Previously derived expressions for the total energy and energy spectral density of elastic waves radiated by a propagating fault are rewritten in terms of a spacio-temporal autocorrelation of the acceleration of relative displacement over the fault plane. This is interpreted in a statistical sense as the average autocorrelation over an ensemble of earthquakes. An explicit form of autocorrelation function is assumed, depending upon two parameters, a correlation length, and a correlation time, and the total energy and energy spectral density are derived in terms of these parameters. By using scaling laws due to Båth and Duda for earthquake volume and radiation efficiency as functions of magnitude, the statistical parameters may also be related to magnitude.

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