Seismic moment tensor representations and radiation patterns in unbounded media with elipsoidal cavities driven by low frequency pressure

Seismic waves generated in elastic media by ellipsoidal cavities driven by low frequency pressure can be solved by Eshelby’s method. In this paper we prove that this method, originally presented for elastostatic ellipsoidal inclusion problems, can also be applied to dynamic problems on the assumption that wavelengths are much longer than the dimensions of cavities. Comparison between the approximate solution for spherical cavities and its relevant precise solution shows that this method may be used for radii of cavities smaller than 100 m and for frequencies below 10 Hz. By this approach we show that, for low frequency seismic waves in the far-field an explosive load on an ellipsoidal cavity can be equivalent to three dipoles oriented along the principal axes of that cavity. Seismic radiation patterns are given analytically and results thus obtained show that an explosion detonated in an ellipsoidal cavity may radiate significant S waves.