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Scattering of elastic waves by nonaxisymmetric three‐dimensional dipping layer
Author(s) -
Eshraghi Hossein,
Dravinski Marijan
Publication year - 1989
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690050405
Subject(s) - mathematics , half space , mathematical analysis , rayleigh wave , plane (geometry) , boundary (topology) , displacement field , displacement (psychology) , rayleigh scattering , scattering , geometry , boundary value problem , surface (topology) , field (mathematics) , surface wave , physics , optics , finite element method , psychology , pure mathematics , psychotherapist , thermodynamics
Using a boundary method, we investigated the scattering of elastic plane harmonic SH, SV, P, and Rayleigh waves by three‐dimensional nonaxisymmetric dipping layers embedded in an elastic half‐space. The valley was subjected to incident Rayleigh wave and oblique incident SH, SV, and P waves. The method utilized spherical wave functions to express the unknown scattered field. These functions satisfy the equation of motion and radiation conditions at infinity but they do not satisfy the stress‐free boundary conditions at the surface of the half‐space. The boundary and continuity conditions are imposed locally in the least‐square‐sense at several points on the layer interface and on the surface of the half‐space. A comparative study was done to examine the validity and limitations of the two‐dimensional approximations (antiplane and plane strain models) of three‐dimensional models. It is demonstrated that the two‐dimensional approximations may be inadequate to represent actual displacement field for three‐dimensional irregularities.