Effects of fault interaction on moment, stress drop, and strain energy release

Solutions for collinear shear cracks are used to examine quantitatively the effects of fault slip zone interaction on determinations of moment, stress drop, and static energy release. Two models, the barrier model and the asperity model, are considered. In the asperity model, the actual distribution of strengths on a fault plane is idealized as a combination of two limiting cases: areas which slip freely at a uniform value of a residual friction stress and unbroken ligaments or ‘asperities’ across which slip occurs only at the time of a seismic event. In the barrier model, slip zones separated by unbroken ligaments (barriers) are introduced into a uniformly stressed medium to approximate the nonuniform fault propagation proposed by Das and Aki. The strain energy change due to introducing collinear slip zones or due to breaking the asperities between them is shown to be given by the usual formula for an isolated slip zone with the stress drop replaced by the effective stress. Significant interaction between slip zones occurs only if the length of the asperity is less than half the length of the slip zones. For the case of two collinear slip zones, fracture of the asperity between them is shown to cause a large moment primarily because of the additional displacement which is induced on the adjacent slip zones. For example, if the asperity length is 0.05l, where l is the length of each adjacent slip zone, then fracture of the asperity causes a moment almost 1.8 times the moment caused by introducing a slip zone of length l. For two collinear slip zones, the local stress drop due to fracture of the separating asperity is shown to become unbounded as the asperity length goes to zero, but in the same limit the stress drop averaged over the entire fault length is approximately equal to the apparent stress drop inferred for an isolated fault of the same moment and total fault length. This apparent stress drop is approximately equal (within a factor of 2 or 3) to the effective stress and hence can be used in the usual formula to give a good estimate of the strain energy change. For the barrier model, numerical results are given for the ratio of the stress drop calculated on the assumption of an isolated slip zone to the true stress drop. For example, in the case of two collinear slip zones of length l separated by a barrier of length 0.2l, this ratio is 0.5, whereas for a barrier length equal to that of the adjacent slip zones, the ratio is 0.24. Stress drop estimates become worse with increasing number of fault segments.