The Effects of Geodetic Configuration of the Network in Deformation Analysis

Transcription

1 The Effects of Geodetc Confguraton of the Network n Deformaton Analyss M. Onur KAPLAN, Tevfk AYAN and Serdar EROL Turkey Key words: Network confguraton, deformaton analyss, optmzaton, confdence ellpses SUMMARY The optmzaton and desgn of montorng scheme should precede the feld observaton and analyss procedures. Optmzed montorng schemes ensure the detecton of predcted deformatons accordng to a selected tolerance crteron. In ths study, the effects of confguraton of Gerede mcro geodetc network n deformaton analyss were researched. In ths network, at frst the deformaton analyss has been carred out wth respect to the results obtaned through the drecton and dstance measurements made n 1983, and Then, measurement plans n two epochs were optmzed. Accordng to the optmzed measurement plan deformaton analyss has been carred out. Fnally, deformaton analyss results, whch were obtaned after optmzaton of measurement plan were compared and nterpreted wth the results that were obtaned before optmzaton of measurement plans. 1/15

2 The Effects of Geodetc Confguraton of the Network n Deformaton Analyss M. Onur KAPLAN, Tevfk AYAN and Serdar EROL Turkey 1. INTRODUCTION The am of deformaton analyss s the detecton; localzaton and modellng of pont movements n multply measured networks. Such an analyss provdes valuable nformaton about the deformatons of physcal and man-made objects on the earth surface. In the deformaton studes, geodetc observatons are repeated at dfferent epochs of tme. The observatons of each epoch are adjusted ndependently. From coordnate dfferences between the epochs, the parameters of the deformaton model are estmated and conclusons on the object deformatons are drawn. The word optmzaton has recently come nto use n geodesy to ndcate desgnng networks based on well-specfed quanttatve consderatons and technques; t suggests plannng for the best soluton. Snce desgn of deformaton networks has major sgnfcance to determne deformaton, the geodetc networks must have optmal desgn. An optmzed montorng scheme ensure the most economc feld campagn, and t helps n dentfyng, elmnatng, or mnmzng the effects of the gross and systematc errors exstng n the observaton data pror to the estmaton of the deformaton parameters n order to avod msnterpretng measurng errors as deformaton phenomena. In ths study, the effects of confguraton of Gerede mcro geodetc network n deformaton analyss were researched. The subject area s located on a fault lne near Gerede around The North Anatolan Fault Zone (NAFZ) n Turkey. The network establshed for the detecton of possble crustal movements n the area coverng 4.2 km 2 conssts of 8 ponts. In ths network, at frst the deformaton analyss has been carred out wth respect to the results obtaned through the drecton and dstance measurements made n 1983, and The deformaton analyss method appled n ths study s called deformaton analyss wth relatve confdence ellpses. Horzontal movements on the deformaton ponts were determned regardng 95% statstcal confdences. Then, the measurement plans n two epochs were optmzed. In ths optmzaton problem, some measurements were out of from the measurements plan. Ths procedure was repeated untl a satsfactory network confguraton was found. Accordng to the optmzed measurement plans, deformaton analyss has been carred out. Fnally, deformaton analyss results, whch were obtaned after optmzaton of montorng schemes, were compared and nterpreted wth the results that were obtaned before optmzaton of measurement plans. 2. OPTIMIZATION OF GEODETIC NETWORK The proper and optmal desgn and subsequent assessment of geodetc network s an ntegral part of most surveyng engneerng projects. Optmzaton and desgn are carred out before 2/15

