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A Mathematical Formulation of Accelerating Moment Release based on the Stress Accumulation Model

Mignan Annaud, Geoffrey C. King, & David Bowman

Published July 2007, SCEC Contribution #1079

Large earthquakes can be preceded by a period of accelerating seismic activity of moderate-sized earthquakes. This phenomenon, usually termed accelerating moment release, has yet to be clearly understood. A new mathematical formulation of accelerating moment release is obtained from simple stress transfer considerations, following the recently proposed stress accumulation model. This model, based on the concept of elastic rebound, simulates accelerating seismicity from theoretical stress changes during an idealized seismic cycle. In this view, accelerating moment release is simply the consequence of the decrease, due to loading, of the size of a stress shadow due to a previous earthquake. We show that a power law time-to-failure equation can be expressed as a function of the loading rate on the fault that is going to rupture. We also show that the m value, which is the power law exponent, can be defined as m = D/3, with D a parameter that takes into account the geometrical shape of the stress lobes and the distribution of active faults. In the stress accumulation model, the power law is not due to critical processes.

Key Words
scale factor, power law, numerical models, seismic moment, loading, mathematical methods, stress, acceleration, earthquakes

Annaud, M., King, G. C., & Bowman, D. (2007). A Mathematical Formulation of Accelerating Moment Release based on the Stress Accumulation Model. Journal of Geophysical Research, 112(B07308). doi: 10.1029/2006JB004671.