A point dislocation in a layered, transversely isotropic and self-gravitating Earth. Part IV: exact asymptotic solutions of dislocation Love numbers for the special case of isotropy

Abstract

SUMMARYWe derive exact asymptotic solutions for the static deformation due to a concentrated or point-like dislocation in a spherical, layered, elastic, isotropic and self-gravitating Earth. The exact asymptotic solutions are quite general and can provide the dislocation Love numbers on the Earth's surface, near the dislocation or ‘source’, and close to any layer interface or boundary. We also discuss the special case where both the source and field points are located on the Earth's surface. We compare our exact asymptotic solutions with previous results obtained from the analytical dual variable and position (DVP) method via curve fitting. Our comparison confirms that the analytical DVP results converge to the exact asymptotic solutions. These new exact asymptotic solutions are particularly helpful when evaluating slowly convergent series of Green's functions using a Kummer transformation, anywhere within the layered Earth, especially for field points located very close to the point dislocation or source.