A Spatial Correlation-Based Anomaly Detection Method for Subsurface Modeling
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A Spatial Correlation-Based Anomaly Detection Method for Subsurface Modeling Wendi Liu1
· Michael J. Pyrcz1,2,3
Received: 11 June 2020 / Accepted: 7 September 2020 © International Association for Mathematical Geosciences 2020
Abstract 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, datadriven 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
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Wendi Liu [email protected]
1
Hildebrand Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin, USA
2
Bureau of Economic Geology, The University of Texas at Austin, Austin, USA
3
Department of Geological Sciences, Jackson School of Geosciences, The University of Texas at Austin, Austin, USA
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Math Geosci
is a useful automation tool for identifying samples in big spatial data on which to focus professional attention. Keywords Anomaly detection · Spatial continuity model · Bivariate Gaussian distribution · Geostatistics
1 Introduction Because of the large size of many subsurface datasets, it may be cost-prohibitive for a professional to fully interrogate the data; therefore, the identification of anomalous spatial samples and modeling and segmentation of unique spatial regions, formations and facies zones is an essential step to focus professional time in subsurface modeling. Proper data cleaning with outlier treatment and segmentation reduces uncertainty in the subsurface model and improves accuracy in subsurface estimates and forecasts. Data-driven anomaly detection approaches based on conventional statistical methods and machine learning have been applied. The most s
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