Effect of modelling strategies for post-seismic relaxation on error characteristics of GPS time series and deterministic parameters

Yıl 2023, Cilt: 10 Sayı: 2, 96 - 111, 01.11.2023

Hüseyin Duman

https://doi.org/10.9733/JGG.2023R0007.T

Öz

With occurrence of an earthquake, an instant displacement on the Earth’s surface (so-called co-seismic displacement) and subsequently a post-seismic relaxation could be experienced. The post-seismic relaxation is a process that is a stress relaxation in the crust’s low viscosity layers and in the upper mantle. Effects of this time-dependent non-linear transient events on Earth’s surface can be monitored by Global Positioning System (GPS) and can be modelled deterministically through an exponential function using GPS time series. The post-seismic relaxation, which is not (can not be) modelled, affects other parameters in the mathematical model. In this study, the post-seismic relaxation effects on GPS time series error characteristics, velocity, and co-seismic displacements were examined by analyzing pre- and post-earthquake observations series both jointly and separately. The post-seismic relaxation time were optimized by Nelder-Mead simplex algorithm, and GPS error time series were analyzed using these optimized relaxation times and additional deterministic parameters with stochastic model combinations of white noise (WN)+flicker noise (FN), WN+FN+random-walk noise (RWN), WN+power-law noise (PL). The time series jointly analyzed can be characterized by RWN or PL in which spectral index is about to -1.25. On the contrary, all the separately analyzed time series is characterized by the WN+FN model combination. Both quality measures and visual inspections of GPS error time series demonstrates that the separately analyzing is a correct approach. Accordingly, the joint analysis can result in biased velocity estimates up to 0.52 mm/year, overestimation of velocity uncertainties up to %94 and co-seismic displacements differences up to 8 cm.

Anahtar Kelimeler

Post-seismic relaxation, Viscoelastic relaxation, Noise analysis, GPS time series, Co-seismic displacement

Deprem sonrası rahatlama evresi modelleme stratejilerinin GPS zaman serileri hata karakteri ve deterministik büyüklüklere etkisi

Öz

Depremin meydana gelmesi ile yeryüzünde ani yer değiştirmeler (kosismik yer değiştirme) ve akabinde deprem sonrası rahatlama evresi süreçleri yaşanır. Deprem sonrası rahatlama evresi, yer kabuğunun düşük viskoziteli katmanında ve üst mantoda biriken gerinimin gevşemesi sürecidir. Zamana bağımlı doğrusal olmayan bu geçiş sürecinin yeryüzündeki etkileri Küresel Konumlama Sistemi (Global Positioning System, GPS) ile izlenebilmekte ve GPS zaman serileri ile matematiksel olarak üstel fonksiyonlarla modellenebilmektedir. Modellen(e)meyen deprem sonrası rahatlama evresi matematiksel modelin diğer parametrelerini etkilemektedir. Bu çalışmada, deprem sonrası rahatlama evresi deprem öncesi ve sonrası ölçülerin hem bütünleşik hem de ayrı ayrı değerlendirilmesinin GPS zaman serileri hata karakterine, hız ve kosismik yer değiştirmelere etkileri irdelenmiştir. Deprem sonrası rahatlama zamanı Nelder-Mead yakınsama algoritması ile optimize edilmiş, bu değerler ve ek deterministik büyüklükler ile GPS hata zaman serileri beyaz gürültü (BG) + kırpışma gürültüsü (KG), BG+KG+rasgele yürüyüş gürültüsü (RYG) ve BG+güç-yasası gürültüsü (GYG) stokastik model kombinasyonları ile analiz edilmiştir. Bütünleşik analiz edilen zaman serileri, RYG ya da spektral indeks değeri ortalama -1.25’lere yaklaşan GYG gürültü modelleri ile temsil edilebilmektedir. Aksine, ayrı ayrı analizlerden birleştirilen GPS hata zaman serilerinin tümü BG+KG modeli ile karakterize edilmektedir. Hem kalite ölçütleri hem de GPS hata zaman serilerinin görsel irdelemeleri, ayrı ayrı analiz edilmelerinin doğru bir yaklaşım olduğunu göstermektedir. Buna göre bütünleşik analiz, hız bileşeninde 0.52 mm/yıl’a kadar yanlı kestirime, hız standart sapmalarında %94’e kadar aşırı tahmin edilmesine ve kosismik yer değiştirmelerde 8 cm’ye kadar farklılıklara sebep olabilmektedir.

