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Source time functions of earthquakes based on a stochastic differential equation
1Department of Physical Science, College of Science and Engineering, Ritsumeikan University, 1-1-1, Nojihigashi, Kusatsu, Shiga, 525-8577, Japan. s-hrn@fc.ritsumei.ac.jp.
Scientific Reports
|March 11, 2022
Summary
Seismic source time functions are modeled using Bessel processes, satisfying empirical laws like non-negativity and the Gutenberg-Richter law. This approach offers a new framework for understanding earthquake source physics.
Area of Science:
- Seismology
- Geophysics
- Stochastic Processes
Background:
- Source time functions (STFs) are crucial observables in seismology, extensively studied through kinematic inversion.
- Existing empirical laws for STFs highlight their complex, fluctuating time-series nature.
Purpose of the Study:
- To model seismic source time functions using a novel stochastic approach.
- To demonstrate that this model satisfies established empirical laws of STFs.
Main Methods:
- Modeling STFs as the convolution of two Bessel processes.
- Mathematical and numerical analysis to verify model properties.
Main Results:
- The convolution of Bessel processes satisfies key STF empirical laws: non-negativity, finite duration, and unimodality.
- The model predicts [Formula: see text] growth rates and [Formula: see text]-type spectra.
- The model's frequency distribution aligns with the Gutenberg-Richter law.
Conclusions:
- The convolution of Bessel processes provides a robust theoretical framework for seismic source time functions.
- This model suggests that stress drop rate and fault impedance may follow Bessel processes.
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