Static deformation of a spherical earth model by internal dislocations

Abstract

A localized displacement dislocation is placed inside a homogeneous non-gravitating elastic sphere. The ensuing deformation is obtained in the form of rapidly converging series for arbitrary values of the Poisson ratio and the source parameters. Surface displacements and strains are computed for various sources for an average earth model. The numerical results are mapped on tangential planes and displayed in several forms. It is found that in the range 30° < θ < 120° the elongation strains fall off with the epicentral distance like Δ^−α where 1$14$ < α < 6, provided one proceeds along an arc which does not intersect a nodal line. In the lower hemisphere (90° < θ < 180°) relative to the source, seismic events such as the Chilean earthquake of May, 1960, should produce strains of the order of 10⁻⁹, which are on the threshold of detectability of modern extensometers, tiltmeters and rotationmeters. The range in which the half-space approximation is valid is determined. It is demonstrated that global deformation patterns of major earthquakes can serve as a useful diagnostic tool for recovering the source's spatial characteristics.