Asymptotic solution of static displacements caused by dislocations in a spherically symmetric Earth

Abstract

This study presents an asymptotic solution of static displacements excited by a point dislocation in a spherical symmetric Earth model as an approximation of the dislocation theory for a spherical Earth model [Sun et al., 1996]. The solution is mathematically simple and physically reasonable since it reflects Earth sphericity and radial structure. Comparison of the asymptotic results with both the exact results and the corresponding flat Earth results shows that for any distance the exact results are approximated better by the asymptotic results than by the flat Earth results. For a homogeneous sphere, both theoretical and numerical investigations indicate that the solution is valid for all types of seismic sources and for an epicentral distance of at least 20° with a relative error less than 1% compared to results calculated for a spherical Earth model [Sun et al., 1996]. For a vertical strike‐slip source, the asymptotic solution is valid for the entire Earth surface. For the 1066A Earth model, it is found that the asymptotic solutions are sensitive to the vertical derivatives of model parameters. The sensitivity can be used to study the vertical structure of the Earth. It is also found that the sphericity effect can be well reflected in the asymptotic solution, and can reach 20% discrepancy in the near field for a deep source. Owing to its mathematical simplicity, this solution can be applied easily to calculate coseismic displacement, just as the theory for a half‐space Earth model like Okada's [1985].