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

Yıl 2019, Cilt: 6 Sayı: 2, 115 - 127, 01.11.2019

Eyüp Sopacı

https://doi.org/10.9733/JGG.2019R0010.T

Öz

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.

Anahtar Kelimeler

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

Öz

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.

Anahtar Kelimeler

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

Kaynakça

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