Spatial data analytics provides new opportunities for automated detection of anomalous data for data quality control and subsurface segmentation to reduce uncertainty in spatial models. Solely data-driven anomaly detection methods do not fully integrate spatial concepts such as spatial continuity and data sparsity. Also, data-driven anomaly detection methods are challenged in integrating critical geoscience and engineering expertise knowledge. The proposed spatial anomaly detection method is based on the semivariogram spatial continuity model derived from sparsely sampled well data and geological interpretations. The method calculates the lag joint cumulative probability for each matched pair of spatial data, given their lag vector and the semivariogram under the assumption of bivariate Gaussian distribution. For each combination of paired spatial data, the associated head and tail Gaussian standardized values of a pair of spatial data are mapped to the joint probability density function informed from the lag vector and semivariogram. The paired data are classified as anomalous if the associated head and tail Gaussian standardized values fall within a low probability zone. The anomaly decision threshold can be decided based on a loss function quantifying the cost of overestimation or underestimation. The proposed spatial correlation anomaly detection method is able to integrate domain expertise knowledge through trend and correlogram models with sparse spatial data to identify anomalous samples, region, segmentation boundaries, or facies transition zones. This is a useful automation tool for identifying samples in big spatial data on which to focus professional attention.

空间数据分析为自动检测异常数据提供了新的机会，以进行数据质量控制和地下分割，以减少空间模型中的不确定性。仅数据驱动的异常检测方法无法完全集成空间概念，例如空间连续性和数据稀疏性。此外，数据驱动的异常检测方法在整合关键的地球科学和工程专业知识方面也面临着挑战。所提出的空间异常检测方法是基于从稀疏采样的井数据和地质解释中得出的半变异函数空间连续性模型。该方法根据给定的滞后向量和半变异函数，在双变量高斯分布的假设下，为每对匹配的空间数据计算滞后联合累积概率。对于成对的空间数据的每种组合，一对空间数据的相关联的头和尾高斯标准化值被映射到从滞后矢量和半变异函数获悉的联合概率密度函数。如果相关联的头和尾高斯标准化值落在低概率区域内，则配对数据被分类为异常。可以基于量化高估或低估成本的损失函数来确定异常决策阈值。所提出的空间相关异常检测方法能够通过趋势和相关图模型与稀疏空间数据整合领域专业知识，以识别异常样本，区域，分割边界或相变区。