Thermodynamic method for generating random stress distributions on an earthquake fault
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.
Citation Information
Publication Year | 2012 |
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Title | Thermodynamic method for generating random stress distributions on an earthquake fault |
DOI | 10.3133/ofr20121226 |
Authors | Michael Barall, Ruth A. Harris |
Publication Type | Report |
Publication Subtype | USGS Numbered Series |
Series Title | Open-File Report |
Series Number | 2012-1226 |
Index ID | ofr20121226 |
Record Source | USGS Publications Warehouse |
USGS Organization | Earthquake Science Center; Menlo Park Science Center |