Constraining Surface Interpolations Using Elastic Plate Bending Solutions with Applications to Geologic Folding

Geologic surface interpolations can be augmented by adding physical constraints to available data. Here a method is outlined that allows one to constrain surface interpolations for two geologic surfaces based on the apparent thickness of the bounded layer. The resulting interpolation scheme is posed as a quadratic programming in which the interpolation of each surface is solved approximately and subject to linear constraints on the apparent thickness. Results can be further improved by adding cubic polynomials to the interpolating functions to regularize the problem. In one-dimensional interpolations of geologic folds, the method improves the results over unconstrained interpolations by eliminating interpenetrations (negative apparent thicknesses) and regions of small apparent thicknesses. In a two-dimensional application for the monocline at Raplee Ridge, UT, the capability of this method is illustrated by overcoming interpenetration of two surfaces, the tops of the Mendenhall oil sand and the Unnamed limestone. The minimum curvature spline interpolation is applied to topographic data taken from an airborne laser swath mapping (ALSM) survey and interpolated by detailed geologic mapping. This method can be extended to allow for multiple layers.