Abstract

Ground‐motion prediction equations (GMPEs) are typically estimated via regression of a ground‐motion parameter of interest (such as peak ground acceleration or spectral acceleration) against source‐, path‐, and site‐related parameters, such as magnitude, distance, or time‐averaged shear‐wave velocity in the upper 30 m (VS30), with physical considerations taken into account. Typically, the predictor variables are treated as error free in the regression; however, there can be significant errors in these parameters because magnitudes are often converted from one scale to another (such as local magnitude to moment magnitude) and VS30 is often inferred from local geology instead of measured. We propose a Bayesian measurement error model that allows one to take into account measurement uncertainty in predictor variables, such as magnitude, in the development of a GMPE. The model treats the value of the predictor variable as a parameter to be estimated, constrained by its observed value and (known) variance of the measurement error. The model is cast in a Bayesian fashion to allow the inclusion of relevant prior information, as well as a probabilistic interpretation of the results. We apply the model to California data of the Next Generation Attenuation‐West2 data set and take into account measurement error in magnitudes and VS30. We find that the median predictions are similar when compared with a standard regression but that the values of the between‐event standard deviation τ and the within‐event/within‐station standard deviation ϕS2S are reduced by about 1%–13%, depending on the spectral period.

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