Practical section drawing through folded layers using sequentially rotated cubic interpolators

Abstract

A new, simple and practical cubic interpolation method, for use in microcomputer-aided section drawing, is presented. Apparent dips at pairs of consecutive points are used to determine the cubic interpolator between them. The process is repeated sequentially to construct the layer trace. Overturned layers are accommodated by rotating the reference frame of the interpolator. The extra degree of freedom introduced by rotating can be constrained using known axial traces, borehole data, or layer thicknesses. Unlike the Busk construction (arcs and tangents) the fold class demanded by the data can be conserved in the interpolation; that is, the technique is not restricted to parallel folds. In the absence of constraining data the reference frame can be rotated so that the ordinate parallels the bisector of consecutive dips, producing a conservative interpolation even where layers are inverted. Alternatively the rotated cubic with the minimum arc-length can be sought, providing an objective ‘minimum’ strain estimate in bed-length balancing.