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. |