Study of “Structure Graph” Proposed by Professor Hideo Kasai: Summary and Evolution

Abstract

Professor Hideo Kasai proposed new methods to represent a variety of contact relations between adjacent geologic units exposed at an outcrop by a labeled directed graph named the structure graph and the stratigraphic graph. The structure graph is a graph composed of a set of vertices indicating geologic objects observed at an outcrop and a set of edges indicating ordered pairs of adjacent objects which are labeled with types of contact relations. The stratigraphic graph can be derived from the structure graph to represent the chronological order. Based on a simple mathematical model, the present paper summarizes properties of two graphs for geologic structures including four types of contact relations, i.e., conformity, unconformity, intrusion and fault together with inference rules to transform a structure graph into a stratigraphic graph. Furthermore, as an advanced application, a flow of procedures is proposed to derive the regional stratigraphic sequence from a set of structure graphs obtained at outcrops through set operation called the graph union, and significance of the flow is evaluated from a viewpoint of 3D modeling of geologic structure.