Diffracted Seismic Signals and Their Numerical Solution

Relationships of tsunami generation and an earthquake source.

“…If (19) can be recast into a form which takes advantage of this behavior by accounting (approximately) for large numbers of modes in a single step, a great deal of labor can be saved. The recasting is done by decomposing the standing wave field into travelling wave components and replacing the summation over l by an integral over the continuous parameter 1965; CHAPMAN and PHINNEY, 1972;RICHARDS, 1973) so we will not dwell on the details. Dropping the overtone index, changing variables, and using the Poisson sum formula there results…”

A note on the equivalence of three major propagator algorithms for computational stability and efficiency

“…Kennett (1974Kennett ( , 1983Kennett ( , 2001) derived an recursive algorithm for propagating the generalized reflection-transmission coefficients directly to avoid the numerical difficulties. An orthogonalization approach which makes the inner product between two 4D velocity-stress vectors vanish by Gram-Schmidt method was developed by Pitteway (1965) for the radio wave problem and used later in seismology by Chapman & Phinney (1972). The orthogonalization improves the numerical stability of the propagator algorithm, but it requires certain restriction of the propagation step.…”

Calculation of Synthetic Seismograms in Layered Media by Means of a Modified Propagator Matrix Method

“…Among the methods in which the integration is performed in the complex wavenumber plane, some authors distorce the path of integration to a path of steepest descent. An example of this is the work of Chapman and Phinney (5). In the present method the spatial Fourier integral is also computed along a path in the complex plane, so as to avoid the singularities, but this path is not a steepest descent path.…”