Confidence-Constrained Support Vector Regression for Geological Surface Uncertainty Modeling

Reconstruction of complex geological surface is widely used in oil and gas exploration, geological modeling, geological structure analysis, and other fields. It is an important basis for data visualization and visual analysis in these fields. The complexity of geological structures, the inaccuracy and sparsity of seismic interpretation data, and the lack of tectonic morphological information can lead to uncertainty in geological surface reconstruction. The existing geological surface uncertainty characterization and uncertain reconstruction methods have a shortcoming in balancing the interpolation error of high-confidence samples and model structure risk. Based on support vector regression (SVR), a method with confidence constraints for uncertainty characterization and the modeling of geological surfaces is proposed in this article. The proposed method minimizes the structural risk by adding a regularization term representing the model complexity, integrates high-confidence samples, such as drilling data, based on confidence constraints, and utilizes well path points by assigning appropriate inequality constraints to the corresponding prediction points. The results based on a real-world fault data set show that the uncertainty envelopes and fault realizations generated by the proposed method are constrained by well observations and well paths, effectively reducing the uncertainty.