Anahtar Kelimeler

Post-sismik rahatlama, Viskoelastik rahatlama, Gürültü analizi, GPS zaman serileri, Kosismik atım

Kaynakça

• Agnew, D. C. (1992). The time‐domain behavior of power‐law noises. Geophysical research letters, 19(4), 333-336.
• Amiri‐Simkooei, A. R., Tiberius, C. C., & Teunissen, P. J. (2007). Assessment of noise in GPS coordinate time series: methodology and results. Journal of Geophysical Research: Solid Earth, 112(B7).
• Aydin, C., Duman, H., Günes, Ö., & Sanli, D. U. (2021). Effect of stochastic model errors on significance test for velocities in analysis of GPS position time series. Journal of Surveying Engineering, 147(1), 04020025.
• Bogusz, J., & Klos, A. (2016). On the significance of periodic signals in noise analysis of GPS station coordinates time series. GPS solutions, 20, 655-664.
• Bos, M. S., Fernandes, R. M. S., Williams, S. D. P., & Bastos, L. (2013). Fast error analysis of continuous GNSS observations with missing data. Journal of Geodesy, 87(4), 351-360.
• Bos, M. S., & Fernandes, R. M. S. (2021). Hector user manual version 1.9.
• Calais, E. (1999). Continuous GPS measurements across the Western Alps, 1996–1998. Geophysical Journal International, 138(1), 221-230.
• Chen, G., Zhao, Q., Wei, N., & Liu, J. (2018). Impacts on noise analyses of GNSS position time series caused by seasonal signal, weight matrix, offset, and helmert transformation parameters. Remote Sensing, 10(10), 1584.
• Dogan, U., Demir, D. Ö., Çakir, Z., Ergintav, S., Ozener, H., Akoğlu, A. M., Nalband, S. S., & Reilinger, R. (2014). Postseismic deformation following the Mw 7.2, 23 October 2011 Van earthquake (Turkey): Evidence for aseismic fault reactivation. Geophysical Research Letters, 41(7), 2334-2341.
• Dong, D., Fang, P., Bock, Y., Webb, F., Prawirodirdjo, L., Kedar, S., & Jamason, P. (2006). Spatiotemporal filtering using principal component analysis and Karhunen‐Loeve expansion approaches for regional GPS network analysis. Journal of geophysical research: solid earth, 111(B3).
• Dzurisin, D. (2003). A comprehensive approach to monitoring volcano deformation as a window on the eruption cycle. Reviews of Geophysics, 41(1).
• Emre, Ö., Duman, T. Y., Özalp, S., Şaroğlu, F., Olgun, Ş., Elmacı, H., & Çan, T. (2018). Active fault database of Turkey. Bulletin of Earthquake Engineering, 16(8), 3229-3275.
• Gualandi, A., Avouac, J. P., Galetzka, J., Genrich, J. F., Blewitt, G., Adhikari, L. B., Koirala, B. P., Gupta, R., Upreti, B. N., Pratt-Sitaula, B., & Liu-Zeng, J. (2017). Pre-and post-seismic deformation related to the 2015, Mw7. 8 Gorkha earthquake, Nepal. Tectonophysics, 714, 90-106.
• Hackl, M., Malservisi, R., & Wdowinski, S. (2009). Strain rate patterns from dense GPS networks. Natural Hazards and Earth System Sciences, 9(4), 1177-1187.
• Hackl, M., Malservisi, R., Hugentobler, U., & Jiang, Y. (2013). Velocity covariance in the presence of anisotropic time correlated noise and transient events in GPS time series. Journal of Geodynamics, 72, 36-45.
• Hammond, W. C., Kreemer, C., Blewitt, G., & Plag, H. P. (2010). Effect of viscoelastic postseismic relaxation on estimates of interseismic crustal strain accumulation at Yucca Mountain, Nevada. Geophysical Research Letters, 37(6).
• He, X., Montillet, J. P., Hua, X., Yu, K., Jiang, W., & Zhou, F. (2016). Noise analysis for environmental loading effect on GPS position time series. Acta Geodynamica et Geomaterialia, 14, 131-142.
• He, X., Bos, M. S., Montillet, J. P., & Fernandes, R. M. S. (2019). Investigation of the noise properties at low frequencies in long GNSS time series. Journal of Geodesy, 93(9), 1271-1282.
• Hetland, E. A., & Simons, M. (2010). Post-seismic and interseismic fault creep II: Transient creep and interseismic stress shadows on megathrusts. Geophysical Journal International, 181(1), 99-112.
• Hosking, J. R. M. (1981). Fractional Differencing. Biometrika, 68(1), 165-176.
• Ingleby, T., & Wright, T. J. (2017). Omori‐like decay of postseismic velocities following continental earthquakes. Geophysical Research Letters, 44(7), 3119-3130.
• Johnson, H. O., & Agnew, D. C. (1995). Monument motion and measurements of crustal velocities. Geophysical Research Letters, 22(21), 2905-2908.
