On the relative scattering of P ‐ and S ‐waves

Summary. Using a single scattering approximation, we derive equations for the scattering attenuation coefficients of P‐ and S ‐body waves. We discuss our results in the light of some recent energy renormalization approaches to seismic wave scattering. Practical methods for calculating the scattering attenuation coefficients for various earth models are emphasized. The conversions of P ‐ to S ‐waves and S‐ to P ‐waves are included in the theory. The earth models are assumed to be randomly inhomogeneous, with their properties known only through their average wavenumber power spectra. We approximate the power spectra with piecewise constant functions, each segment of which contributes to the net, frequency‐dependent, scattering attenuation coefficient. The smallest and largest wavenumbers of a segment can be plotted along with the wavevectors of the incident and scattered waves on a wavenumber diagram. This diagram gives a geometric interpretation for the frequency behaviour associated with each spectral segment, including a ‘transition’ peak that is due entirely to the wavenumber limits of the segment. For regions of the earth where the inhomogeneity spectra are concentrated in a band of wavenumbers, it should be possible to observed such a peak in the apparent attenuation of seismic waves. We give both the frequency and distance limits on the accuracy of the theoretical results.