Application of Regression Models to Multi-Faulted Subsurface Geologic Structures

The pre-fault geometry of multi-faulted subsurface geological structures was reconstructed using regression-analysis methods. Regression-analysis models were developed for faults with vertical displacement, with horizontal displacement, and with both vertical and horizontal-displacement components. Except for vertical-displacement faults, the models are non-linear. Substantive algorithms, based on the structural effects of faulting, are proposed and used to derive approximate numerical solutions to the regression equations. The procedure is tested with hypothetical faulted structures, vertical faults in the subsurface Arbuckle Formation (Kansas), and transcurrent faults in selected oil fields of southern California. A method based on the distribution of large residuals from a computed surface is proposed for detecting unmapped subsurface faults.