Adapting conditional simulation using circulant embedding for irregularly spaced spatial data

TL;DR

This paper introduces an approximate conditional simulation method based on circulant embedding, extended for irregularly spaced spatial data, enabling faster and practical uncertainty quantification in large-scale geostatistical applications.

Contribution

It develops two algorithms, local Kriging and nearest neighbor Kriging, extending circulant embedding for irregular data, improving computational efficiency for large spatial datasets.

Findings

Methods are accurate for practical inference.

Significant speedup allows near real-time simulation.

Applicable to large, irregular spatial datasets.

Abstract

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 \textit{new}, \textit{approximate} conditional simulation approach is applied that builds on \textit{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 nearest neighbor Kriging, 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 \textit{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.