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

In order to formulate the distribution of strata in a survey area Ω in terms of subspaces b1, b2,...,bn bounded by boundary surfaces S1, S2,...,Sn-1, we introduce a new concept called C1 and C2 type of boundary surface as a mathematical model of conformity and unconformity, respectively. Let St be a boundary surface which divides a given successive sequence of subspaces(br,br+1,...,bk) into two successive sequences (br,...,bt) and (bt+1,...,bk). Then a surface Sk is called C1 type of boundary surface if and only if St also divides a successive sequence (br,..., bk, bk+1) into two successive sequences (br,...,bt) and (bt+1,...,bk, bk+1). On the other hand, the boundary surface Sk is called C2 type of boundary surface if and only if Sk divides a successive sequence(b1,b2,...,bk, bk+1)into a successive sequences(b1,...,bk)and a single subspace bk+1. It is proved that all subspacesb1, b2,..., bn are uniquely defined by boundary surfaces S1, S2,..., Sn-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”.