Thermodynamic method for generating random stress distributions on an earthquake fault

Open-File Report 2012-1226
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Abstract

This report presents a new method for generating random stress distributions on an earthquake fault, suitable for use as initial conditions in a dynamic rupture simulation. The method employs concepts from thermodynamics and statistical mechanics. A pattern of fault slip is considered to be analogous to a micro-state of a thermodynamic system. The energy of the micro-state is taken to be the elastic energy stored in the surrounding medium. Then, the Boltzmann distribution gives the probability of a given pattern of fault slip and stress. We show how to decompose the system into independent degrees of freedom, which makes it computationally feasible to select a random state. However, due to the equipartition theorem, straightforward application of the Boltzmann distribution leads to a divergence which predicts infinite stress. To avoid equipartition, we show that the finite strength of the fault acts to restrict the possible states of the system. By analyzing a set of earthquake scaling relations, we derive a new formula for the expected power spectral density of the stress distribution, which allows us to construct a computer algorithm free of infinities. We then present a new technique for controlling the extent of the rupture by generating a random stress distribution thousands of times larger than the fault surface, and selecting a portion which, by chance, has a positive stress perturbation of the desired size. Finally, we present a new two-stage nucleation method that combines a small zone of forced rupture with a larger zone of reduced fracture energy.

Additional publication details

Publication type Report
Publication Subtype USGS Numbered Series
Title Thermodynamic method for generating random stress distributions on an earthquake fault
Series title Open-File Report
Series number 2012-1226
DOI 10.3133/ofr20121226
Year Published 2012
Language English
Publisher U.S. Geological Survey
Publisher location Reston, VA
Contributing office(s) Earthquake Science Center, Menlo Park Science Center
Description Report: 112 p.; Computer Code ZIP; Sample Data ZIP
Country United States
Online Only (Y/N) N
Additional Online Files (Y/N) Y