In this study, we propose a method using the GRASS GIS environment, which 
incorporates faulting into the theory and algorithm based on the computer 
processing for geologic structures formed through the sedimentation and the 
erosion. The geologic structures formed through the sedimentation and the erosion 
can be expressed by the surfaces surround the distributed areas of geologic units, 
and the logical relation between the distribution of geologic units and surfaces 
are termed logical model of geologic structure. When we regard the changeable 
process of geologic structure formed through sedimentation and erosion as the 
relations between the distribution of geologic units and the surfaces, there is a 
definite rule of its formative process corresponds with the logical model of 
geologic structure, and it is expressed as a recursive definition. Concerning the 
faulting we define the rule which suggests the surface of fault divides a three-
dimensional geologic unit and the open space into two areas, and the geologic 
structures of each area can be preserved. Therefore, faulting can be reasonably 
included into the recursive definition, which leads logical model of geologic 
structures formed through the sedimentation and the erosion, and the faulted 
geologic structure can be expressed as recursive definition. In addition, this 
recursive definition can lead a logical model of geologic structure cut by plural 
faults. With introducing a logical model of faulted geologic structure, we propose 
the faulted geologic map can be generated without any changes of the existent 
processing system based on a logical model of geologic structure. Further, the 
example of application for the logical model of faulted geologic structures is 
shown using a 3-D visualization tool "Nviz" in GRASS GIS.

Geologic information plays an important role in the fields of civil engineering, 
construction and environmental preservation. Various studies have been proceeding 
to construct a three-dimensional (3-D) model of geologic structure using the GRASS 
GIS environment for practical use. 3-D modeling of geologic structure is composed 
of two elements; the logical model of geologic structure and the gridded surfaces 
(DEM: Digital Elevation Model). If the two elements are given, the geologic 
function that assigns the geologic unit to every point in space A can be defined 
uniquely. Based on this geologic function, the distribution of geologic units can 
be visualized on an objective surface including the topographic surface and the 
vertical section by classifying them with different colors. i.e. it is possible to 
visualize the 3-D model of geologic structure. The geologic structure formed 
through sedimentation and erosion is formulated as a recursive definition and it 
can be derived by a technical procedure. However, the formulation of faulted 
geologic structure has been left as an unresolved problem.
 The present study proposed a mathematical formulation of geologic structure formed 
by faulting. We assume that fault surface divides the preexisting geologic units 
into two parts; the foot wall and hanging wall. If the relation between the 
geologic units and the surfaces in each part is preserved, the logical model of 
geologic structure on both sides is expressed in the same form as the case of the 
geologic structure before the faulting. Focusing on this rule, we define a new 
recursive definition to derive the logical model of geologic structure that 
involves fault movements as well as sedimentation and erosion. The recursive 
definition provides a powerful tool to derive the logical model of complex geologic 
structures formed by the sedimentation, erosion and faulting through a simple 
mechanical procedure. 
 It is expected that this study would advance the computer processing of the 
faulted geologic structure and activate the application of such geologic 
information in various fields.