Abstract
Using spherical vector wave functions, the general problem of the scattering of plane transverse waves by a transeismic sphere is formulated. The far-field result for a small sphere is presented. One part of the scattered field arises from the density contrast between the sphere and the external medium, and another part arises from the rigidity contrast. Each contrast results in a scattered compressional wave having radial displacements, and a transverse wave having displacements parallel to the sphere's surface. The four fields are represented graphically. The density contrast produces a dipolar compressional field and a toroidal transverse field. The displacements of both are symmetric about a line in the direction of polarization of the incident wave, and are otherwise independent of the direction of incidence. The rigidity contrast produces a quadrupolar compressional field, and a transverse field for which the directivity pattern is given. A model is presented which gives the relative displacement directions of this last field. The scattered fields due to the density contrast behave as though they were due to a pure displacement oscillation of the sphere, and those due to the rigidity contrast as though they were due to a pure distortional oscillation.
