Amplification of moment and strain energy release due to interaction between different size fault slip zones

Previous work of Rudnicki and Kanamori, which used collinear crack solutions to examine quantitatively the effects of fault slip zone interaction on moment, stress drop, and strain energy release, is extended by considering the effects of interaction between different size slip zones. The calculations demonstrate that the presence of a large preexisting slip zone can substantially amplify the low frequency seismic signal due to slip on a nearby smaller slip zone. For example, if the length of the larger slip zone is l, that of the smaller is l/10, and the distance between the nearest ends of the zones is l/100, the seismic moment due to slip on the larger zone induced by slip on the smaller zone is about 5 times that due to slip on an isolated zone of length l/10. Furthermore, because of the interaction between slip zones, the moment due to slip on the smaller zone is about 2.5 times the value for an isolated zone of the same size and subjected to the same effective stress. Conversely, estimates of stress drop based on the measured value of the moment and the total length on which slip occurs substantially underestimate the actual stress drop. Although the stress drop on the larger slip zone is zero, the induced slip there does contribute to WO, the difference between the strain energy change and the frictional work. In fact, it is demonstrated that WO = τeM/2μ where τe is the effective stress, M is the actual value of the seismic moment, and μ is the shear modulus.