Static deformation of a multilayered sphere by internal sources

Abstract

The Thomson-Haskell matrix device is used to solve the problem of the static deformation of a multilayered spherical Earth model by buried sources. The model consists of p-1 concentric spherical shells plus an inner core; each shell as well as the core being homogeneous, isotropic and perfectly elastic. The point source is represented as a discontinuity in the motion-stress vector across the spherical surface passing through the source. Explicit series expressions in terms of layer matrices are obtained for the displacements and stresses at any point in the medium for three sources: a vertical strike-slip fault, a vertical dip-slip fault and a centre of explosion. The singular case corresponding to the Legendre polynomial of the first degree (n=1) has been discussed in detail.