3 the measurements are actually made. The purpose of an optmal desgn s to solve for both the network confguraton and observatons accuracy n order to meet the desred crtera. Optmzaton means mnmzng or maxmzng an objectve functon whch represents the crtera adopted to defne the qualty of a network. Generally the qualty of a control network s characterzed by ts precson, relablty,strength, and economy (Seemkooe 2001). Dfferent optmzaton problems are usually classfed nto dfferent orders; Grafarend (1974) dentfes four orders of desgn: Zero-order desgn (ZOD): desgn of a referance system Frst-order desgn (FOD): desgn of the network confguraton Second-order desgn (SOD): selecton of the weghts for the network observatons Thrd-order desgn (TOD): addton of observatons to mprove an exstng network. There are two methods that can be used to solve the desgn problem, namely, analytcal method and tral and error method. In the tral and error method, a soluton to the desgn problem s postulated upon whch the desgn crtera are computed. If ether of these crtera were not satsfed, a new soluton s requred and the crtera functons are recomputed. The procedure s repeated untl a satsfactory network s found. In contrast, the analytcal method offers specfc algorthms for the soluton of partcular desgn problems, whch do not requre human nterventon. The term analytcal desgn s used to descrbe a method that solves a partcular desgn problem by a unque seres of mathematcal steps (Kuang 1991). In deformaton analyss,the optmal desgn of network and optmzaton of measurement plan play crucal role. Objectves of the optmzaton of a deformaton network are: To meet a predetermned accuracy goal To establsh a self-checkng and relable mathematcal model To yeld suffcent sensvty n respect to certan a pror known functons of the parameters To desgn an observaton plan whch s feasble under pratcal and fnancal constrants. In ths study, the frst measurement plan was optmazed accordng to am functon. As the am functon, t was researched the geometry that respond both the mathematcal-statstcal test and the frst deformaton values n deformaton ponts. Therefore, the test statstc was d T = T Q 2σ 1 d 2 0 d (1) selected as the am functon. The measurement plan that has mnor mpact on test statstc was researched. Durng ths procedure, the geometry of the control network was not changed. In ths procedure, frstly the measurement that had the least effect on test statstc was out of the measurement plan. After detectng the frst redundant measurement, the second redundant measurement was researched. Ths procedure contnued teratvely untl a satsfactory 3/15

4 network confguraton- respond to the frst deformaton greatness n deformaton ponts- was obtaned. In the end, accordng to the last measurement plan, deformaton analyss was done. 3. DEFORMATION ANALYSIS Any object, natural or man-made, undergoes changes n space and tme. Deformaton refers to the changes a deformable body undergoes n t s shape, dmenson, and poston. Snce the results of deformaton surveys are drectly relevant to the safety of human lfe and engneerng surveyng, recently deformaton analyss has become more mportant. In general, the deformaton analyss s managed n three steps n geodetc networks. In the frst step, the measurements that were carred out n t 1 and t 2 measurement epochs are adjusted separately, accordng to free adjustment method; outlers and systematc errors are detected and elmnated n ths step. In the second step, global test procedure s carred out and by ths test t s ensured that f the network pont, whch were assumed as stable, stayed actually stable n t = t 2 t 1 tme nterval or not. In here, n the global test, after the free adjustment calculatons of the networks separately, the combned free adjustment s appled both epoch measurements. Durng the combned free adjustment computaton, the poston of the assumed stable ponts, are gven as one sngle group of ponts for both epochs, on the other hand the postons of deformaton ponts n t 1 nstant are assumed as f one group of ponts and the postons n the t 2 nstant are assumed as another group of ponts. In addton to ths, n combned free adjustment, the partal-trace mnmum soluton s appled for the stable ponts (tr(q stable, stable ) = mn). After determnng a group of stable ponts as the results of global test, the deformaton ponts are handled one by one and t s nspected that f ther postons are changed or not (Ayan 1982; Ayan et al. 1991, Erol 2003). In ths study The Relatve Confdence Ellpses Method was appled. All the observatons n the two perods were adjusted together as free nets by takng as datum ponts, whch were assumed to be stable wth respect to each other. For ths process the datum pont coordnate unknowns were taken as a one-valued set, but the other ponts were consdered as a twovalued set, each value correspondng to each perod. The dfference vector between the coordnates estmated from the combned adjustment of the ponts P was wrtten as dy Y2 Y d = = (2) d X X x and wth the cofactor matrx Qd, the test statstc was T = d T Q 2σ 1 d 2 0 d, F 2,f; α ; f = n u + d (3) 4/15

