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Scattering of Elastic Waves by a Spherical Inclusion

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Scientific rept. no. 1

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A complete and exact solution for the problem of an incident P wave scattered by an elastic spherical inclusion is presented and described. The solution can be obtained from either analytical formulas or stable numerical procedures. A method of estimating the number of terms that must be retained in the harmonic series in order to achieve a specified accuracy is given. The results are investigated by calculating synthetic seismograms, scattering diagrams, and scattering cross sections for a broad frequency band and for both low-velocity and high-velocity inclusions. The fields within the shadow zone are formed primarily from three different types of waves, P waves transmitted through the sphere, P waves diffracted around the sphere, and S waves converted at the boundary of the sphere. Starting with the exact solution for the scattering of a plane P wave by a homogeneous spherical inclusion, various types of approximate solutions are developed and discussed. The standard Rayleigh and Mie approximations are extended to the case of inclusions having arbitrary contrasts in material properties. For the low contrast case, solutions are developed which are valid over a wide frequency range. Several aspects of these solutions are discussed, including the importance of near-field terms and the relative strength of the scattered P and S fields. The various types of approximate solutions are compared with each other and with the exact solution by calculating and displaying their normalized scattering cross sections.

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  • Seismology

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