Dependency of supershear transition and ground motion on the autocorrelation of initial stress

Theoretical and observational studies show that earthquakes on strike slip faults can have rupture speeds exceeding the shear wave speed. Due to the close relationship between the rupture velocity and the radiated wave field, it is important to understand the conditions leading to supershear ruptures and their effect on the resulting ground motion. We compute dynamic strike slip ruptures in a 3D elastic half space using heterogeneous frictional properties on faults that are 60 km long. We use a grid spacing of 60 m allowing us to compute ground motion for frequencies from 0 to 5 Hz. We analyze the resulting ground motion using isochrones to explain phenomena we observe. We model the amplitudes of the initial shear stress as a self-similar random field with Cauchy distributed amplitudes. The wavenumber amplitude spectrum of initial stress decays as a power law with exponent v that controls the decay and the spatial correlation of the initial stress. The faster the decay (corresponding to larger value of v), the more correlated is the stress on the fault, i.e., the stress field appears spatially smoother. The strength on the fault is computed under the assumption of a constant S-factor, where S is the ratio of strength excess over stress drop. On a fault with uniform strength and stress drop the S-factor has to be less than a critical value for the supershear transition to occur. For models with heterogeneous initial stress we find that both the S-factor and the value of the spectral decay constant v affect the occurrence of supershear rupture. We observe that for a given, but small enough. S-factor a smooth model (v >= 2) can run at supershear speed while a rough model (v similar to 1) will rupture at subshear speeds for the same S-factor. Based on the theory of fracture, a non-dimensional number K was introduced to quantify the condition when a transition to supershear rupture velocity can occur during an earthquake. Transition will occur when K exceeds a critical value. We introduce a modified dimensionless parameter K-ac that is based on the original parameter K. The parameter K-ac incorporates a length scale W-ac that reflects the degree of the autocorrelation of the stress field. We compute K, for a large number of available dynamic ruptures that propagate at subshear and supershear speeds and find: i) there is a critical value K-ac((c)) below which all ruptures propagate subshear; ii) for values larger than K-ac((c)) there is only a finite probability that the rupture goes supershear, i.e. it is a necessary but not a sufficient condition for the occurrence of supershear rupture propagation. (C) 2010 Elsevier B.V. All rights reserved.