On energy radiation from seismic sources

Abstract

This note clarifies the relationships among various expressions for the energy radiated by elastodynamic seismic sources. The radiated energy can be expressed in terms of the far-field particle velocities provided that the stressparticle velocity relationship asymptotically approaches the plane wave relationship with increasing distance from the source. This condition is satisfied for all sources that can be characterized by a moment density tensor. For the case in which the source can be characterized as a point, i.e., the wavelengths of all emitted radiation are much greater than source dimensions, the radiated energy is expressed in terms of the moment tensor. The relation between these far-field representations and Kostrov's representation of radiated energy in terms of fault surface traction and particle velocity is established. Kostrov's representation is arranged in various forms to reveal the source of radiated energy as the deviations of the fault surface tractions and particle velocities from the values which would occur during quasi-static fault motion between the same end states. Moreover, the excess of the static strain energy change over the work done by the fault surface tractions, called Wo by Kanamori, is shown to be a good approximation to the radiated energy when fault propagation speed is near the Rayleigh wave velocity and the time rate of change of fault surface traction is small.