5 2 Where, σ 0 was the estmated unt varance of the combned adjustment, f was the degree of freedom of ths adjustment, F 1 α;2,f freedom 2 and f n level of sgnfcance α. If T>F 2, f; α, the zero hypothess H o : E (d ) = 0 was rejected. Deformaton vectors were computed from s 2 2 d = dx + dy (4) and ther drectons were computed from dy α = arctg (5) dx Confdence ellpses can be drawn geometrcally usng the results of the zero-hypothess d = 0 (wth d = dx 2 + dy 2 as magntude of the dfference vector): frst drawng the dsplacement vector and then the confdence ellpse at ts top. If the dsplacement vector s not completely lyng n the confdence ellpse, the hypothess the pont has not moved s rejected. 4. NUMERICAL APPLICATION A sgnfcant part of Turkey s subjected to frequent and damagng earthquakes. Turkey s located on the relatvely small Anatolan plate and, whch s squeezed between three other major tectonc plates- the north movng Afrcan and Araban plates located to the south, and the south movng Eurasan plate located to the north. The combnaton of these plate movements s forcng the Anatolan plate to move west nto the Aegean Sea. Ths movement produces fault structures at the boundary between the plates, most sgnfcantly The North Anatolan Fault Zone (NAFZ). The NAFZ stretches 1500 km across Turkey and has been the source of eght earthquakes of magntude seven or greater n the last century. In ths study, the effects of confguraton of Gerede mcro geodetc network on deformaton analyss were researched. The subject area s located on a fault lne near Gerede around The North Anatolan Fault Zone (NAFZ) n Turkey. The network establshed for the detecton of possble crustal movements n the area coverng 4.2 km 2 conssts of 8 ponts. There are 23 dstances and 48 drectons measurement n Gerede mcro geodetc network. The measurements were carred out between 1983 and Before startng to optmze the frst measurement plan t was necessary to decde that: whch measurements nfluences are stronger n the network, dstances or drectons? For ths reason frstly two epoch measurements were adjusted through the free adjustment procedure accordng to the frst measurement plan. In the end, the adjusted coordnates have been obtaned. In ths study, from now on these free adjusted coordnates that were carred off 5/15

6 accordng to the frst measurement plan are called: adjusted coordnates group one (ACG1). Fgure 1: Confguraton of the mcro geodetc network n Gerede After these computatons, alternately dstance measurements were out of from the frst measurement plan. Accordng to the new measurement plans, control network was adjusted. The adjusted coordnates, whch were obtaned accordng to the new measurement plans are called from now on: adjusted coordnates group two (ACG2). The computatons that were explaned above for dstance measurements were done agan for drecton measurements. Ths tme the dstance measurements stayed steady, and changes were done n drecton measurements n the frst measurement plan. In the end adjusted coordnates were obtaned. These coordnates are called: adjusted coordnates group three (ACG3). Fnally, the dfferences both ACG1-ACG2 and ACG1-ACG3 were researched. Dfferences both ACG1-ACG2 and ACG1-ACG3 are gven n Table 1, Table 2, Table 3 and Table4. Table 1: Adjusted coordnate dfferences when 1-3 Table 2: Adjusted coordnate dfferences dstance measurement s out of from when 4-5 the frst measurement plan dstance measurement s out of from the frst measurement plan Compt ACG1-ACG2 ACG1-ACG2 PN. dy(mm) dx(mm) dy(mm) dx(mm) Compt ACG1-ACG2 ACG1-ACG2 PN. dy(mm) dx(mm) dy(mm) dx(mm) /15

