Abstract
The graphical expression for the logical model of geologic structure in terms of a labeled binary tree is examined based on graph theory. In the binary tree for a logical model, a vertex (a root, a branch node or a leaf) represents a subspace bounded by surfaces. Two branches outgoing from a vertex represent a subdivision of the subspace by a surface; left and right children show subspaces lower and upper than the surface, respectively. As the result of examination, it is found that the binary tree for geologic structure formed by sedimentation and erosion has the following properties; (1) the root or the branch node represents the union of all of its descendants, (2) if the Law of Superposition holds true, a left child is older than a right child, (3) in the path from the root to a leaf, the closer the branch to the root, the higher the priority of the surface corresponding to the branch, (4) the surface whose order of priority is lower than older ones is the top surface of sedimentary layer and the surface whose order of priority is higher than older ones is the erosion surface. Using these properties, we can read important information such as the stratigraphic sequence, the priority of surface and the sequence of sedimentation and erosion from a binary tree representing a logical model of geologic structure. It is confirmed that the procedure of geological interpretation is closely related to the algorithm of tree searching; the inorder search provides the chronological order of geologic units and surfaces, and the preorder search defines the priority of surfaces.
