Adapting conditional simulation using circulant embedding for irregularly spaced spatial data

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