Internal deformation caused by a point dislocation in a uniform elastic sphere

This paper presents a new method of computing internal displacement, stress, strain, and gravitational changes caused by a point dislocation in a spherical Earth model. Specifically, the asymptotic solutions of the radial functions are introduced. The conventional method expresses the deformation field as an infinite series of spherical harmonics, and it cannot avoid the problem of the series not converging near the dislocation. The proposed method using asymptotic solutions can overcome this problem and compute the deformation field even near the dislocation. This paper focuses on deformations in a homogeneous sphere to elucidate the problem and solve it with simplicity. The proposed method is used to compute the volumetric strains caused by four independent dislocation types: vertical strike-slip, vertical dip-slip, horizontal tensile fracturing and vertical tensile fracturing. The effect of sphericity on the deformation field is also investigated by comparing the computational results with those for a homogeneous semi-infinite medium. The discrepancy between the results of the homogeneous sphere and those of the half-space reached up to 15-20 per cent at an epicentral distance of 2 degrees-5 degrees. In particular, large differences were observed in the following cases: (i) the dislocation type is tensile fracturing, (ii) the depth of the source is large and (iii) the strain is measured at a large depth (for any source depth).