Boundary modeling with moving least squares

Abstract

Modeling geological boundaries is an important step in geological modeling workflows that aim to quantify the location, volume, and uncertainty of a resource. Several well established explicit and implicit techniques can be used to identify the limits of an ore zone; however, most techniques are unable to account for uncertainty in a straightforward manner, where uncertainty originates from the sparseness of sample data relative to the volume of the resource in question. An implicit technique that benefits from simplicity and has the capabilities to incorporate and account for uncertainty in boundary geometry is signed distance function (SDF) modeling. Sample data that is in the form of line segments from drill holes presents challenges for interpolators such as kriging and radial basis functions. Utilizing linear regression as an interpolator several advantages to the problem are realized. The particular variant of regression that is used is moving least squares (MLS) that permits the exact integration of line data from drill holes and human interpretations without the need for discretization or numerical integration approaches. Integrating line data is critical for including explicit interpretations into implicit boundary models because geologic interpretations commonly involve polygons digitized on two dimensional sections through a field of drill holes.