Earthquake rate analysis

Abstract

Earthquake rate analysis explores the quantitative relationship between earthquake occurrence rates and geological deformation rates. One application is the estimation of tectonic deformation rates from seismicity, for comparison with tectonic models. Another application is the use of geological models to help quantify seismic hazards. Seismicity is described by a catalog of the largest earthquakes in the region. The contribution of small earthquakes towards causing geological deformation is insignificant, although the occurrence rate of small events may be predictable from the occurrence rate of large events by a b value relationship. The critical information about each earthquake is its seismic moment, or, better still, its seismic moment tensor. When moment is not available directly, it can be estimated from the earthquake magnitude, although this increases uncertainties considerably. The average annual moment from all the earthquakes in the catalog is the seismic moment rate. Uncertainties in seismic estimates of moment rate arise from the short time period of observations, from the magnitude-moment relationship, from the shape of the distribution function giving number of earthquakes as a function of magnitude and from uncertainties in the physical properties of the Earth near the source. Geological models for deformation rates are described by slip rates on individual faults or by regional strain rates. A regional strain rate can be derived as a limiting case where there are numerous individual faults. Such a strain rate is a particularly useful concept where information about each of the faults is limited. In the case of either faulting or regional strain, the average seismic moment rate is proportional to the deformation rate. Geological uncertainties arise from difficulties in estimating slip rates or strain rates, from fault creep and other aseismic deformation, from uncertainty in the part of the fault that fails during earthquakes and boundaries of the deforming region and from uncertainty about the Earth's physical properties. The seismic moment rate is the critical factor for relating the earthquake occurrence rate and the geological deformation rate. Using this intermediate parameter, one can infer earthquake occurrence rates from deformation rates, or infer deformation rates from earthquake occurrence rates. Generally, it is found that deformation rates and earthquake occurrence rates are consistent within uncertainties. Where both are well constrained, they are generally consistent within a factor of two or three.