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

Abstract

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.

Keywords

• 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

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