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 mus be designed to match the velocity
difference across the plate boundary and have zero net force and zero
net moment