Mapping apparent stress and energy radiation over fault zones of major earthquakes

Using published slip models for five major earthquakes, 1979 Imperial Valley, 1989 Loma Prieta, 1992 Landers, 1994 Northridge, and 1995 Kobe, we produce maps of apparent stress and radiated seismic energy over their fault surfaces. The slip models, obtained by inverting seismic and geodetic data, entail the division of the fault surfaces into many subfaults for which the time histories of seismic slip are determined. To estimate the seismic energy radiated by each subfault, we measure the near-fault seismic-energy flux from the time-dependent slip there and then multiply by a function of rupture velocity to obtain the corresponding energy that propagates into the far-field. This function, the ratio of far-field to near-fault energy, is typically less than 1/3, inasmuch as most of the near-fault energy remains near the fault and is associated with permanent earthquake deformation. Adding the energy contributions from all of the subfaults yields an estimate of the total seismic energy, which can be compared with independent energy estimates based on seismic-energy flux measured in the far-field, often at teleseismic distances. Estimates of seismic energy based on slip models are robust, in that different models, for a given earthquake, yield energy estimates that are in close agreement. Moreover, the slip-model estimates of energy are generally in good accord with independent estimates by others, based on regional or teleseismic data. Apparent stress is estimated for each subfault by dividing the corresponding seismic moment into the radiated energy. Distributions of apparent stress over an earthquake fault zone show considerable heterogeneity, with peak values that are typically about double the whole-earthquake values (based on the ratio of seismic energy to seismic moment). The range of apparent stresses estimated for subfaults of the events studied here is similar to the range of apparent stresses for earthquakes in continental settings, with peak values of about 8 MPa in each case. For earthquakes in compressional tectonic settings, peak apparent stresses at a given depth are substantially greater than corresponding peak values from events in extensional settings; this suggests that crustal strength, inferred from laboratory measurements, may be a limiting factor. Lower bounds on shear stresses inferred from the apparent stress distribution of the 1995 Kobe earthquake are consistent with tectonic-stress estimates reported by Spudich et al. (1998), based partly on slip-vector rake changes.