Numerical simulations of earthquake source process by a three-dimensional crack model. Part I. Rupture process.

Abstract

A three-dimensional crack propagation is investigated in order to model dynamical rupture process on the fault with non-uniform static strength and sliding frictional stress, which is subjected to a finite shear stress. The displacement-time history on the crack is obtained from numerical solutions for equations of motion with a finite stress fracture criterion. If the strength is uniform and slightly above the initial stress the rupture propagates elliptically with a nearly P wave velocity in the direction of the initial stress and with a nearly S wave velocity in the direction perpendicular to it, but if the strength is at a considerably high level, the rupture propagation tends to become nearly circular with a velocity close to that of S wave. Non-uniform strength distributions considered here are the cases with a line barrier which divides the fault into two parts, with a square-shaped block barrier in the center of the fault, random strength distribution of Weibull's type and a random barrier distribution. These non-uniform distributions sometimes generate multiple shocks. In some cases with a line barrier, the rupture appears to propagate backward as has been observed in the 1964 Alaska, the 1973 Vladiostok, and the 1970 deep Colombian earthquakes. The shape of the rupture front in the second or third event is nearly circular centered at the starting point of the first event, not at the second. This suggests that the triggering mechanism of multiple shocks is the arrival of Block and line barrier can generate nearly the same multiple shock's seismic waves. In the case of random strength distribution with no strong barriers, no unbroken region remains. In the case of random barriers, the rupture propagates irregularly and in some cases there remain unfractured regions. The displacement time history in these cases does not show very complex shapes.