COLLECTION AND ANALYSIS OF SEISMIC WAVE PROPAGATION DATA. SUPPLEMENT 3: SCATTERING OF ELASTIC PLANE WAVES BY AN ELLIPTICAL INCLUSION OR CAVITY,
Abstract
Previous studies of the scattering of elastic waves have been limited to spherical and cylindrical scatterers. The present study is an investigation of the scattering of a plane compressional wave incident from an arbitrary direction on an elliptical obstacle (either cavity or a rigid inclusion). By varying the ellipticity, shapes ranging from the finite-length slit to the cylinder may be considered. Analytical solutions are obtained for the scattered displacements in the form of product series expansions valid throughout the entire media. Due to the interaction of P-waves and S-waves at the boundary of the scatterer, the boundary conditions are not separable. As a consequence the coefficients of the series solution are determined from a coupled, infinite system of algebraic equations. The solutions are highly convergent, however, and the system can be truncated to a reasonable size for numerical computation. In addition, simplified asymptotic solutions are given for the far-field displacements. It is found that the scattered displacements attenuate like r to the minus one-half power, with the radial displacement associated with the dilatational potential and the tangential displacement associated with the shear potential. The asymptotic solutions are used to obtain the scattered radiation pattern in the far field. Finally, for the special case of a slit the radiation patterns for different directions of incident wave and different ratios of wave length to slit length are compared. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1966
- Accession Number
- AD0489526
Entities
People
- Ivor K. Mcivor
Organizations
- University of Michigan