The inverse problem of determining the strength and profile of an incident elastic wave in an isotropic medium, caused by the motion of a rigid spherical inclusion, is one of a class of analogous problems that has interested geophysicists and mechanical engineers.
Mow effectively worked out the problem for the case of an incident P-wave and the relationship between the Fourier transform of the motion of the sphere and the strength of the incident wave was found to be simple enough to invert easily in closed form.
It would seem that Iwashimizu's very concise paper should include Mow's result as well as the analogous result for an incident S-wave. However, Mow's result is not derivable from the third of equations ( ) in reference . In fact, equations ( ) and ( ) do not seem to follow from equations ( ) and ( ). (There is a typographical error in equation ( ).) Equally important, the expressions in equations ( ) and ( ) in this paper are too complicated to recognize, by inspection, the behaviour of the sphere.
It might be useful, therefore, to derive the Fourier transforms of the motion functions in the S-wave case in a form simple enough to invert easily.