Surface deformation and energy release rates for constant stress drop slip zones in an elastic half‐space

Abstract

Free surface displacements, stress intensity factors, and energy release rates are calculated for planar slip zones in an elastic half‐space subjected to a prescribed shear stress drop. Although the method can treat arbitrarily shaped planar zones and distributed stress drops, for simplicity, results are presented only for circular and elliptic zones and uniform stress drops. Calculations of the stress intensity factors and energy release rates for various geometries indicate that solutions for the half‐space differ by less than 10% from those in the full space if the distance from the slip zone center to the free surface is greater than the downdip width of the slip zone. In addition, the influence of the free surface is greater for decreasing dip angle. For slip zones that are near the free surface and, especially, those that break the surface there is a coupling between slip and normal relative displacement. That is, for a prescribed shear stress drop and zero normal stress change, slip induces relative normal displacement. As example applications, these solutions are used to reexamine the coseismic geodetic data from three earthquakes: 1966 Parkfield, 1983 Borah Peak, and 1987 Whittier Narrows. The geometries, moments, and stress drops are similar to those inferred in previous studies using dislocation methods. However, the stress drop inferred here may be more reliable because stress drop is one of the parameters adjusted to fit the observed surface deformations. In addition, the method makes it possible to estimate the critical energy release rate at the termination of rupture. Values for the Parkfield, Borah Peak, and Whittier Narrows earthquakes are 1.5.×106 J/m2, 1.2×106 J/m2, and 2×108 J/m2, respectively.