Fault branching and rupture directivity

Could the directivity of a complex earthquake be inferred from the ruptured fault branches it created? Typically, branches develop in forward orientation, making acute angles relative to the propagation direction. Direct backward branching of the same style as the main rupture ( e. g., both right lateral) is disallowed by the stress field at the rupture front. Here we propose another mechanism of backward branching. In that mechanism, rupture stops along one fault strand, radiates stress to a neighboring strand, nucleates there, and develops bilaterally, generating a backward branch. Such makes diagnosing directivity of a past earthquake difficult without detailed knowledge of the branching process. As a field example, in the Landers 1992 earthquake, rupture stopped at the northern end of the Kickapoo fault, jumped onto the Homestead Valley fault, and developed bilaterally there, NNW to continue the main rupture but also SSE for 4 km forming a backward branch. We develop theoretical principles underlying such rupture transitions, partly from elastostatic stress analysis, and then simulate the Landers example numerically using a two-dimensional elastodynamic boundary integral equation formulation incorporating slip-weakening rupture. This reproduces the proposed backward branching mechanism based on realistic if simplified fault geometries, prestress orientation corresponding to the region, standard lab friction values for peak strength, and fracture energies characteristic of the Landers event. We also show that the seismic S ratio controls the jumpable distance and that curving of a fault toward its compressional side, like locally along the southeastern Homestead Valley fault, induces near-tip increase of compressive normal stress that slows rupture propagation.