Modeling Aftershocks as a Stretched Exponential Relaxation

TL;DR

This study challenges the traditional power law model of aftershock decay, demonstrating that a stretched exponential better describes aftershock sequences across multiple regions and declustering methods, suggesting a simpler relaxation process.

Contribution

The paper introduces a new perspective by replacing the power law decay model with a stretched exponential model for aftershocks, supported by extensive data analysis.

Findings

All tested aftershock sequences follow a stretched exponential decay.

Results are consistent across different regions and declustering techniques.

Suggests a simpler relaxation process underlying aftershock sequences.

Abstract

The decay rate of aftershocks has been modeled as a power law since the pioneering work of Omori in the late nineteenth century. Considered the second most fundamental empirical law after the Gutenberg-Richter relationship, the power law paradigm has rarely been challenged by the seismological community. By taking a view of aftershock research not biased by prior conceptions of Omori power law decay and by applying statistical methods recommended in applied mathematics, I show that all aftershock sequences tested in three regional earthquake catalogs (Southern and Northern California, Taiwan) and with three declustering techniques (nearest-neighbor, second-order moment, window methods) follow a stretched exponential instead of a power law. These results infer that aftershocks are due to a simpler relaxation process than originally thought, in accordance with most other relaxation processes observed in Nature.