Structural determinations from diamond drilling

Abstract

Several problems may arise in the geometrical determinations of strike and dip from core drilling. If the stratigraphic or structural surfaces are plane, as the bedding planes of a homocline, two problems may exist, depending upon whether the drill cores do or do not penetrate to some recognizable horizon. The first of these is solved by a simple graphic interpolation, and is not discussed in this paper. The second, however, is solved for the most general case of three non-parallel drill holes, no one of which is necessarily vertical.Errors are necessarily present in this solution, due to:1. Inaccuracies in the measurement of the initial directions and dips of the drill holes.2. Deviations of the drill holes from their initial directions.3. Inaccuracies in the measurement of the angles between the axes of the drill cores, and the stratigraphic or structural planes.The second and third of these causes result in initial errors in the measurement of the core angles. Hence, for this simplest case, error formulae are developed for finding the final errors in the angles of strike and dip, under certain specified assumptions.To illustrate the solution, a problem is stated and solved. This problem is of a general nature, selected to show the necessary operations when the three drill holes occur in different octants. The error formulae are subsequently applied.For curved surfaces, as where folded beds are present, the same two problems arise, depending upon whether the drill holes do or do not penetrate to some recognizable horizon. Only the first of these problems is considered. It is shown, in this case, that 9 drill holes are required to obtain a satisfactory solution. The method consists essentially in fitting nine known points to a ternary quadric surface; and in determining the equations of the planes tangent to this surface at any of the nine points, or at any other points on the surface. The strikes and dips are then derived from these equations.