The Estimation of Minimum-Misfit Stochastic Models from Empirical Ground-Motion Prediction Equations

In areas of moderate to low seismic activity there is commonly a lack of recorded strong ground motion. As a consequence, the prediction of ground motion expected for hypothetical future earthquakes is often performed by employing em- pirical models from other regions. In this context, Campbell's hybrid empirical ap- proach (Campbell, 2003, 2004) provides a methodological framework to adapt ground-motion prediction equations to arbitrary target regions by using response spectral host-to-target-region-conversion filters. For this purpose, the empirical ground-motion prediction equation has to be quantified in terms of a stochastic model. The problem we address here is how to do this in a systematic way and how to assess the corresponding uncertainties. For the determination of the model param- eters we use a genetic algorithm search. The stochastic model spectra were calculated by using a speed-optimized version of SMSIM (Boore, 2000). For most of the em- pirical ground-motion models, we obtain sets of stochastic models that match the empirical models within the full magnitude and distance ranges of their generating data sets fairly well. The overall quality of fit and the resulting model parameter sets strongly depend on the particular choice of the distance metric used for the stochastic model. We suggest the use of the hypocentral distance metric for the stochastic simulation of strong ground motion because it provides the lowest-misfit stochastic models for most empirical equations. This is in agreement with the results of two recent studies of hypocenter locations in finite-source models which indicate that hypocenters are often located close to regions of large slip (Mai et al., 2005; Mani- ghetti et al., 2005). Because essentially all empirical ground-motion prediction equa- tions contain data from different geographical regions, the model parameters corre- sponding to the lowest-misfit stochastic models cannot necessarily be expected to represent single, physically realizable host regions but to model the generating data sets in an average way. In addition, the differences between the lowest-misfit sto- chastic models and the empirical ground-motion prediction equation are strongly distance, magnitude, and frequency dependent, which, according to the laws of un- certainty propagation, will increase the variance of the corresponding hybrid empir- ical model predictions (Scherbaum et al., 2005). As a consequence, the selection of empirical ground-motion models for host-to-target-region conversions requires con- siderable judgment of the ground-motion analyst.