Introduction

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.