastern United States the constants X, K, and C for the above equations must be calculated by measuring amplitudes of the envelope of the coda-wave waves from recorded New England events as a function of lapse time on vertical-component seismograms. Different instrumentation has different operating characteristics, and as a result of the various seismic system instrumentation types and characteristics, the method of momentmagnitude determination described above must be rederived and applied individually to the observations from each form of recording of Weston Observatory and NESN stations. Due to low signal-to-noise ratios or weak signals, I could not make measurements for all northeastern United States events on all of the network stations. I began my research project by measuring peak coda amplitudes and corresponding lapse times on vertical-component seismograms recorded on each of Weston Observatory s seismic systems. Next I plotted the coda wave amplitude measurements as a function of lapse time. From these coda-wave amplitude versus lapse time plots, I calculated the slopes of the coda amplitude decay and then computed a mean coda amplitude decay slope X for each seismic system. For the calculation of the constant C I researched to identify published calculated seismic moments of northeastern United States events. Those are listed in Table 5. I 16
made measurements of coda amplitude as a function of lapse time for these events with know seismic moment, plotted the coda amplitude measurements versus lapse time, and calculated their y-intercepts K based on a least squares fit. Using Equation (5) with the known seismic moments and their respective y-intercepts K, I calculated the mean constant C. Lastly, I calibrated Equation (2) for each type of Weston Observatory seismic system by inserting the calculated constants X and C, listed in Table 6, into Equation (2). The equations I devised by this method for each seismic system are the formulas for computing seismic moment from coda waves for the Weston Observatory and NESN data. Using the definition of moment magnitude: M w = 2 / 3 logm o - 10.7 (Hanks and Kanamori, 1979), I calculated moment magnitude down to M 3 for all earthquakes in the northeastern United States earthquake catalog. 17
6. Data Analysis 6.1 The Measurement of Coda Waves Rautian and Khalturin (1978) define the time where the coda begins as being twice the S wave traveltime and the end of the coda as the time when the signal-to-noise ratio equals about 1. I viewed the coda wave by looking at the seismogram of the event to be analyzed and moved my focus slowly forward past the event s arrival and past twice the S wave traveltime. I then continued to move my focus along the seismogram until I passed the coda wave and saw evidence of background noise where the coda was no longer visible. I would then reverse direction and note where the coda wave became visible above the background noise. Measurements of the coda wave were then taken at times before this visually determined end of the coda wave. I applied this procedure to seismograms from all systems of recording. It was not easy to make coda amplitude measurements for some stations or some events. Small events, with large epicentral distances to the stations, as well as cases of bursts of high-amplitude background noise, such as noise from vehicles driving by the stations, caused seismic traces to have low signal-to-noise ratios. Noise visible within the seismic signals is due to low frequency microseisms, high frequency noise from footsteps, and high frequency noise from construction activity, wind, vehicular traffic, etc. In these situations the window where the coda wave measurements could be made, (from twice the S wave time to the time that the coda has a signal-to-noise ratio of 1) was small or even non-existent, making coda amplitude measurements hard or impossible to make. 18
After analyzing the majority of the earthquakes in this study I found that for events smaller than 2.5 M N and 2.5 M c, on all forms of recording systems, there were few or no station observations where the coda waveforms allowed amplitude measurements within the time and amplitude criteria, set out by Rautian and Khalturin (1978). Thus, only events larger than 2.5 M N and 2.5 M c were analyzed to determine moment-magnitudes for this study. 6.2 An 1 and An 2 System Data Analysis When analyzing the An 1 photographic paper recordings and the An 2 photographic and heat sensitive paper recordings, I measured peak-to-peak coda amplitudes with a ruler and a magnifying eyepiece. A few of the events recorded by An 1 and An 2 could not be analyzed because their paper records were missing from Weston Observatory s archives. Some of the paper recordings of the earthquakes of northeastern United States were dim or had faded over the years. In these cases, the seismic traces were blurred and unable to be clearly viewed and analyzed. 6.3 An 3 System Data Analysis Coda amplitude measurements for events recorded with the An 3 system were made with a ruler directly on the develocorder film instrument display screen. The seismograms from a number of stations of the An 3 system were recorded simultaneously and very closely to one another on the same daily reel of film. When large earthquakes occurred, the stations with high gain settings recorded large amplitude seismic signals, causing the seismic traces to overlap one another on the film. Thus, I had difficulty 19