7 Table 3: Adjusted coordnate dfferences when 1-3 drecton measurement s out of from the frst measurement plan. Compt ACG1-ACG3 ACG1-ACG3 PN. dy(mm) dx(mm) dy(mm) dx(mm) Table 4: Adjusted coordnate dfferences when 4-5 drecton measurement s out of from the frst measurement plan. Compt ACG1-ACG3 ACG1-ACG3 PN. dy(mm) dx(mm) dy(mm) dx(mm) In the lght of dfferences both ACG1-ACG2 and ACG1-ACG2 t was concluded that the effects of drecton measurements were stronger than the effects of dstance measurements n the control network. Hence, t was decded that drecton measurements had to be remaned n the observaton plan. In the end, by gettng out dstance measurements from the frst measurement plan, the frst measurements plan was optmzed. Before startng to optmze the measurement plan, the test statstc T d T Q 2σ 1 d 2 0 d = (6) was selected as the am functon and the measurement plan that had mnor mpact on test statstc was researched. For ths am, alternately dstance measurements were out of from the frst measurement plan. Accordng to new measurement plans free adjustment and analyss procedures were done. In the end of analyses, test statstc values were obtaned. These test statstc values were compared wth the frst statstc values that were obtaned accordng to the frst measurement plan. Fnally t was decded that 1-3, 1-4, 2-3, 4-5, 4-6, and 5-7 dstance measurements had lower effect n test statstc value. The results are gven n Table 5, Table 6, Table 7, Table 8, Table 9 and Table 10. 7/15

8 Table 5: Test statstc values when 1-3 dstance Table 6: Test statstc values when 1-4 dstance measurement s out of from the frst measurement s out of from the frst measurement plan. measurement plan. Compt. 13 Frst Stuaton Second Stuaton Crtcal Value Compt. 14 Frst Stuaton Second Stuaton Crtcal Value Table 7: Test statstc values when 2-3 Table 8: Test statstc values when 5-7 dstance measurement s out from dstance measurement s out from the frst measurement plan the frst measurement plan. Compt. 23 Frst Stuaton Second Stuaton Crtcal Value Compt. 57 Frst Stuaton Second Stuaton Crtcal Value Table 9: Test statstc values when 4-5 dstance Table 10: Test statstc values when 4-6 dstance measurement s out of from measurement s out of from the frst measurement plan the frst measurement plan. Compt. 45 Frst Stuaton Second Stuaton Crtcal Value Compt. 46 Frst Stuaton Second Stuaton Crtcal Value In respect of these results, t was tred to be out more than one dstance from the frst measurement plan at the same tme. For ths am, frstly three dstances; 1-3, 1-4, and 5-7 were out of from the frst measurement plan and deformaton analyss was done accordng to new measurement plan. The results of the new measurement plan n test statstc are gven n Table 11. Accordng to Table 11, t s sad that the nfluences of these three measurements n test statstc s nsgnfcant. Thus, these three measurements can be omtted from the frst measurement plan. 8/15

9 After ths computaton, four dstances; 1-3, 1-4, 2-3, and 5-7 were out of from the frst measurement plan. In addton to these computatons the effects of fve dstances n test statstc were researched. For ths am, fve dstances; 1-3, 1-4, 2-3, 5-7, and 4-5 were out of from the frst measurement plan. Fnally, all of these computatons were done for 1-3, 1-4, 2-3, 4-5, 5-7, and 4-6 dstance measurements. By ths computaton, the effects of these sx measurements n test statstc values n deformaton ponts were researched. In the end, deformaton analyss was done accordng to the last measurement plan. The effects of these changes n test statstc n deformaton ponts are gven n Table 12, Table 13 and Table 14. Table 11: Test statstc values when 1-3, 1-4 Table 12: Test statstc values when 1-3, and 5-7 dstance measurements are out and 2-3 dstance measurements are out of from the frst measurement plan of from the frst measurement plan Compt. 13/14/57 Frst Stuaton Second Stuaton Crtcal Value Compt. 13/14/57/23 Frst Stuaton Second Stuaton Crtcal Value Table 13: Test statstc values when 1-3, 1-4, 5-7, 2-3, and 4-5 dstances are out of from the frst measurement plan. Compt. 13/14/57/23/45 Frst Stuaton Second Stuaton Crtcal Value Table 14: Test statstc values when 1-3, 1-4, 5-7, 2-3, 4-5, and 4-6 dstances are out of from the frst measurement plan. Compt. 13/14/57/23/45/46 Frst Stuaton Second Stuaton Crtcal Value /15

