Hypocenter interval statistics between successive earthquakes in the two-dimensional Burridge-Knopoff model

TL;DR

This study analyzes the spatial and temporal distribution of earthquake hypocenter intervals using a 2D Burridge-Knopoff model, revealing that their statistics follow q-exponential distributions consistent with real earthquake data, influenced by model parameters.

Contribution

It demonstrates that the Burridge-Knopoff model reproduces realistic hypocenter interval statistics using nonextensive statistical mechanics, highlighting the model's relevance.

Findings

Hypocenter intervals follow q-exponential distributions with q<1.

Statistics depend on friction, stiffness, and magnitude threshold.

The relation q_t + q_r ≈ 2 is semi-quantitatively supported.

Abstract

We study statistical properties of spatial distances between successive earthquakes, the so-called hypocenter intervals, produced by a two-dimensional (2D) Burridge-Knopoff model involving stick-slip behavior. It is found that cumulative distributions of hypocenter intervals can be described by the $q$-exponential distributions with $q<1$, which is also observed in nature. The statistics depend on a friction and stiffness parameters characterizing the model and a threshold of magnitude. The conjecture which states that $q_t+q_r \sim 2$, where $q_t$ and $q_r$ are an entropy index of time intervals and spatial intervals, respectively, can be reproduced semi-quantitatively. It is concluded that we provide a new perspective on the Burridge-Knopoff model which addresses that the model can be recognized as a realistic one in view of the reproduction of the spatio-temporal interval statistics of earthquakes on the basis of nonextensive statistical mechanics.