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Subsurface datasets inherently possess big data characteristics such as vastvolume, diverse features, and high sampling speeds, further compounded by thecurse of dimensionality from various physical, engineering, and geologicalinputs. Among the existing dimensionality reduction (DR) methods, nonlineardimensionality reduction (NDR) methods, especially Metric-multidimensionalscaling (MDS), are preferred for subsurface datasets due to their inherentcomplexity. While MDS retains intrinsic data structure and quantifiesuncertainty, its limitations include unstabilized unique solutions invariant toEuclidean transformations and an absence of out-of-sample points (OOSP)extension. To enhance subsurface inferential and machine learning workflows,datasets must be transformed into stable, reduced-dimension representationsthat accommodate OOSP.  Our solution employs rigid transformations for a stabilized Euclideaninvariant representation for LDS. By computing an MDS input dissimilaritymatrix, and applying rigid transformations on multiple realizations, we ensuretransformation invariance and integrate OOSP. This process leverages a convexhull algorithm and incorporates loss function and normalized stress fordistortion quantification. We validate our approach with synthetic data,varying distance metrics, and real-world wells from the Duvernay Formation.Results confirm our method's efficacy in achieving consistent LDSrepresentations. Furthermore, our proposed "stress ratio" (SR) metric providesinsight into uncertainty, beneficial for model adjustments and inferentialanalysis. Consequently, our workflow promises enhanced repeatability andcomparability in NDR for subsurface energy resource engineering and associatedbig data workflows.

Rigid Transformations for Stabilized Lower Dimensional Space to Support Subsurface Uncertainty Quantification and Interpretation