On Formal Expression of Spatial Distribution of Strata Using Boundary Surfaces —C₁ and C₂ Type of Contact—

Abstract

In order to formulate the distribution of strata in a survey area Ω in terms of subspaces b₁, b₂, …, b_n bounded by boundary surfaces S₁, S₂, …, S_n-1, we introduce a new concept called C₁ and C₂ type of boundary surface as a mathematical model of conformity and unconformity, respectively. Let S_t be a boundary surface which divides a given successive sequence of subspaces (b_r, b_r+1, …, b_k) into two successive sequences (b_r, …, b_t) and (b_t+1, …, b_k) . Then a surface S_k is called C₁ type of boundary surface if and only if S_t also divides a successive sequence (b_r, …, b_k, b_k+1) into two successive sequences (b_r, ..., b_t) and (b_t+1, …, b_k, b_k+1) . On the other hand, the boundary surface S_k is called C₂ type of boundary surface if and only if S_k divides a successive sequence (b₁, b₂, …, b_k, b_k+1) into a successive sequences (b₁, …, b_k) and a single subspace b_k+1. It is proved that all subspaces b₁, b₂, …, b_n are uniquely defined by boundary surfaces S₁, S₂, …, S_n-1 if subspaces are bounded by either C₁ or C₂ type of boundary surfaces. According to the formulation of strata in terms of subspaces bounded by boundary surfaces, we can define a function g which assigns a label corresponding to a stratum to every point in Ω. The formulation of subspaces and the labeling function provide theoretical bases of the computerized geologic mapping system“CIGMA”.