Displacement and strain fields due to faulting in a sphere

Abstract

The residual displacement and strain fields are computed at the free surface of a non-gravitating, homogeneous, isotropic, elastic sphere resulting from faulting inside the sphere. As a mathematical representation of faulting, we assume a displacement dislocation surface. The resulting field is exhibited through the use of equi-displacement and equi-strain lines. The effect of the depth of the source is demonstrated by obtaining the field patterns for two focal depths. Detailed calculations reveal that for nearly horizontal and nearly vertical faults, the field due to a dip-slip source shows a strong dependence on the dip angle. A small change in the latter can change both the sign and order of magnitude of the calculated strain. The theory is applied to strain observations from a major earthquake: a comparison is made between the strain steps recorded at Kipapa, Isabella, and the Green Observatory from the Alaska earthquake of March 28, 1964 and the calculated values. It is shown that the theoretical values are within an order of magnitude of the observed values and are of the right sign.