Va. Korneev et Lr. Johnson, SCATTERING OF P-WAVE AND S-WAVE BY A SPHERICALLY SYMMETRICAL INCLUSION, Pure and Applied Geophysics, 147(4), 1996, pp. 675-718
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.