Point sources of elastic deformation: elementary sources, dynamic displacements

Abstract

We construct a catalogue of all the possible elementary point sources of seismic waves. There are three general classes of sources, two spheroidal and one toroidal. We consider excitation functions for these point-like sources as well as for sources of finite size in far-, intermediate- and near-field for an infinite homogeneous isotropic medium. The sources corresponding to seismic-moment tensors for the second-, third- and fourth-ranks are considered in more detail; we identify 10 different seismic sources in this range: one monopole, two or three dipoles, three quadrupoles, etc. For the step-function of the scalar seismic-moment release, the amplitude spectrum for the third-rank sources is proportional to the angular frequency ω in the region below the corner frequency ωcr. The fourth-rank sources have an ω2 spectrum in the same range. The possibility of separate and simultaneous inversion of seismic body-wave data and static deformation data for sources of different order is discussed. Some equivalent-force moment higher-rank sources are ‘shielded’ by lower-rank sources of the same order; the former sources cannot be inverted from seismic data without additional assumptions. Because of their simple radiation pattern, the lower order multipoles, i.e. the monopole and dipoles, are the first sources other than the double-couple which should be considered for inversion.