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.

中文翻译：

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使用循环嵌入来适应不规则空间数据的条件模拟

使用条件模拟计算随机场的集合是检索以可用数据为条件的场的准确估计和量化这些实现的不确定性的理想方法。然而，生成随机实现的方法对计算的要求很高，尤其是当估计以大量观察数据和大域为条件时。在本文中，应用了一种基于循环嵌入的新的近似条件模拟方法(CE)，一种模拟平稳高斯过程的快速方法。标准 CE 仅限于在规则间隔的网格上模拟静止的高斯过程（可能是各向异性的）。在这项工作中，我们探索了两种可能的算法，即局部克里金法和近似网格嵌入，它们将 CE 扩展到不规则间隔的数据点。我们确定这些方法的准确性适用于实际推理，并且计算的加速允许生成接近交互式时间框架的条件场。这些方法是由美国地质调查局的软件ShakeMap推动的，该软件提供了大地震发生后近乎实时的震动强度地图。以 2019 年在加利福尼亚州里奇克莱斯特举行的活动为例来说明我们的方法。