Development of Geology-Oriented Logical System (GEO-LOGICS): Search for Mathematical Bases of Geological Data Processing

“Geology-Oriented Logical System” (GEO-LOGICS) is a new research branch of geology proposed by Wadatsumi et al. (1987) to construct a logical system of geology in a mathematical form as theoretical bases for geological data processing. The present paper reviews the results of research during 30 years since Japan Society of Geoinformatics was established in 1990. Continuous space and time are frequently divided into geologic units and geologic time spans respectively and a wide variety of relations between discrete objects are major research targets in geology. From this point of view, new theories and algorithms have been developed mainly based on Discrete Mathematics. Major results are: (1) three axions that formulate fundamental properties of sedimentary strata also known as the law of original horizontality, the law of lateral continuity and the law of superposition, (2) a labeled directed graph that represents contact relations of geologic units exposed at an outcrop, (3) a flow chert of data processing to derive the regional stratigraphy from observation data at many outcrops, (4) a simple mathematical model that simulates fundamental procedures of biostratigraphy, (5) a logical relation between geologic units and surfaces, named the logical model of geologic structure, which defines a 3D geologic structure mathematically, (6) a labeled binary tree that represents the logical model of geologic structure and (7) a bitwise operation method to perform a variety of set operations of subspaces defined by the logical model. Further development of GEO-LOGICS is desirable to promote a wide variety of geological data processing.