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There are at least two quite distinct applications of Equivalent Medium
Theory in seismic exploration, and these applications drive two rather
different lines of research. The first is a scaling operation. Sonic
logs may be sampled one hundred times more densely than is required for
modeling seismic data, and this might be too expensive to contemplate in
case of 3-D models. Both Folstad and Schoenberg (1992) and Karrenbach (1993)
have shown how the Schoenberg-Muir calculus can be used to `filter'
fine-sampled data and then resample at a suitably coarser depth interval.
In the other application, instead of substituting fine heterogeneity for
a coarser one, we are interested in coming up with a homogeneous
equivalent model. A typical situation would be where we want to think
of our earth model as being blocky, but we want the block models to
reflect the frequency-dependent loss due to scattering. It
is this second application that drives my work in this paper.

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Stanford Exploration Project

11/17/1997