The Effect of a Shallow Thrust-Fault Reflecting Boundary Condition on Teleseismic Radiated Energy: Study Using Dynamic Finite-Element Rupture Models and Synthetic Body Wave Seismograms

It has been suggested that dislocation models of teleseismic waves may seriously underestimate seismic moments of shallow thrust-fault events (Brune, 1996). Dislocation models allow seismic waves, such as reflected phases, to propagate through the fault boundary unimpeded, i.e., they are "transparent" to seismic radiation. Brune hypothesizes instead that the two sides of the fault separate during rupture creating a reflecting boundary condition that is "opaque" to seismic radiation. If so, then energy becomes trapped in the overhanging wedge, radiated energy to teleseismic distances is reduced, and the moment is underestimated. We tested this by producing and comparing synthetic P and SH seismograms for earthquakes with and without a reflecting or "opaque" fault boundary condition. We used friction laws in dynamic, three-dimensional finite-element models to create slip-histories for models with partially to completely reflecting faults in the Mode II and Mode III directions. The inclusion of gravity created sufficient lithostatic stress that any Mode I opening was negligible. We have three "opaque" models in order of most to least opaque: crack-like (slip-weakening) with zero sliding friction, crack-like with constant sliding friction, and pulse-like (slip- and rate-weakening). The slip-history of our dislocation model with a "transparent" fault boundary condition (Haskell-like model), is the integral of Brune's (1970) far-field time function. Slip-histories for these "opaque" and "transparent" models are normalized such that they have the same potency. In addition, the Haskell-like model slip-history is designed to have the same final slip, peak slip-rate, and slip start times as the pulse-like model at each location on the fault for a close comparison. Synthetic seismograms were calculated for the above four models at a variety of azimuths and epicentral distances, and the peak-to-peak amplitudes were numerically evaluated. Note that we normalized the peak-to-peak amplitudes of the three "opaque" models by the Haskell-like model. Therefore, a peak-to-peak value < 1 indicates that dislocation theory would underestimate the seismic moment of the opaque model and a value > 1 indicates that dislocation theory would overestimate the seismic moment of the opaque model. Our results for the P wave peak-to-peak amplitudes are: 1.64 for crack-like with zero sliding friction, 0.96 for crack-like with constant sliding friction, and 1.09 for pulse-like. For SH waves the values are: 2.02 for crack-like with zero sliding friction, 1.02 for crack-like with constant sliding friction, and 1.05 for pulse-like. Interestingly, two out of the three models (constant sliding friction and pulse-like) have peak-to-peak amplitudes either very close or slightly larger than the "transparent," Haskell-like model. The somewhat unrealistic, zero sliding friction model (which is "opaque" to all Mode II and Mode III sliding) has a larger peak-to-peak amplitude than the Haskell-like, but this can be explained by the fact it oscillates about the equilibrium, zero frequency solution. Thus, it appears that a reflecting boundary condition has little to no effect on the radiated energy to teleseismic distances. If anything, a completely reflecting boundary increases the radiated energy. Hence, we do not find any problem with standard dislocation theory in estimating seismic moment.