To adapt random process theory techniques for statistical estimation of peak ground motion to more realistic earth models, we constrain the parameters of duration, geometrical spreading, and spectral shape by modeling the main ground motion as being the result of major contributions by the direct S wave and supercritically reflected S waves. The results of our modeling are constrained to be consistent with values from full-wave synthetics for the test models. The combination of estimation theory and theoretical amplitude spectrum of the main ground motion within the ergodic window successfully predicts the mean peak vertical ground displacements, velocities, and accelerations of the 1982 Miramichi earthquakes in New Brunswick, Canada. In addition, upon considering the effects of source depth and crustal structure for the November 25, 1988, Saguenay earthquake (M = 5.8) in Québec, Canada, the predicted mean peak horizontal ground accelerations match the observed data very well. The effects of source depth and crustal structure on the peak ground motion are complicated for different source sizes and at different epicentral distance ranges.

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