Three-dimensional projection of curvilinear geological features through direction cosine interpolation of structural field observations

Abstract

A UNIX program in AWK is presented for densifying and projecting distributed 3D data points that occur on a common geological structural surface. Polynomial and hybrid B-spline interpolation techniques are optimized for both sparse and abundant regional, clustered structural data sets. This tool, named push.awk, will be most useful in geological situations in which structures are constrained by several geometrical observations, are parts of relatively continuous irregular curviplanar surfaces and whose behavior can be predicted approximately linearly with depth at some point along the structure. Suggested applications are the determination of some types of variably plunging folds in mine exploration, depth prediction of regionally continuous shear zones and brittle faults, development of 3D structural fabric trajectories, horizon propagation, and plutonic boundary geometry evaluation. Simple uniaxial and variable projection methods need to be used in an appropriate context and in conjunction with the entire range of available statistical and interpretive 3D tools in order to achieve high-quality geological visualizations. It is the effective incorporation of geometric field data into visualization and predictive geotechnologies that will increase the potential for subsurface interpretation in complex geological settings.