Analysis of Seismic Attenuation and Multiple Scattering with a Version of the Shannon Entropy

Multiple scattering and intrinsic friction both contribute to the attenuation of seismic waves, and are difficult to distinguish in seismic experiments. In this paper we will examine attenuation using theoretical tools that put scattering and friction on more or less an equal footing. Multiple scattering is, after all, a process that increases the disorder of mechanical motions in a continuum. If it occurs well below the resolution of an experiment, the energy it carries is, in a sense, classifiable as thermal. The Shannon entropy, defined on snapshots of a propagating wave, is a measure of disorder in something like the above sense. Its rate of monotonic increase, as a wave experiences either or both of multiple scattering and attenuation, may be a useful means to quantify intrinsic and extrinsic Q. Synthetic experiments and a field VSP data set appear to support this idea.