measuring the coda amplitudes of some of the large events on the high gain stations due to the overlapping of the traces. Because each station in the An 3 system utilized a different gain due to varying site background noise, all measured amplitude values for the An 3 system were reduced to the same gain setting by incorporating a station-specific gain correction into their respective moment magnitude formulas. A list of the specific station gains for the An 3 system is given in Appendix A. The gain correction is made by dividing each coda amplitude measurement by the total gain. The total gain (G) is calculated using the following equation: G = gain x (amplitude response to ground displacement) (6) For the An 3 system, the amplitude response was calculated by taking the period of the coda, (measuring the time from one coda-wave peak to the next coda-wave peak) from the seismograms of each event and extracting an amplitude response to ground displacement from the frequency response curve, shown in Appendix B. The momentmagnitude formula for the An 3 system is thus modified to: log 10 (M o ) = log 10 (A/G) + X log 10 (t) + C (7) where M o = seismic moment (dyne-cm), A = peak coda wave amplitude (mm), G = total gain derived in Equation (6), X = slope of the coda amplitude decay line for the plot of amplitude versus time, t = lapse time (sec) after the origin of the event, and C = log (M o ) K, where K = y-intercept of the coda amplitude decay line for the plot of amplitude versus lapse time. 20
6.4 Ds 1 System Data Analysis The coda amplitude measurements for events recorded with the Ds 1 system were made by placing a digital crosshair on the coda amplitudes of the archived seismograms that were digitally displayed on a computer screen. After taking Ds 1 coda amplitude measurements, all measured amplitude values for the Ds 1 system were reduced to the same gain setting. Each of the Ds 1 system s stations utilized a different gain setting due to varying site background noise. Therefore, I incorporated a station-specific gain correction into the moment-magnitude formula for each individual Ds 1 station by the same method described above for the An 3 system. A list of the specific station gains for the Ds 1 system is listed in Appendix A. The frequency response curve for the Ds 1 system used to calculate the amplitude response to ground displacement is shown in Appendix C. The modified moment-magnitude formula for the Ds 1 system is represented by Equation (7). Not every event recorded by the Ds 1 system could be analyzed to determine its moment-magnitude. The Ds 1 digital system had the disadvantage of having limited recording space. Thus, the seismograms of the very large northeastern United States events were cut off right after the initial arrival of the S wave, and the rest of the event after the S wave arrival was not recorded. For this reason I could not make M o determinations of these very large events recorded during the operation of the Ds 1 system. 21
6.5 Ds MIM and Ds 2 System Data Analysis I viewed and analyzed the seismograms of the events recorded with the Ds MIM and Ds 2 systems on a PC computer with an OS/2 operating system using a digital seismic analysis program written by Nanometrics, Inc. Amplitude measurements were made after twice the S wave arrival time, as seen in Figure 1, and further along the coda wave decay train until the coda was no longer visible above the background noise. Short-duration, regular amplitude high-frequency pulses occur every 0.5 sec on the BRY station seismograms and can be viewed in Figure 5. These noise pulses are generated by the instrument at the BRY site, but it is not completely understood what component in the instrument is generating this noise. For this station, and for occasions when high frequency noise is evident in the signal causing the low frequency coda waves to be hidden, a 3-Hz low-pass filter was applied before the coda amplitude measurements were made. The 3-Hz low-pass filter applied to the seismogram enables the low frequency coda waves to be observed while eliminating the high frequency noise pulses. The coda amplitude energy of an event must be larger than the background noise as well as having a high signal-to-noise ratio below the corner frequency of the event for coda amplitude measurements to be made for the determination of moment magnitude. A spectrum of the coda wave and background noise of the 6/16/95 Lisbon, NH event (shown in Figure 1), recorded on the New England Seismic Network station MIM, is displayed in Figure 6. This spectrum shows that at frequencies below the event s corner frequency of 7 Hz, there is more energy in the seismic signal than the background noise. 22
Therefore, a low-pass filter of 7 Hz was often administered to remove any high frequency noise. As discussed in Section 3.3 of this thesis, Boatwright (1994) demonstrated that the corner frequencies of northeastern United States events he studied were above 3 Hz. The coda amplitudes of an event must be below the corner frequency for coda amplitude measurements to be made. However, for seismograms containing very low frequency noise due to low frequency microseisms or instrumental instabilities disturbing the coda wave train, a high-pass filter was deemed necessary. In the case of microseisms, of which in many occasions I measured to have 6 sec periods, a high-pass 6-pole Butterworth filter with a corner of 0.2 Hz was applied to the seismogram. Since the corner frequency of the majority of northeastern United States earthquakes is above 3 Hz, the 0.2 Hz high-pass filter can filter out the low frequency noise yet preserve enough of the low frequency coda wave to be analyzed. 23
