Seismic risk of circum-pacific earthquakes I. Strain energy release

Commonly used earthquake “whole process” frequency - magnitude and strain energy - magnitude laws are merged to obtain an analytic expression for an upper bound magnitude to regional earthquake occurrenceM ₃, which is expressed primarily in terms of the annual maximum magnitudeM ₁ and the magnitude equivalent of the annual average total strain energy releaseM ₂. Values ofM ₃ are also estimated graphically from cumulative strain energy release diagrams. Both methods are illustrated by application to the high seismicity of the circum-Pacific belt, using Duda’s (1965) data and regionalisation. Values ofM ₃ obtained analytically, with their uncertainties, are in agreement with those obtained graphically. Empirical relations are then obtained betweenM ₁,M ₂, andM ₃, which could be of general assistance in regional seismic risk considerations if they are found to be of a universal nature. For instance.M ₃ andM ₂ differ by one magnitude unit in subregions of the circum-Pacific.