Path Durations for Use in the Stochastic-Method Simulation of Ground Motions

The stochastic method of ground-motion simulation assumes that the energy in a target spectrum is spread over a duration D T .D T is generally decomposed into the duration due to source effects (D S ) and to path effects (D P ).For the most commonly used source, seismological theory directly relates D S to the source corner frequency, accounting for the magnitude scaling of D T .In contrast, D P is related to propagation effects that are more difficult to represent by analytic equations based on the physics of the process.We are primarily motivated to revisit D T because the function currently employed by many implementations of the stochastic method for active tectonic regions underpredicts observed durations, leading to an overprediction of ground motions for a given target spectrum.Further, there is some inconsistency in the literature regarding which empirical duration corresponds to D T .Thus, we begin by clarifying the relationship between empirical durations and D T as used in the first author's implementation of the stochastic method, and then we develop a new D P relationship.The new D P function gives significantly longer durations than in the previous D P function, but the relative contribution of D P to D T still diminishes with increasing magnitude.Thus, this correction is more important for small events or subfaults of larger events modeled with the stochastic finite-fault method.