7. Results 7.1 Determination of X for Each System The average coda decay slopes resulting from the coda amplitude measurements plotted as a function of lapse time for the events recorded by each of Weston Observatory s various instruments were calculated after fitting the data with a least squares fit. The average coda decay slopes are presented in Figures 7 a,b,c,d,e, and f. The events are of varied magnitude and depth and the recordings are at various epicentral distances (ranging from 20 to 1000 km). The coda decay slopes from each type of instrument for all the earthquakes analyzed in this study are almost all approximately parallel to each other respectively, as seen in these figures, even though the events are of varying size. This demonstrates that the coda decay is independent of magnitude for the magnitude range I analyzed. When analyzing the traces of a local event recorded at different NESN stations with epicentral distances between 100 km and 362.3 km, as seen in Figure 8, it is observed that they exhibit nearly identical coda amplitude decay, and thus coda amplitude measurements can be made without correcting for epicentral distance. After plotting the coda amplitude measurements verse lapse time separately for each station of Weston Observatory s Ds 2 system, shown in Figure 9, I observed that the coda wave of a particular event has a similar amplitude measurement at a particular time following the origin time of the earthquake at each network station, even though the stations are of varying epicentral distance. I measured coda wave amplitudes of northeastern United States events with epicentral distances even farther than 632.8 km 24
and found that this observation still holds true. In view of similar observations, Aki (1969) concluded that the power spectral amplitude of coda waves at a given time after the origin time of an event seems to be nearly independent of the epicentral distance and is therefore not very sensitive to path effects. This is important because it means coda wave amplitudes may be measured for the determination of moment-magnitude due to the fact that the coda wave is not altered by path effects and varying epicentral distances. 7.2 Testing Scattering Theories with the NESN Data After I measured the coda wave amplitudes from the northeastern United States events for this study and plotted the log of amplitude versus the log of lapse time, I compared the results with what would be expected from theories describing the coda wave generation models summarized in Chapter 2. I observed a straight line for the decay of the coda wave amplitude with time. This result agrees with the single scattering theory, which describes the coda amplitude decay rate as being constant from short lapse times to long lapse times. Thus, I chose to follow the formulation of the single scattering model. The multiple scattering theory describes the coda as having a different rate of decay at short lapse times than at long lapse times. In this study, if the coda amplitude measurements with long lapse times had a different slope X than coda amplitude measurements with short lapse times, then a modified Biswas and Aki (1984) moment magnitude formula for the northeastern United States would have to be broken down into two separate equations, one for coda amplitudes measured at short lapse times (<100sec) and one for coda amplitude measured at long lapse times (>100sec). However, the coda 25
wave amplitude decay in this study is found to have a constant linear decay for short lapses time as well as long lapse times, and the results do not deviate from the line regardless of lapse time. Therefore, the multiple scattering theory is not needed to describe the observed coda waves for the northeastern United States earthquakes analyzed in this study. In Figure 10 three events containing coda amplitude measurements with varying lapse times of <100sec, >100sec, and >400sec are plotted. Since the events have very similar slopes of coda amplitude decay and do not exhibit variations as a function of event magnitude or lapse time, only one moment magnitude formula needs to be developed for coda amplitude measurements made at all lapse times. In Figure 11, the 1/17/00 ME event is plotted, for which coda amplitude measurements at both short lapse times and long lapse times were made. As shown in Figure 11, the short lapse time coda amplitude decay equation: y = -2.89x + 9.12 (8) and long lapse time coda amplitude decay equation: y = -3.06x + 9.54 (9) are very close to each other. Because a significant difference in coda amplitude decay between short lapse time and long lapse time measurements from the same event is not evident, I did not find it necessary to calculate separate moment magnitude formulas. Dainty and Toksöz (1981) stated that the ratio of attenuation distance, defined as the average distance the seismic energy travels before being attenuated by 1/e, is the deciding factor for determining when to use the single scattering method versus the multiple scattering method. Dainty and Toksöz (1981) explain that if the ratio of 26
attenuation distance to the mean free path is equal to or less than one, then the single scattering method applies, but if the ratio of attenuation distance to the mean free path is greater than one, then the multiple scattering method applies. Pulli (1984) studied the attenuation of coda waves in New England and found that for his data set, comprised of New England earthquakes, the ratio of attenuation distance to the mean free path is about equal to one for all cases. Thus, Pulli (1984) applied the single scattering method to the formation of coda waves in New England and described the effects of multiple scattering as being minimal for his data set. The earthquake data set in this study is comprised also of earthquakes from the northeastern United States thus the single scattering method may also be applied to model the formation of the coda wave in this study. 7.3 Uncertainty in M Determinations The Biswas and Aki (1984) M formula was modified for each of Weston Observatory s NESN recording instruments. This is because the manner of measuring coda amplitude was different for each recording instrument due to the fact that the different instruments operate using different recording systems. The moment-magnitude formula described by Equation (2) was modified for each recording type by inserting the average slope, calculated from the data in Figures 7a,b,c,d,e, and f, respectively, and the constant C, calculated using the data analysis techniques described earlier in Chapter 6 of this thesis. The adjusted moment-magnitude formulas for use with the NESN data for northeastern United States events are listed in Table 7. After determining the moment-magnitude formulas, M calculations were made for all northeastern United States events for which coda wave amplitudes were measured. 27
