The occupation of a box as a toy model for the seismic cycle of a fault
Abstract
We illustrate how a simple statistical model can describe the quasiperiodic occurrence of large earthquakes. The model idealizes the loading of elastic energy in a seismic fault by the stochastic filling of a box. The emptying of the box after it is full is analogous to the generation of a large earthquake in which the fault relaxes after having been loaded to its failure threshold. The duration of the filling process is analogous to the seismic cycle, the time interval between two successive large earthquakes in a particular fault. The simplicity of the model enables us to derive the statistical distribution of its seismic cycle. We use this distribution to fit the series of earthquakes with magnitude around six that occurred at the Parkfield segment of the San Andreas fault in California. Using this fit, we estimate the probability of the next large earthquake at Parkfield and devise a simple forecasting strategy.
- Publication:
-
American Journal of Physics
- Pub Date:
- October 2005
- DOI:
- 10.1119/1.2013310
- arXiv:
- arXiv:physics/0502048
- Bibcode:
- 2005AmJPh..73..946G
- Keywords:
-
- 01.40.-d;
- 91.30.Bi;
- 91.30.Px;
- 91.30.Dk;
- 91.45.Vz;
- 93.30.Hf;
- Education;
- Seismic sources;
- Earthquakes;
- Seismicity;
- North America;
- Physics - Geophysics;
- Physics - Data Analysis;
- Statistics and Probability
- E-Print:
- Final version of the published paper, with an erratum and an unpublished appendix with some proofs