Phase response curves for models of earthquake fault dynamics

TL;DR

This paper investigates how external perturbations affect earthquake fault models based on the Burridge-Knopoff system, analyzing phase response curves to understand the impact on fault dynamics and oscillation behavior.

Contribution

It introduces a systematic analysis of phase response curves for various fault models, including mono-block and multi-block systems, highlighting how responses depend on fault parameters and heterogeneity.

Findings

Phase response curves vary with fault parameters.

Response depends on whether the stimulus targets shorter or longer oscillating blocks.

Heterogeneous faults show different responses based on stimulus location.

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.