Examples of the data analysis made from each recording instrument are given in Table 8. The final moment-magnitude based earthquake catalog for the northeastern United States is listed in Table 9. In order to quantify the uncertainties in my M values, I calculated from the set of station M values the difference between M and M w for those events that I analyzed that have known M w values, as listed in Table 5. The results are listed in Table 10. The M w and M values are closely comparable to one another with a minimum difference of 0.0, both magnitudes being equal to each other, and a maximum difference of 1.1 magnitude units. The only bias observed in the comparison of M w and M in Table 10 is that M may break down at magnitudes 5.5. This observation is only evident from An 1 because An 1 is the only system which recorded such large local events. Due to the insufficient amount of large magnitude earthquakes in the northeastern United States it is difficult to analyze this relationship between M w and M any further. If a large event 5.5 were to occur and the Ds 2 system were to record it, then the accuracy of M for larger events could be investigated more thoroughly. During 1987, Weston Observatory was in a transition stage, changing its analog system (An 3 ) to a digital system (Ds 1 ). Therefore, the two systems were recording events simultaneously. I compared the moment-magnitude determinations of the 1987 events recorded on the An 3 system to the moment-magnitude determinations of the same events recorded by the Ds 1 system. I observed that the calculated moment-magnitudes of three of the events recorded on both systems have a 0.1 difference in the M determinations, and one has a 0.3 difference in the M values. This observation is presented in Table 11. 28
Neither of the systems had values consistently larger or smaller than the other despite the different operating mechanisms and the different ways of coda amplitude measurement. I conclude that the results of both the An 3 and Ds 1 systems have the same accuracy. 7.4 Comparison of M with M N and M c Determinations for Analog Data With the M values calculated for events in Table 9, I made correlation plots between M and M N as well as between M and M c. The comparisons between the new moment-magnitude results and the corresponding M N magnitudes, calculated by Weston Observatory, for all the various recording instruments are plotted in Figure 12a. The comparisons between the new moment-magnitude results and the corresponding M c magnitudes, calculated by Weston Observatory, for all the various recording instruments are plotted in Figure 12b. The calculated values of M for the An 1 system are on average slightly smaller than their corresponding M N values, as seen in Figure 12a. The calculated values of M for the An 1 system are quite closely matched to their corresponding M c values, as seen in Figure 12b. The An 1 M versus M N plot in Figure 12a is very similar to the An 1 M versus M c plot in Figure 12b, which concurs with Ebel s (1985) observation that M N and M c values were calibrated well against each other with a difference of only 0.2 magnitude units. However during the years of 1938 1962, M N values and their corresponding M c values had a large degree of inconsistency at magnitudes of M N < 2.5. The events represented by the triangles in Figure 12b for An 1 have M c magnitudes 2.2 and actually have corresponding M N magnitudes > 2.5. Therefore, M seems on average to be larger 29
than the M c magnitudes for events with magnitudes 2.2. Any inconsistencies here are probably due to the difficulty in measuring coda durations on analog records when background noise causes low signal-to-noise ratios. Because coda duration is a function of background noise, low signal-to-noise ratios do not allow for accurate measurements to be made. The correlation between M and M N as well as the correlation between M and M c for the An 2 system observed in Figure 12a and Figure 12b show, for magnitudes 3.8, that M is systematically larger for both magnitude scales. However, the M values of the events with known M w recorded on An 2 are almost equivalent to their corresponding M w values. This may mean that measurements of Lg peaks and coda durations for the calculation of M N and M c were inaccurately made, perhaps due to low signal-to-noise ratios. The An 3 correlation plots for M vs. M N and for M vs. M c are also displayed in Figures 12a and 12b, respectively. For M N 2.6, accurate coda amplitude measurements were very difficult to make due to low signal-to-noise ratios. Therefore, as observed in the An 3 plot in Figure 12a, there is a degree of inconsistency between the M and M N scale for earthquakes of M N 2.6. The relationship calculated from Figure 12a for 2.5 M N 3.9 recorded on the An 3 system is represented by the equation: M = 0.89M N + 0.37 (10) where M = coda moment magnitude developed in this study and M N = m blg, where m blg is the Nuttli (1973) magnitude. Atkinson (1993) estimated M values from catalog values of M N and defines the relationship well for 3 M N < 6 : 30