Notes on Ohkuma’s Method for Direct Sum Representation of Geologic Unit Using Bitwise Operation of Tuples

Abstract

Ohkuma and Shiono(2016) presented a Visual Basic .NET program GeoCalcVB to perform set operations of subspaces p(x₁, … , x_n) defined by surfaces S₁, … , S_n, where x_i is a three-digit binary number that assigns the relation between a subspace and a surface S_i. As an application of the program, Ohkuma proposed an algorithm to transform a subspace defined by surfaces into a form of direct sum. The present paper describes the outline of Ohkuma’s algorithm together with mathematical background and examples. It is expected that the algorithm helps to improve computer modeling system of 3D geologic structure.