Adapting conditional simulation using circulant embedding for irregularly spaced data and exploring its limits

Abstract

For both scenario and real earthquakes, it is important to estimate the resulting shaking intensity in the near-epicentral region. These estimates can be constrained with ground motion recordings from real earthquakes, as is currently done in near-real-time by the United States Geological Survey (USGS) ShakeMap software. For scenario earthquakes, the ground motions are only estimated by the application of empirical models. The ground motion estimates are expressed as maps of the mean and standard deviation of the estimated intensity, but the consequences of the shaking on society and the built environment depend critically on the spatially correlated aleatory variability of the ground motions. This variability has been accounted for by generating random, spatially correlated realizations of the ground motions. Methods for generating these realizations, however, are computationally demanding, especially when the estimates are conditioned on numerous observed intensity values. In this presentation, a new and approximate conditional simulation approach is applied for use in ShakeMap. This approach, termed circulant embedding (CE), builds on a fast method for simulating Gaussian processes. However, standard CE is restricted to simulating stationary Gaussian processes (possibly anisotropic) on regularly spaced grids. It is also known that if the range parameter of a spatial process is large relative to the domain, this method fails. In this work we explore new algorithms that adapt CE for (a) irregularly spaced data points, and (b) methods for working with large range parameters in order for CE to be widely applicable. It is found that one method provides better accuracy and efficiency, and the solution to failure of CE results in manageable error for an exponential covariance function. However this error increases for larger shape parameters. We also illustrate the computational efficiency of this approach relative to previous methods. These ideas are illustrated with ground motion intensity measures and also validated through simulation studies.