Finite-Element Propagation of Acoustic Waves on a Spherical Shell
, by Chuck Sword, Jon Claerbout, and Norm Sleep
We model propagation of waves on the surface of the Earth,
using a finite element approach.
A spherical shell is covered by a fine triangular mesh,
and propagation matrices are found that step an acoustic wave field
on this mesh forward in time.
The propagation matrices are determined by
means of variational (finite-element)
techniques. By varying the distribution of mass within the individual triangular faces, different dispersion curves are obtained.
These curves can be made to conform, over a certain range of frequencies,
to desired dispersion relations.
Techniques developed in the course of this work may be applicable to the
problem of migrating irregularly-sampled 3--D reflection seismic data.