San Andreas Fourier Models

3-D Fourier Elastic and Viscoelastic Deformation Modeling

Bridget Smith-Konter
Department of Geological Sciences
University of Texas at El Paso
El Paso, Texas 79968-0555
http://www.geo.utep.edu/pub/bkonter

David Sandwell
Institute of Geophysics and Planetary Physics

Scripps Institution of Oceanography
University of California, San Diego
La Jolla, CA 92093-0225
http://topex.ucsd.edu/sandwell

Long-term tectonic loading, instantaneous fault rupture, and transient postseismic rebound are key components of the earthquake cycle that expose important spatial and temporal chaaracteristics of crustal deformation. In order to better understand such behavior, we have developed semi-analytic elastic and viscoelastic (static and time-dependent) models for 3-D displacement and stress caused by a body-force dislocation. All solutions of the model are derived (and computed) in the Fourier domain to exploit the speed of the convolution theorem and thus horizontal complexity of a model fault system has no effect on the speed of the computation. A single-depth computation consisting of a horizontal grid of 2048x2048 elements, for example, requires less than 40 seconds of CPU time on a Mac G5.

Selected Publications

Stress Evolution of the San Andreas Fault System: recurrence interval vs. locking depth, B. Smith-Konter and D. T. Sandwell, submitted to Geophys. Res. Lett., 2008.
Spatial characterization of the interseismic velocity field in southern California, S. Wdowinski, B. Smith-Konter, Y. Bock, and D. T. Sandwell, Geology, doi:10.1130/G22938A.1., 2007.
A Model of the Earthquake Cycle Along the San Andreas Fault System for the Past 1000 Years [Smith and Sandwell, 2006] (pdf)
Bridget's Thesis: Three-dimensional Deformation and Stress Models: Exploring One-Thousand Years of Earthquake History Along the San Andreas Fault System [Ph.D. Dissertation, January 2005] (pdf, 6.5M)
A 3-D Semi-analytic Viscoelastic Model for Time-dependent Analyses of the Earthquake Cycle [Smith and Sandwell, 2004] (pdf)
Accuracy and Resolution of Shuttle Radar Topography Mission Data [Smith and Sandwell, 2003] (pdf)
Coulomb Stress along the San Andreas Fault System [Smith and Sandwell, 2003] (pdf)

Animations and Movies

San Andreas earthquake cycle stress accumulation and release, Southern SAF perspective, 1600-2006 (.mov, 24.9 MB)
San Andreas earthquake cycle stress accumulation and release, Entire SAF perspective, 1600-2006 (.mov, 21.6 MB)
San Andreas viscoelastic deformation model , 1800-2004 (.mov, 135 MB)
San Andreas viscoelastic Coulomb stress model, 1800-2004 (.mov, 35 MB)
San Andreas: Earthquake Machine (.mov, BIG 1.15 GB)
San Andreas Fault System: A 1000-year Perspective of the Earthquake Cycle (.mov, 189 MB)
Example viscoelastic models

Visualizations

1906 San Francisco Earthquake (to be featured in The National Geographic) [Fledermaus scene file, ctrl click to download]
San Andreas Fault System Coulomb Stress Accumulation Rate [Fledermaus scene file, ctrl click to download]

Model Derivations and Source Code

Fourier elastic half-space model derivation (pdf)
Example source code (elastic half-space model) (tar)
Fourier viscoelastic model derivation (pdf)
Example source code (viscoelastic half-space model) (tar)
Analytic and numeric tests (pdf)

This research was supported by the NASA Solid Earth and Natural Hazards Program (NAGS - 9623), the NASA Earth System Science Fellowship Program (ESSF - 0131), the NSF Earth Science Program (EAR - 0105896), and the Southern California Earthquake Center (SCEC).

Institute of Geophysics and Planetary Physics
Scripps Institution of Oceanography
University of California, San Diego