An Application of the Energy-Moment Tensor Relation to Estimation of Seismic Energy Radiated by Point and Line Sources

We derive expressions for the seismic energy radiated from point and line sources in terms of the moment tensor of the source. Using moment tensors based on previously published fault plane solutions for the 1960 Chilean earthquake, the precursor to that event, and the 1964 Alaskan earthquake, we present power spectra for various fault length, rupture velocity, and source duration combinations. The results showed that, for point sources, a half-sine-wave increase in applied moment is necessary to insure a finite radiated energy asymptote at high frequencies. The results for a line source with finite propagation velocity were smoother than those for an equivalent point source. However, for reasonable combinations of fault plane parameters, the total radiated energy did not differ appreciably between the two source models. On the other hand, the energy radiated from a moving line source is quite sensitive to the rupture propagation velocity when that approaches the phase velocity of a mode. In our numerical experiments for these three events, we were always able to find combinations of source parameters which agreed with those from other investigators and that produced radiated energies consistent with either independent estimates or reported Ms values.