Elastic Deformation Model
Bridget Smith and David Sandwell
J. Geophy. Res., 2003
Quick Contents:
Coulomb Stress along the San Andreas Fault System [Smith and Sandwell, 2003]
Fourier elastic half-space model derivation
Example source code (elastic half-space model)
For the last several decades, the most commonly used analytic models of
fault-induced deformation have been based on the dislocation solutions of
Chinnery [1961, 1963], Rybicki [1973], and Okada [1985, 1992]. The latter
provide analytic expressions for stress, strain, and displacement in an
elastic half-space due to a displacement discontinuity. While these
dislocation models are accurate and computationally efficient when
applied to individual faults or small fault systems, they may become
computationally prohibitive when representing fault geometry over
the entire North American-Pacific plate boundary. However, if model calculations are performed in the
spectral domain, the computational effort is substantially reduced.
Rather than calculate the Fourier transform of the analytic solutions
mentioned above, we instead solve the 3-D elasticity equations in the
wave-number domain and then inverse Fourier transform to obtain space
domain solutions.
To summarize our analytic approach, the elasticity
equations are used to derive a set of transfer functions (in the
wave-number domain) for the 3-D displacement of an elastic half-space
due to an arbitrary distribution of vector body forces. The numerical
components of this approach involve generating a grid of force couples
that simulate complex fault geometry, taking the 2-D Fourier transform
of the grid, multiplying by the appropriate transfer function, and
finally inverse Fourier transforming. The force model must be designed
to match the velocity difference across the plate boundary and have
zero net force and zero net moment
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