Dip and strike from three not parallel drill cores lacking key beds (stereographic method)

Abstract

Attention is called to the stereographic solution of the problem solved mathematically by John B. Mertie, Jr. 1 The problem is to find the dip and strike of beds cut by three not parallel bore holes, when no recognizable key beds are present in the drill cores. The data comprise the angles of trend and plunge for each bore hole, and the angles which the beds make with the axis of each drill core.The basis of the method and the mode of procedure in its application are briefly described.Small errors in the original data produce in most cases a triangle of error or an equivalent figure in which one or two curves approach a third one closely. In such cases the presence of errors is indicated, but no simple relation exists between the size or location of this triangle with reference to the correct point of intersection and the magnitude of the errors.There are two chief inevitable sources of error: (1) with increasing depth the bore holes tend to deviate from their original position in space. (2) As the horizontal distance between bore holes increases, the dip and strike of the beds tend to change. To keep both sources of error at a minimum, divergent bore holes should be drilled as close together as possible, and only the uppermost (significant) parts of the drill cores should be used in the determination of structure.