Forecasting temporal variation of aftershocks immediately after a main shock using Gaussian process regression

TL;DR

This paper introduces a Gaussian process regression-based method for real-time forecasting of aftershock distributions immediately after a main earthquake, improving early hazard assessment.

Contribution

The paper develops a Bayesian approach using GPR to estimate aftershock parameters and detection functions simultaneously with credible intervals, enabling early aftershock prediction.

Findings

Accurately estimates aftershock parameters within three hours post-main shock.

Provides credible intervals for distribution parameters and detection functions.

Demonstrates stable performance on real earthquake data.

Abstract

Uncovering the distribution of magnitudes and arrival times of aftershocks is a key to comprehend the characteristics of the sequence of earthquakes, which enables us to predict seismic activities and hazard assessments. However, identifying the number of aftershocks immediately after the main shock is practically difficult due to contaminations of arriving seismic waves. To overcome the difficulty, we construct a likelihood based on the detected data incorporating a detection function to which the Gaussian process regression (GPR) is applied. The GPR is capable of estimating not only the parameters of the distribution of aftershocks together with the detection function but also credible intervals for both of the parameters and the detection function. A property that distributions of both the Gaussian process and aftershocks are exponential functions leads to an efficient Bayesian computational algorithm to estimate the hyperparameters. After the validations through numerical tests, the proposed method is retrospectively applied to the catalog data related to the 2004 Chuetsu earthquake towards early forecasting of the aftershocks. The result shows that the proposed method stably estimates the parameters of the distribution simultaneously their credible intervals even within three hours after the main shock.