Phase response curves for models of earthquake fault dynamics

Abstract

We systematically study effects of external perturbations on models describing earthquake fault dynamics. The latter are based on the framework of the Burridge-Knopoff spring-block system, including the cases of a simple mono-block fault, as well as the paradigmatic complex faults made up of two identical or distinct blocks. The blocks exhibit relaxation oscillations, which are representative for the stick-slip behavior typical for earthquake dynamics. Our analysis is carried out by determining the phase response curves of first and second order. For a mono-block fault, we consider the impact of a single and two successive pulse perturbations, further demonstrating how the profile of phase response curves depends on the fault parameters. For a homogeneous two-block fault, our focus is on the scenario where each of the blocks is influenced by a single pulse, whereas for heterogeneous faults, we analyze how the response of the system depends on whether the stimulus is applied to the block having a shorter or a longer oscillation period.

A study of earthquake recurrence based on a one-body spring-slider model in the presence of thermal-pressurized slip-weakening friction and viscosity

“…This is similar to the simulation results with the periodical earthquake occurrences obtained by some authors (e.g., Rice and Tse, 1986;Ryabov and Ito, 2001;Erickson et al, 2008;Mitsui and Hirahara, 2009) based on the one-body model with rate-and statedependent friction or velocity-weakening friction. However, the present result is inconsistent with the simulation results, from which either the time-predictable model or the slippredictable model cannot interpret the temporal variation in cumulative slip, based on the same model obtained by others (e.g., He et al, 2003;Bazzarri, 2012b;Bizzarri and Crupi, 2014;Kostić et al, 2013a, b;Franović et al, 2016). The differences between the two groups of researchers might be due to distinct additional constrains in respective studies.…”

“…Figures 4-7 show that when U c and η are constants during the computational time periods, the general patterns of temporal variations in cumulated slip do not change. Some of the previous studies (e.g., Bizzarri, 2012a, b;Franović et al, 2016) suggest that the patterns of temporal variations in cumulated slip can change with time. The changes of U c and η with time should play the main roles.…”

“…Modeling earthquake recurrence based on different models has been long made and is reviewed by Bizzarri (2012a, b) and Franović et al (2016). Among the models, the spring-slider model has been used to study fault dynamics and earthquake physics (see Wang, 2008).…”

“…The one-, two-, three-, and few-body models with various friction laws have also been applied to approach fault dynamics (see Turcotte, 1992). The studies for various friction laws based on spring-slider models are briefly described below: (1) for rate-and state-dependent friction (e.g., Rice and Tse, 1986;Ryabov and Ito, 2001;Erickson et al, 2008Erickson et al, , 2011He et al, 2003;Mitsui and Hirahara, 2009;Bizzarri, 2012a;Abe and Kato, 2013;Kostić et al, 2013a;Bizzarri and Crupi, 2014;Franović et al, 2016); (2) for velocity-weakening friction (e.g., Carlson and Langer, 1989;Huang and Turcotte, 1992;Brun and Gomez, 1994;Wang and Hwang, 2001;Wang, 2003;Kostić et al, 2013b); (3) for simple static-dynamic friction (e.g., Abaimov et al, 2007;Hasumi, 2007).…”

Examining phase response curve of nerve cell by using three different methods

“…, heart beat rhythm 5,6 , human walking motion 7,8 , circadian clock 9,10 , oscillation in chemical reactions 11,12 and earthquake dynamics. 13 In short, systems with dynamical elements that compose of spontaneous rhythms are used for Phase Response Curves (PRCs).…”