Epicentre solutions for point multipole sources in an elastic half-space

Abstract

Expressions given previously for the dynamic elastic Green's function of a half-space have been in the form of a single integral. These expressions clearly reduce to closed analytic forms when the field (receiver) point is at the epicentre, but have not formerly been written out. Broad-band acoustic emission experiments have now provided motivation to do so. A formalism due to Willis (1973) is used to obtain analytic expressions for the space derivatives, to any order, of the displacement field below a point impulsive force to the surface of a half-space. A reciprocal theorem then yields the epicentre surface displacements due to a buried point force multipole source. A few examples are illustrated graphically.