# Fault heterogeneity and the connection between aftershocks and afterslip

## TL;DR

This paper presents an analytical and numerical study linking aftershock rates to afterslip dynamics, showing that fault heterogeneity influences seismic activity patterns and reproduces key empirical laws.

## Contribution

It introduces a model incorporating fault heterogeneity and friction variability, demonstrating how aftershock rates relate to afterslip and reproducing observed seismic laws.

## Key findings

- Aftershock rate is proportional to afterslip rate with a correction factor.
- Omori law arises from logarithmic afterslip evolution.
- Synthetic catalogs reproduce Gutenberg-Richter law with realistic b-value.

## Abstract

Whether aftershocks originate directly from the mainshock and surrounding stress environment or from afterslip dynamics is crucial to the understanding of the nature of aftershocks. We build on a classical description of the fault and creeping regions as two blocks connected elastically, subject to different friction laws. We show analytically that, upon introduction of variability in the fault plane's static friction threshold, a non trivial stick-slip dynamics ensues. In particular we support the hypothesis \citep{PA04} that the aftershock occurrence rate is proportional to the afterslip rate, up to a corrective factor that is also computed. Thus, the Omori law originates from the afterslip's logarithmic evolution in the velocity-strengthening region. We confirm these analytical results with numerical simulations, generating synthetic catalogs with statistical features in good agreement with instrumental catalogs. In particular we recover the Gutenberg-Richter law with a realistic $b$-value ($b\simeq 1$) when Coulomb stress thresholds obey a power law distribution.