Abstract
The examination of method to describe mathematically geological information observed in outcrops is necessary to construct the outcrop database. For the purpose, we propose the structure graph, the structure matrix, and the structure formula by using the graph theory and the binary relation, and examine their theoretical backgrounds. The structure graph represents an outcrop structure and a geological sequence as a labeled directed graph G = (V, R, ∅), where V is a set of vertexes (geological objects), R is a set of arcs (contact relation between geological objects), and ∅ ; is a function that maps every ordered pair (vi, vj) in E to a type of contact. The arc is directed from the lower object to the upper one. The structure matrix (sij) is refined from the adjacency matrix (aij); sij = ## if (vi, vj) ∈ E and sij=0 if otherwise, where sij is a(i,j) element of the structure matrix, and ## is the symbol to show the type of contact between objects vi and vj. The structure formula expresses an outcrop structure and a geological sequence as a formula in a form of v1##1v2##2…##n-1vn. Further we express a complicated structure as a formula with parentheses (), [ ) or (] such as (v1##1v2##2…##n-2vn-1)##n-1vn. Thus we can mathematically express the geologic structure of the outcrop and the geological sequence.
