3D DATA STRUCTURES AND APPLICATIONS IN GEOLOGICAL
SUBSURFACE MODELING
R. Li, Y. Chen, F. Dong and L. Qian
Dept. of Geomatics Engineering, The University of Calgary
2500 University Dr., N.W., Calgary, AB, Canada
Tel: (403) 220-4112 Fax: (403) 284-1980
E-mail: rli@acs.ucalgary.ca
WWW: http://loihi.ensu.ucalgary.ca/
J.D. Hughes
Institute of Sedimentary and Petroleum Geology
Geological Survey of Canada
3303-33St NW, Calgary, Alberta T2L 2A7
KEY WORDS: 3D data structures, octree, Peano keys, subsurface, GeoView
ABSTRACT:
In this paper, a brief discussion is given to the existing problems in 3D geological subsurface modeling. Two groups of 3D data
structures are then identified with the focus on the octree representation and its Peano coding. Two spatial operations based on
Peano keys are described in details. Finally, the experimental results of the developed system, GeoView, are given.
1. BACKGROUND
Geographic Information Systems (GIS) have been widely used
and have shown their power in spatial analysis, database
management and various other applications. The extensive use
of computers in oil and mining explorations has introduced the
possibility of applying the GIS technology to the field of
geology and geophysics.
However, geological subsurface modeling involves usually a
large volume of digital information which is spatially
referenced in three dimensions. The use of traditional
interpretation methods (e.g., contour maps, cross sections,
fence diagrams, isometric surfaces) limits the view of the
geological world to two dimensions, or at best quasi-three
dimensions (Fisher and Wales, 1992). The accumulation of the
geological information calls for a GIS system capable of
handling 3D data efficiently. This system should combine the
search and analysis of databases with the versatility for
visualization using computer graphics technology (Jones,
1989). Currently, most GIS systems are based on two
dimensional data structures and could not handle information
in the third dimension efficiently. Attempts have been made to
extend spatial operations to 3D by adding the third
dimensional information into 2D data structures, such as
including elevation data as attributes (Arc/Info, 1992).
Although such systems have 3D information in databases, the
full 3D functionality cannot be expected, such as 3D modeling,
query of 3D spatial elements and association of non-spatial
data to solid elements, etc.
Geological applications pose special challenges to the
development of GIS. Geological phenomena are 3-dimensional
in nature. When fit into 2-dimensional GIS systems, they are
not accurately modeled, analyzed or displayed (Smith and
Paradis, 1989). In geological modeling, all applications require
increasingly quantitative and accurate underground material
characterizations within the 3D subsurface environment. The
3D data are required because the depth dimension is in the
same general range as the surface dimensions, and the true
spatial relationships are important to the problem analysis
(Turner, 1989).
3D geological modeling has identified a number of
requirements on GIS systems. An ideal system should provide
a variety of facilities, such as data storage of a large amount of
volume data, input to and output from models, support for a
range of data structures and for transformation between
different data structures, integration of data from different
sources, assistance with construction of models, integration of
complex spatial relationship between geological layers,
geostatistical techniques for data interpolation before model
input, determination of model parameters, design of sampling
strategies, and error analysis (Mason, et. al., 1994). Additional
important facilities may be dynamic visualization and
animation of the third dimensional spatial information.
This paper presents the results of a research project initialized
in 1993 and conducted jointly by The University of Calgary
and the Geological Survey of Canada to model and visualize
3D geological subsurface information using 3D data structures.
In this paper, a review of 3D data structures is given. A few 3D
spatial operations developed and implemented in our system
are discussed. The system itself is introduced in the last
section, which has been implemented on a Silicon Graphics
Workstation by using C programming language, Motif and
Graphic Language (GL).
2. THREE DIMENSIONAL DATA STRUCTURES
Although 3D GIS is badly needed in geological applications,
progress in this field has been relatively slow. This might
generally due to difficulties in defining complex geological
information and specifically to the need for finding data models
and data structures suitable for handling large quantities of 3D
geoscientific data. Many recent advances in the design of GIS
are applicable, but in general this technology is oriented
towards two rather than three-dimensional information (Jones,
1989).
508
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B4. Vienna 1996
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