| 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. |
| Genre: | USGS Numbered Series |
| ProdID: | 70042144 |
| Citation Author: | Barall, Michael; Harris, Ruth A. |
| Citation Contributing Office: | Earthquake Science Center, Menlo Park Science Center |
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| Citation Language: | English |
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| Citation Online Only Flag: | N |
| Citation Phsyical Description: | Report: 112 p.; Computer Code ZIP; Sample Data ZIP |
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| Citation Publisher: | U.S. Geological Survey |
| Citation Series: | Open-File Report |
| Citation Series Code: | OFR |
| Citation Series Number: | 2012-1226 |
| Citation Search Results Text: | Thermodynamic method for generating random stress distributions on an earthquake fault; 2012; OFR; 2012-1226; Barall, Michael; Harris, Ruth A. |
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| Citation Year: | 2012 |
| Type: | citation/reference |
| Text: | Thermodynamic method for generating random stress distributions on an earthquake fault; 2012; OFR; 2012-1226; Barall, Michael; Harris, Ruth A. |
| URL (COMPANION FILES): | http://pubs.usgs.gov/of/2012/1226/of2012-1226_computer_code.zip |
| URL (COMPANION FILES): | http://pubs.usgs.gov/of/2012/1226/of2012-1226_sample_data.zip |
| URL (THUMBNAIL): | http://pubs.er.usgs.gov/thumbnails/ofr_2012_1226.jpg |
| URL (DOCUMENT): | http://pubs.usgs.gov/of/2012/1226/pdf/of2012-1226.pdf |
| URL (INDEX PAGE): | http://pubs.usgs.gov/of/2012/1226/ |
| Date Other: | Thu, 27 Dec 2012 00:00 -0600 |
| Publisher: | U.S. Geological Survey |
