Asymptotic Dislocation Theory of a Spherical Earth for Calculating Co-seismic Displacement

This study presents an asymptotic theory for calculating displacements excited by a point dislocation in a spherically symmetric earth model as an approximation of the dislocation theory for a spherical earth model (Sun et al., 1996), employing the reciprocity theorem (Okubo, 1993) and asymptotic solutions of an elastic earth to tidal, load and shear forces (Okubo, 1988). This theory is mathematically simple and physically reasonable since it reflects the earth’s sphericity and radial structure. Comparison of the asymptotic results with both the exact results and the corresponding flat-earth results shows that for any distances the exact results are approximated better by the asymptotic results than by the flat-earth results. Especially, the asymptotic theory is obviously superior to the flat-earth theory due to a big sphericity effect for the tensile opening on a vertical fault. Owing to its mathematical simplicity, this theory can be applied easily to calculate co-seismic displacements. The validity of the theory for a stratified earth needs to be further tested and discussed.