Delineation of geological features from limited hard and/or soft data is crucial to predicting subsurface phenomena. Ubiquitous sparsity of available data implies that the reliability of any delineation effort is inherently uncertain. We present probabilistic support vector machines (pSVM) as a viable method for both hydrofacies delineation from sparse data and quantification of the corresponding predictive uncertainty. Our numerical experiments with synthetic data demonstrate an agreement between the probability of a pixel classifier predicted with pSVM and indicator Kriging. While the latter requires manual inference of a variogram (two‐point correlation function) from spatial observations, pSVM are highly automated and less data intensive. We also investigate the robustness of pSVM with respect to its hyper‐parameters and the number of measurements. Having investigated these features of pSVM, we deploy them to delineate, from lithological data collected in a number of wells, the spatial extent of an aquitard separating two aquifers in Southern California.

中文翻译：

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支持向量机在水相中的概率重建

从有限的硬和/或软数据中划定地质特征对于预测地下现象至关重要。可用数据的普遍稀疏性意味着任何划定工作的可靠性本质上是不确定的。我们提出概率支持向量机（pSVM）作为从稀疏数据中划定水相和量化相应预测不确定性的一种可行方法。我们使用合成数据进行的数值实验表明，使用pSVM预测的像素分类器的概率与指标Kriging的一致性。后者需要从空间观测值中手动推断出变异函数（两点相关函数），而pSVM是高度自动化的，且数据密集度较低。我们还针对pSVM的超参数和测量次数研究了鲁棒性。在研究了pSVM的这些特征之后，我们将它们部署用于根据在多个井中收集的岩性数据来界定在南加州将两个含水层分隔开的阿奎德的空间范围。