Adapting conditional simulation using circulant embedding for irregularly spaced spatial data

Computing an ensemble of random fields using conditional simulation is an ideal method for retrieving accurate estimates of a field conditioned on available data and for quantifying the uncertainty of these realizations. Methods for generating random realizations, however, are computationally demanding, especially when the estimates are conditioned on numerous observed data and for large domains. In this article, a new, approximate conditional simulation approach is applied that builds on circulant embedding (CE), a fast method for simulating stationary Gaussian processes. The standard CE is restricted to simulating stationary Gaussian processes (possibly anisotropic) on regularly spaced grids. In this work, we explore two possible algorithms, namely, local Kriging and approximate grid embedding, that extend CE for irregularly spaced data points. We establish the accuracy of these methods to be suitable for practical inference and the speedup in computation allows for generating conditional fields close to an interactive time frame. The methods are motivated by the U.S. Geological Survey's software ShakeMap, which provides near real-time maps of shaking intensity after the occurrence of a significant earthquake. An example for the 2019 event in Ridgecrest, California, is used to illustrate our method.

Automated summary

This article introduces a new approximate conditional simulation method for generating ensembles of random fields. The method is based on circulant embedding and extends the algorithm to irregularly spaced data points. The methods have been shown to be accurate for practical inference and significantly speed up computation.