SCATTERING OF P-WAVE AND S-WAVE BY A SPHERICALLY SYMMETRICAL INCLUSION

Scattering of an arbitrary elastic wave incident upon a spherically sy mmetric inclusion is considered and solutions are developed in terms o f the spherical vector system of Petrashen, which produces results in terms of displacements rather than displacement potentials and in a fo rm suitable for accurate numerical computations. Analytical expression s for canonical scattering coefficients are obtained for both the case s of incident P waves and incident S waves. Calculations of energy flu x in the scattered waves lead to elastic optical theorems for both P a nd S waves, which relate the scattering cross sections to the amplitud e of the scattered fields in the forward direction. The properties of the solutions for a homogeneous elastic sphere, a sphere filled by flu id, and a spherical cavity are illustrated with scattering cross secti ons that demonstrate important differences between these types of obst acles. A general result is that the frequency dependence of the scatte ring is defined by the wavelength of the scattered wave rather than th e wavelength of the incident wave. This is consistent with the finding that the intensity of the P-->S scattering is generally much stronger than the S-->P scattering. When averaged over all scattering angles, the mean intensity of the P-->S converted waves is 2V(p)(2)/V-s(4) tim es the mean intensity of the S-->P converted waves, and this ratio is independent of frequency. The exact solutions reduce to simple and eas ily used expressions in the case of the low frequency (Rayleigh) appro ximation and the low contrast (Rayleigh-Born) approximation. The case of energy absorbing inclusions can also be obtained by assigning compl ex values to the elastic parameters, which leads to the result that an increase in attenuation within the inclusion causes an increased scat tering cross section with a marked preference for scattered S waves. T he complete generality of the results is demonstrated by showing waves scattered by the earth's core in the time domain, an example of high- frequency scattering that reveals a very complex relationship between geometrical arrivals and diffracted waves.