On the determination of radiated seismic energy and related source parameters

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Abstract
The determination of radiated seismic energy on the one hand, and of source size and static stress drop on the other, depends in principle on a representation of different parts of the source spectrum. In practice with band-limited data from a sparse network, the required source parameterization is often the same. Spectral models parameterized by the source's central moments of degree zero and two are introduced as an approximation to the general representation of the amplitude spectrum in terms of the central moments of even degree. Phase spectra are not used, apart from polarity. These models are shown to simulate well the principal features of common circular and Haskell type of models, including the corner frequency shift of P waves with respect to S waves, and the relation between rupture velocity and maximum seismic efficiency. Spectral bandwidths and the determination of radiated energy and apparent stress are contrasted to time domain pulse widths and the determination of source size and static stress drop in these models. The consequences of a reduced number of source parameters are examined, in particular for circular models and point source approximations; in these cases, results for radiated energy can be obtained in closed form. The scaling of radiated energy with moment is assumed to be linear for simple sources, but in stochastic models of complex sources the scaling may be between linear and quadratic. A relatively large increase of radiated energy with moment would be accompanied by an underestimate of source size and an overestimate of stress drop. However, the determination of radiated energy may still be correct.

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