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.
Suggested Citation
Barall, M., Harris, R.A., 2012, Thermodynamic method for generating random stress distributions on an earthquake fault: U.S. Geological Survey Open-File Report 2012-1226, Report: 112 p.; Computer Code ZIP; Sample Data ZIP, https://doi.org/10.3133/ofr20121226.
ISSN: 2331-1258 (online)
ISSN: 0196-1497 (print)
| 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 |