Imagine a high frequency seismic surface source which radiates energy into the subsurface. Let frequency and bandwidth go to infinity and let the spatial sampling interval shrink infinitely small, then reflected energy could be recorded and resolved from infinitely small scale obstacles. Lowering the frequency content of the source and increasing spatial sampling intervals only enables us to record wave propagation effects (reflection, diffraction) at a larger scale. Thus we can only hope to resolve obstacles (layers, diffractors) properly, that are of the order of that minimum/dominant wave length. However, if there are material discontinuities, which are much smaller in scale than our minimum/dominant wavelength, then a wave, while propagating through a medium, will ``feel'' some average effect. Folstad et al. 1992 showed synthetic comparisons of fine and large scale wave propagation effects, using a Backus averaging of elastic constants. Thus, for a given finite resolution, we can only measure the properties of the ``equivalent medium'' at that scale. Small scale variations still influence effects at a larger scale, but in some averaged sense. I introduce one application of equivalent medium theory in form of homogeneous overburden replacement. Using such a group-theoretical approach, I find NMO (or focusing) velocities by calculating an anisotropic elastic replacement medium and carrying out small offset approximations along the vertical and horizontal axes. I compare this approach (low frequency) to a Dix rms velocity calculation (high frequency).

11/17/1997