Constraints on the Energy Budget of Deep Earthquakes

Processes such as melting and thermal shear instability have been suggested as mechanisms for deep earthquake generation, which is still not understood. If such displacement-driven processes are important in deep earthquake rupture, then an effect on the energy budget may be expected. Therefore, we determine seismically-radiated energies and stress drops (from corner frequency), and examine these for moment-dependence of the seismically-radiated energy to moment ratio and seismic efficiency estimates. We calculate source spectra for 111 globally-distributed earthquakes with depths from 100 to 650 km and Mw from 6.3 to 8.3. The spectra are computed from teleseismic broadband P waves recorded by the GSN. We correct for instrument response, depth-dependent attenuation, radiation pattern, geometrical spreading, and near-source velocity. Squared velocity spectra are integrated and scaled to yield the seismically-radiated energy. The ratio of radiated seismic energy to moment times rigidity gives the apparent stress. For these earthquakes, this parameter has more than an order of magnitude scatter. A modest change in apparent stress over this moment range could occur, but is not resolvable in the scatter. Apparent stresses appear to increase by about a factor of two with depth. Static stress drop can be estimated from the spectral corner frequency, but it is well to bear in mind that this requires the assumption of a rupture velocity. Static stress drops estimated from corner frequencies vary more than two orders of magnitude for these events. An upper bound on the seismic efficiency can be computed from twice the apparent stress divided by the static stress drop. This bound, the Savage-Wood efficiency, is found to be greater than 0.25 for all events, and may increase slightly with moment. The Savage-Wood efficiency of events in the 350 to 550 km depth range is about three times higher than that of events above and below, mainly because static stress drops are smaller. Our previous studies have found events from 350 to 550 km depth to rupture longer with measurably more complexity, and with far fewer aftershocks. In these results, independent, but scarce, evidence that rupture velocity may differ significantly from 0.8 of shear velocity (such as for the 1994 Bolivian earthquake) was not taken into account. The difficulty in separating static stress drop from rupture velocity using only durations or corner frequencies remains. In some ways seismically-radiated energy is more reliably estimated than static stress drop, unless independent information on the spatial extent of rupture is available from surface rupture or aftershocks. To the extent that rupture velocity does not vary systematically with moment, our preliminary assessment is that the effect on the energy budget of displacement-driven processes such as melting or thermal shear instability does not change markedly and systematically for deep earthquakes over the magnitude range studied here.