Coseismic displacements caused by point dislocations in a three-dimensional heterogeneous, spherical earth model

We present a method to study the coseismic displacements caused by point dislocations in a 3-D heterogeneous, spherical earth model. Specifically, first we express the solutions by the sum of unperturbed displacements on a spherically symmetric earth model and the effects of the Earth's laterally inhomogeneous structures (3-D effect). Then we deliberately decompose the 3-D effect into two contributions: the effect of seismic sources and the effect of the Earth's lateral increments, which are obtainable, respectively, by perturbation of seismic source functions and perturbation of equilibrium equation. Next we present new formulations for six point seismic sources: a vertical strike-slip, two vertical dip-slips perpendicular to each other and three tensile openings on three perpendicular planes. A combination of the six dislocations is useful to compute the 3-D effect resulting from an arbitrary seismic source at an arbitrary position. Finally, based on a 3-D earth model we calculate the coseismic displacements resulting from three types of point dislocations. Results show that the maximum 3-D effect on coseismic displacements, which varies concomitantly with the dislocation type and the source depth, is about 1–2 per cent of the corresponding unperturbed solutions. Among those parameters the effect due to the heterogeneities in S-wave velocity is biggest.