10 In the end all of these calculatons, t was concluded that when1-3, 1-4, and 5-7 dstance measurements were out of from the frst measurement plan, there were not mportant changes n test statstcs n deformaton ponts. In ths way, the most satsfactory network confguraton, whch responds to frst deformaton values n deformaton ponts, was obtaned. The measurement plans both the frst one and the last one are gven n Table 15 and Table 16. These two tables ndcate that the last measurement plan has 13% less dstance measurements than the frst measurement plan. Table 15: The frst dstance measurement plan n Table 16: The last dstance measurement plan n FP LP S(m) FP LP S(m) In Table 17, the results of deformaton analyss that were obtaned from the frst measurement plan are gven. Moreover, n Table 18, the results of the last analyss, whch were obtaned from the last measurement plan, are gven. When these two tables compare, t comes out that: The largeness of deformaton vectors n deformaton ponts 2, 3, 4,5, and 6 stays the same There are no sgnfcant changes between the ellpss parameters. Table 17: The results of the deformaton analyss obtaned from the frst measurement plan Pont Number dy(cm) dx(cm) A-Konf(cm) B-Konf(cm) θ (gon) d(cm) t(gon) /15

11 Table 18: The results of the deformaton analyss obtaned from the last measurement plan Pont Number dy(cm) dx(cm) A-Konf(cm) B-Konf(cm) θ (gon) d(cm) t(gon) Furthermore, the horzontal dsplacement vectors between two epochs are shown n Fgure 2 and Fgure 3 together wth 95 % confdence ellpses. It s clear that all of the dsplacement vectors are only just fallng outsde the relatve confdence ellpses and they are margnally sgnfcant both the results of the frst analyss and the results of the last analyss. Fgure Scale: 1/33000 Ellpse Scale: 8/5 Fgure 2: The horzontal dsplacement vectors between 1983 and 1985 together wth 95% confdence ellpses accordng to the frst analyss results that was done related to the frst measurement plan. 11/15

12 Fgure Scale: 1/33000 Ellpse Scale: 8/5 Fgure 3: The horzontal dsplacement vectors between 1983 and 1985 together wth 95% confdence ellpses accordng to the last analyss results that was done related to the last measurement plan. 5. CONCLUSIONS In ths study, the effects of geodetc confguraton of the network n deformaton analyss were researched. It was studed to get the most satsfactory network confguraton that responds to the frst deformaton values n deformaton ponts. In the last measurement plan, dstance measurements were 13% decreased. Three dstance measurements, 1-3, 1-4, and 5-7 were out of from the frst measurement plan and the frst measurement plan was smplfed. In the end of the deformaton analyss that was done accordng to the last measurement plan, the largest movement occurred wth 1.12 cm n the pont number 2. The mnor movement occurred wth 0.45 cm n the pont number 6. Fnally, t s obtaned that the last analyss results are the same wth the frst analyss results. REFERENCES Ayan, T., Bağıl Güven Elpsler le Deformasyon Analz, Harta Dergs, Sayı 91, Ankara Ayan, T., Jeodezk Ağlarda Deformasyon Analzne Genel Bakış, İTÜ Dergs, Clt 40, Sayı 1, İstanbul Caspary, W.F., Concepts of Network and Deformaton Analyss, Monograph 11, School of Surveyng, The Unversty of New South Wales, Australa /15