• Kasdin, N. J. (1995). Discrete simulation of colored noise and stochastic processes and 1/f/sup α/power law noise generation. Proceedings of the IEEE, 83(5), 802-827.
• Langbein, J. (2008). Noise in GPS displacement measurements from Southern California and Southern Nevada. Journal of Geophysical Research: Solid Earth, 113(B5).
• Langbein, J. (2017). Improved efficiency of maximum likelihood analysis of time series with temporally correlated errors. Journal of Geodesy, 91, 985-994.
• Langbein, J., & Johnson, H. (1997). Correlated errors in geodetic time series: Implications for time‐dependent deformation. Journal of Geophysical Research: Solid Earth, 102(B1), 591-603.
• Lomb, N. R. (1976). Least-squares frequency analysis of unequally spaced data. Astrophysics and space science, 39, 447-462.
• Mandelbrot, B. B., & van Ness, J. W. (1968). Fractional Brownian motions, fractional noises and applications. SIAM review, 10(4), 422-437.
• Mao, A., Harrison, C. G., & Dixon, T. H. (1999). Noise in GPS coordinate time series. Journal of Geophysical Research: Solid Earth, 104(B2), 2797-2816.
• Marone, C. J., Scholtz, C. H., & Bilham, R. (1991). On the mechanics of earthquake afterslip. Journal of Geophysical Research: Solid Earth, 96(B5), 8441-8452.
• Özdemir, S. (2016). TUSAGA ve TUSAGA-Aktif istasyonlarının hassas koordinat ve hızlarının hesaplanması üzerine. Harita Dergisi, 155, 53-81.
• Perfettini, H., & Avouac, J. P. (2004). Postseismic relaxation driven by brittle creep: A possible mechanism to reconcile geodetic measurements and the decay rate of aftershocks, application to the Chi‐Chi earthquake, Taiwan. Journal of Geophysical Research: Solid Earth, 109(B2).
• Press, W. H. (2007). Numerical recipes: The art of scientific computing (3rd ed.). Cambridge University Press. Santamaría‐Gómez, A., Bouin, M. N., Collilieux, X., & Wöppelmann, G. (2011). Correlated errors in GPS position time series: Implications for velocity estimates. Journal of Geophysical Research: Solid Earth, 116(B1).
• Santamaría‐Gómez, A., & Ray, J. (2021). Chameleonic noise in GPS position time series. Journal of Geophysical Research: Solid Earth, 126(3), e2020JB019541.
• Scargle, J. D. (1982). Studies in astronomical time series analysis. II-Statistical aspects of spectral analysis of unevenly spaced data. Astrophysical Journal, Part 1, vol. 263, Dec. 15, 1982, p. 835-853., 263, 835-853.
• Tiryakioglu, I., Yavasoglu, H., Ugur, M. A., Özkaymak, Ç., Yilmaz, M., Kocaoglu, H., & Turgut, B. (2017). Analysis of October 23 (Mw 7.2) and November 9 (Mw 5.6), 2011 Van earthquakes using long-term GNSS time series. Earth Sciences Research Journal, 21(3), 147-156.
• Vallianatos, F., & Sakkas, V. (2021). Multiscale Post-Seismic Deformation Based on cGNSS Time Series Following the 2015 Lefkas (W. Greece) Mw6. 5 Earthquake. Applied sciences, 11(11), 4817.
• Wdowinski, S., Bock, Y., Zhang, J., Fang, P., & Genrich, J. (1997). Southern California permanent GPS geodetic array: Spatial filtering of daily positions for estimating coseismic and postseismic displacements induced by the 1992 Landers earthquake. Journal of Geophysical Research: Solid Earth, 102(B8), 18057-18070.
• Wessel, P., Luis, J. F., Uieda, L., Scharroo, R., Wobbe, F., Smith, W. H., & Tian, D. (2019). The generic mapping tools version 6. Geochemistry, Geophysics, Geosystems, 20(11), 5556-5564.
• Williams, S. D. P. (2003a). Offsets in global positioning system time series. Journal of Geophysical Research: Solid Earth, 108(B6).
• Williams, S. D. P. (2003b). The effect of coloured noise on the uncertainties of rates estimated from geodetic time series. Journal of Geodesy, 76, 483-494.
• Williams, S. D. P., Bock, Y., Fang, P., Jamason, P., Nikolaidis, R. M., Prawirodirdjo, L., Miller, M., & Johnson, D. J. (2004). Error analysis of continuous GPS position time series. Journal of Geophysical Research: Solid Earth, 109(B3).
• Zhang, J., Bock, Y., Johnson, H., Fang, P., Williams, S., Genrich, J., Wdowinski, S., & Behr, J. (1997). Southern California Permanent GPS Geodetic Array: Error analysis of daily position estimates and site velocities. Journal of geophysical research: solid earth, 102(B8), 18035-18055.
• URL-1: https://www.harita.gov.tr/public/sunum/, (Erişim Tarihi: 19 Şubat 2023).