Inverting for slip on three-dimensional fault surfaces using angular dislocations

The increasing quality of geodetic data (synthetic aperture radar interferometry [InSAR] dense Global Positioning System [GPS] arrays) now available to geophysicists and geologists are not fully exploited in slip-inversion procedures. Most common methods of inversion use rectangular dislocation segments to model fault ruptures and therefore oversimplify fault geometries. These geometric simplifications can lead to inconsistencies when inverting for slip on earthquake faults, and they preclude a more complete understanding of the role of fault geometry in the earthquake process. We have developed a new three-dimensional slip-inversion method based on the analytical solution for an angular dislocation in a linear-elastic, homogeneous, isotropic, half-space. The approach uses the boundary element code Poly3D that employs a set of planar triangular elements of constant displacement discontinuity to model fault surfaces. The use of triangulated surfaces as discontinuities permits one to construct fault models that better approximate curved three-dimensional surfaces bounded by curved tiplines: shapes that commonly are imaged by three-dimensional reflection seismic data and inferred from relocated aftershock data. We demonstrate the method's ability to model three-dimensional rupture geometries by inverting for slip associated with the 1999 Hector Mine earthquake. The resulting model avoids displacement anomalies associated with the overlapping rectangular dislocations used in previous models, improving the fit to the geodetic data by 32%, and honors the observed surface ruptures, thereby allowing more direct comparisons between geologic and geodetic data on slip distributions.