Analyzing Slip Models to Estimate Distributions of Seismic Energy Radiated by Earthquakes

From information provided by slip models developed for major earthquakes, it is straightforward to estimate the seismic energy flux adjacent to a given patch of the larger fault zone. This near-fault energy flux, estimated from the time-dependent slip of the adjacent subfault, however, is a poor approximation to the seismic energy that propagates into the far-field. Indeed, most of the near-fault energy remains in the vicinity of the earthquake and is associated with the static deformation there. Analysis of a seismic source model that incorporates the physics of dynamic rupture propagation (M-model of Boatwright, 1980) indicates that the ratio of far-field to near-fault energy depends only on the rupture velocity, increasing from 0.11 to 0.40 as rupture velocity increases from 0.6 to 0.95 of the shear wave speed. Observations of stress changes associated with stick-slip friction events in the laboratory are consistent with these low ratios. Thus, one can estimate the desired far-field energy from measurements of the near-fault energy flux using the rupture velocity specified for the slip model. We have applied this procedure, to convert near-fault to far-field energy, to estimate distributions of seismic energy radiation and apparent stress over the fault surfaces of five earthquakes for which slip models have been published: 1979 Imperial Valley, 1989 Loma Prieta, 1992 Landers, 1994 Northridge, and 1995 Kobe. From a given slip model, the total seismic energy, estimated by summing the contributions from all of the subfaults, agrees well with published teleseismic and regional estimates. Moreover, different slip models for the same earthquake yield estimates of radiated energy that are similar. Apparent stresses for subfaults of these modeled fault zones are quite inhomogeneous with values that generally increase with depth, ranging up to about 8 MPa. Moreover, it appears that the strength of the crust, as inferred from laboratory experiments, may be the factor that limits the level of apparent stress at a given depth in a particular tectonic setting. Boatwright, J., A spectral theory for circular seismic sources; Simple estimates of source dimension, dynamic stress drop, and radiated seismic energy, Bull. Seismol. Soc. Am., 70, 1-27, 1980.