13 Erol, S, Ayan, T., An Investgaton on Deformaton Measurements of Engneerng Structures wth GPS and Levellng Data Case Study, Internatonal Symposum on Modern Technologes, Educaton and Professonal Practce n the Globalzng World, Sofa Grafarend, E.W., Optmzaton of Geodetc Networks, Internatonal Symposum on Problems Related to the Redefnton of North Amercan Geodetc Networks, The Unversty of New Brunswck, Canada Kaplan, M.O., Desgn and Analyss of Control Networks that are Establshed to Determne Deformatons, MSc. Thess, Istanbul Techncal Unversty, Istanbul Kaplan, M.O., Deformaton Analyss wth Relatve Confdence Ellpses n Mcro Geodetc Network n Gerede Secton of The North Anatolan Fault, Internatonal Symposum on Modern Technologes, Educaton and Professonal Practce n the Globalzng World, Sofa Kuang, S.L., Optmzaton and Desgn of Montorng Schemes, Ph.D. dssertaton. Dep. of Surveyng Engneerng Techncal Report No. 157, Unversty of New Brunswck, Canada Mackenze, P., Desgn and Assessment of Horzontal Survey Networks, Thess, The Unversty of Calgary, Calgary, Alberta Seemkooe, A.A., 2001 Comparson of Relablty and Geometrcal Strength Crtera n Geodetc Networks, Journal of Geodesy 75: , ACKNOWLEDGEMENTS The Geodetc Insttute, Unversty of Karlsruhe, provded the 2D deformaton analyss software KADEAN 2D. The authors would lke to thank the Geodetc Insttute, Unversty of Karlsruhe. BIOGRAPHICAL NOTES Onur Kaplan born n Turkey. Educaton: 2003: Doctor of Phlosophy; ITU, Insttute of Scence and Technology, Geodesy and Photogrammetry Engneerng Program : Master of Scence; ITU, Insttute of Scence and Technology, Geodesy and Photogrammetry Engneerng Program completed n May : Bachelor of Scence, YTU, Geodesy and Photogrammetry Engneerng Department completed n July-2000 Attendance of Workshops, symposa and conferences: Internatonal Symposum of Modern Technologes, Educaton and Professonal Practce n the Globalzng World, November 2003, Sofa, Bulgara 13/15

14 Turkey Natonal Geodesy Commsson (TUJK) Geographc Informaton Systems and Geodetc Networks Workshop, Workshop of Turkey Natonal Geodesy Commsson, September 2003, Selçuk Unversty, Konya, Turkey Turkey Natonal Geodesy Commsson (TUJK) 2002 Year Scentfc Workshop Tectonc and Geodetc Networks, Panel on the new Regulaton on producton of Maps and Map Informaton, October, 2002, Earthquake Research Center of Boğazç Unversty, İznk, Turkey Thess MSc. Thess: May 2003: Desgn and Analyss of Control Networks Establshed to Determne Deformatons, Supervsor Prof. Dr. Tevfk Ayan Foregn Language Englsh and Italan Scentfc and Techncal Interests Deformaton Analyss Optmzaton of Geodetc Network CONTACTS Onur Kaplan Istanbul Techncal Unversty, Cvl Engneerng Faculty Department of Geodesy and Photogrammetry, Maslak-İstanbul TURKEY Tel Fax Emal: kaplanonur@hotmal.com Tevfk Ayan Istanbul Techncal Unversty, Cvl Engneerng Faculty Department of Geodesy and Photogrammetry, Maslak-İstanbul TURKEY Tel Fax Emal: ayan@tu.edu.tr 14/15

15 Serdar Erol Istanbul Techncal Unversty, Cvl Engneerng Faculty Department of Geodesy and Photogrammetry, Maslak-İstanbul TURKEY Tel Fax Emal: erol@tu.edu.tr 15/15