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Surface strain accumulation and the seismic moment tensor

U.S. Geological Survey, 345 Middlefield Road, Menlo Park, California 94025

Abstract

Although the scalar moment accumulation rate within the seismogenic zone beneath a given area is sometimes deduced from the observed average surface strain accumulation rate over that same area (e.g., Working Group on California Earthquake Probabilities, 1995), the correspondence between the two is very uncertain. The equivalence between surface strain accumulation and scalar moment accumulation is based on Kostrov's (1974) relation between the average strain rate over a volume and the moment-rate tensor for that volume. The average strain rate over the volume is replaced by the average strain rate measured at the free surface to deduce an approximate moment-rate tensor. Only in exceptional circumstances will that moment-rate tensor correspond to a double-couple mechanism, a mechanism that can be represented by a scalar moment accumulation rate. More generally, the moment tensor must be resolved into the superposition of two or more double-couple mechanisms, and that resolution can be done in many ways, each with its own scalar moment rate. Thus the resolution is not unique. This is demonstrated by deducing scalar moment accumulation rates for a GPS network that covers most of California south of San Francisco. It is shown that resolutions into different double-couple mechanisms lead to scalar moment accumulation rates differing by factors of 2. We suggest that the minimum scalar moment rate equivalent to principal surface strain rates ₁ and ₂ acting over the area A is M₀^(min) = 2µHA Max (¦₁¦, ¦₂¦, ¦₁ + ₂¦), where µ is the rigidity and H the depth of seismogenic zone, and the function Max is equal to the largest of its arguments. Within the uncertainites of measurement, the scalar moment accumulation rate in southern California based on that approximation is in balance with the average historic seismic moment release rate so that no current earthquake deficit need be accumulating.