Elastic Scattering by a Spherical Inclusion
Abstract
The scattering problem of an arbitrary elastic wave incident upon a spherically symmetric inclusion is considered. General results expressed in the form of canonical scattering coefficients are obtained for the cases of incident P waves and incident S waves. Optical theorems relating the scattering cross- section to the amplitude of the scattered field in the forward direction are also derived for both of these eases. Analytical expressions for scattering coefficients of a homogeneous elastic sphere, a sphere filled by fluid, and a spherical cavity are presented, and scattering cross-sections are calculated for these different types of obstacles. It is shown that the scattering scale factor for low frequencies is defined by the wavelength of the scattered wave rather than the wavelength of the incident wave. Low velocity fluid inclusions have a resonant type of scattering with numerous peaks in the spectrum. Various approximate solutions are derived from the exact solutions, including the low contrast (Born) case and the low frequency (Rayleigh) case. The modifications of the low contrast solution necessary to maintain conservation of energy are discussed. Low-frequency asymptotics of the scattering coefficients for a homogeneous sphere of arbitrary contrast are obtained together with expressions for the scattered fields from both P and S incident waves. These expressions can be used for energy absorbing inclusions by assigning complex values to the elastic parameters. Waves scattered by the earth's core are examined as an example of high-frequency scattering.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 30, 1993
- Accession Number
- ADA274713
Entities
People
- Lane R. Johnson
- Valeri A. Korneev
Organizations
- University of California, Berkeley