Point Sources of Elastic Deformation: Elementary Sources, Static Displacements

ABSTRACT

Summary. We construct a catalogue of all possible elementary point sources for static deformation in an elastic solid. the familiar double-couples, CLVD's, centres of compression and dilatation, etc., are all members of the complete catalogue. the sources are classified according to the rank of the seismic moment tensor, and according to the weight (or order) of the irreducible tensor representation of the 3-D rotation group. These sources can be classified as belonging to one of three general classes. the static excitation functions are calculated for an infinite, homogeneous, isotropic medium for all these sources. We show that, except for sources belonging to these three general classes, all other sources — which are numerous for the tensors of high rank — are null static sources. That is, sources that do not produce any static displacement outside of the source region. Due to the presence of null sources, an inversion of the static deformation data is non-unique. the expansion of the equivalent-force tensors and the stress glut tensors (or seismic moment tensors) into a set of the symmetric trace-free source tensors is proposed. the sources corresponding to seismic moment tensors of the second, third and fourth ranks are considered in more detail. We identify the third-rank sources with rotational dislocations or disclinations.