Abstract
Computer processing of underground structures is one of the most important problems in Geoinformatics to promote an advanced use of computer in geology and a wide variety of related fields. The present paper summarizes a mathematical basis of data processing for a 3D modeling of geologic structure that has been formed through a sequence of sedimentation and erosion. At the first, we present a mathematical model that defines recursively a logical relation between geologic units and surfaces. Next, based on the model, we formulate a flow of data processing for 3D modeling as the following six steps: (1) classification of geologic units, (2) ordering of geologic units and events, (3) derivation of a logical relation between geologic units and surfaces, (4) estimation of surfaces, (5) determination of a function g that assigns a geologic unit to every point, and finally (6) visualization of 3D geologic structure based on the function g. The formulation provides a theoretical basis for development of computer algorithms.
