Slip Complexity in a Crustal-Plane Model of an Earthquake Fault.

We study numerically the behavior of a two-dimensional elastic plate (a crustal plane) that terminates along one of its edges at a fault boundary. Slip-weakening friction at the boundary, inertial dynamics in the bulk, and uniform slow loading via elastic coupling to a substrate combine to produce a complex, deterministically chaotic sequence of slipping events. We observe a power-law distribution of small events and an excess of large events. For the small events, the moments scale with rupture length in a manner that is consistent with seismological observations. For the large events, rupture occurs in the form of narrow propagating pulses. [S0031-9007(96)00703-X] PACS numbers: 91.30. Bi, 03.40. Dz, 05.45. + b, 64.60. Ht The discovery of dynamic complexity in the uniform, one-dimensional Burridge-Knopoff (BK) model of an earthquake fault [1,2] has brought new urgency to some questions about models of seismic sources. Perhaps the most pressing of these questions concerns the role of elasticity in the crustal plane—an ingredient that is necessarily missing in any one-dimensional model but which must be important for an understanding of the dynamics of slipping events. Off-fault elasticity is relevant to many features of real earthquake faults such as stress concentrations at rupture fronts, long-range elastic interactions, and seismic radiation. Previous studies [3‐7] indicate the following: The completely uniform, one-dimensional BK model, with velocity-weakening stick-slip friction, is a deterministically chaotic dynamical system that exhibits a broad range of earthquake-like events. The frequency-magnitude distribution for these events includes a scaling region of small localized events that is qualitatively similar to a Gutenberg-Richter (GR) law [8], and a region of large delocalized events whose frequency exceeds that of the extrapolated GR law and which account for most of the moment release. The large events propagate along the fault at roughly the sound speed in the form of “Heaton pulses” [9]. In order to be well posed mathematically, the model requires a cutoff or an ad hoc mechanism for initiating rupture at very small length scales. The questions of whether such mechanisms imply inherent discreteness of these models and whether that discreteness, in turn, implies the need for small-scale heterogeneity in realistic fault models are beyond the scope of this investigation. The important point is that the large-scale properties—complexity of large events and existence of a GR regime—are independent of the discretization length or the heterogeneity scale, and therefore appear to be robust features of this class of models. Our purpose in the investigations reported here has been to test the above features of the one-dimensional BK models in a two-dimensional model that includes elasticity in the crustal plane. Like the one-dimensional models, our two-dimensional model is still a caricature of the physically realistic situation, but it brings us a large step closer to an understanding of the dynamic behavior of this class of systems. It remains unrealistic in at least two respects, both of which are dictated by computational feasibility. First, our crustal plane is an elastic plate that moves only normal to itself and is coupled elastically to a rigid substrate. In this way, we obtain an essential simplification of our equations of motion and retain a very important dynamic time scale associated with coupling