Modelling of earthquakes by using Rate-and-State friction laws on the Burridge-Knopoff spring-block system

Abstract

Although physical mechanism of earthquakes has not been clearly answered yet, it can be explained substantially with friction laws when the slip event subjects to the brittle crust. In such cases earthquakes are a result of frictional instability accompanied by stick-and-slip motion. Earthquakes, foreshocks, aftershocks, slow slip events have been modelled by using Rate-And-State Friction (RSF) laws. In this study Dieterich, Ruina and Perrin type RSF laws have been studied on the Burridge-Knopoff (BK) spring-block system, which was originally proposed with a velocity dependent friction law. In order to comply with the reality, fault geometry and its physical structure are chosen appropriate to the San Andreas/Parkfield fault. Since the proposed systems are stiff nonlinear dynamics, they are offered with numeric procedure adapted to solve stiff differential equations. By applying stability analysis, the critical boundaries between stable and unstable sliding (seismic cycle) are determined. The model is simulated by tuning the RSF law parameters for unstable sliding regime. As a result of the studies it has been found that, the magnitude of the slip event is proportional to the distance from the curve which separates stable and unstable sliding regimes. Besides, when system parameters deviates with a fixed amount from the stability curve, the system shows the same dynamics. To the best of my knowledge, the defined criterion is being published for the first time within the scope of this work. This study will pave the way for further researches of earthquake and weak triggering effects.

Keywords

• Earthquake,Rate-and-State Friction Law,Burridge-Knopoff,Geodynamics,Nonlinear dynamics

Hız-ve-durum sürtünme yasaları ve Burridge-Knopoff yay blok sistemi kullanılarak depremlerin dinamik modellenmesi

Abstract

Depremlerin fiziksel oluşum mekanizmaları henüz tam anlamıyla bilinememekle birlikte, kırılgan kabukta gerçekleştiği durumda büyük ölçüde sürtünme yasaları ile açıklanabilmektedir. Bu durumda depremler, tutma-bırakma hareketi sonucu oluşan sürtünme kararsızlığının (frictional instability) bir sonucudur. Hız-ve-Durum yasaları (Rate-and-State Friction law, RSF) ile doğadaki deprem olaylarına benzer artçı depremler, yavaş depremler, sismik ve sismik olmayan hareketler modellenebilmektedir. Bu çalışmada Dieterich, Ruina ve Perrin tipi RSF yasaları tek serbestlik dereceli Burridge-Knopoff (BK) yay-blok sistemine entegre edilerek irdelenmiştir. Modellemenin gerçekçi olması bakımından fay geometrisi ve fiziksel yapısı San Andreas/Parkfield fayına uygun olarak belirlenmiştir. Çalışmada kullanılan dinamik sistemler doğrusal olmayan sert (stiff) diferansiyel denklemlerden oluşmaktadır. Bu nedenle önerilen modellerin doğrusal olmayan karakteri ile çözümü için nümerik öneriler sunulmuştur. Modellere kararlılık analizi uygulanmış ve sistemin sürtünme kararlılığı (sismik olmayan hareket) ve kararsızlığı (sismik döngü) sergilediği kritik bölgeler belirlenmiştir. RSF parametre uzayı değiştirilerek sadece sürtünme kararsızlığı sergilediği durumlar için sistem simüle edilmiştir. Yapılan çalışmalar sonucu RSF yasalarından kaynaklı sistemin oluşturacağı dinamiklerin büyüklüğünün kararlılık eğrisinden sapma ile orantılı olduğu bulunmuştur. Bu eğriden sabit oranda sapma olduğunda ise sistemin aynı dinamikleri sergilediği görülmüştür. Yapılan literatür taramasında, bulunan ölçütün ilk kez bu çalışma kapsamında elde edildiği belirlenmiştir. Bu çalışma, ileride depremleri tetikleyen güçsüz sinyallerin araştırılmasına fayda sağlayacaktır.

Keywords

• Deprem,Hız-ve-Durum Sürtünme Yasaları,Burridge-Knopoff,Jeodinamik,Doğrusal olmayan dinamikler

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