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.


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