2.5-D to 3D Geological Modelling

Vertical and oblique photogrammetry are two of several datasets that can be used to build a comprehensive 3-D geological model of a given area. The regional terrain model with draped geology and the more local oblique photogrammetry geological model presented above illustrate the contribution that each of these 2.5-D mapping techniques can bring to more precise geological mapping. This naturally leads to a possible extrapolation of this map into the construction of a 3-D geology model. Geological bodies are volumes of rock that in many cases had originally continuous bounding surfaces. Given sufficient data density, standard interpolation techniques are available to create surface models required to represent and visualize a given geological body (Mallet, 1992, De Kemp, 1999).

In the case presented below, we describe the outline of a conceptual method to build a three-dimensional geological model by creating geometric objects derived from such 2.5-D map, once integrated with interpreted balanced cross-sections and subsurface exploration data. The animation captured out of the geological modelling software (Figure 7) shows the different steps involved in creating such a model comprising 3-D geological surfaces and voxets (sets of three-dimensional point data or voxels). The model and animation are at their early stages of development and contain unsatisfactory representations of the geology of certain parts of the area, but serve here to illustrate the conceptual approach that we intend to pursue further through the refinement of the model and the development of modelling tools.

We used the gOcadTM geological modelling software (Mallet, 1992) to extract geologic surfaces from key lithostratigraphic boundaries and build a rough 3-D block-diagram of the Moose Mountain area of the Canadian Foothills (Figure 7). This software focuses on different aspects of geoscience modelling, with tools adapted to geophysics, geology and reservoir engineering applications. Structural modelling draws on a set of surfacing tools to construct the lithologically continuous and faulted geological surfaces, critical to build a geological model of a thrust-fold belts. Interpolation of the surfaces between the construction points (constraints) is performed by the Discret Smooth Interpolation (DSI) algorithm that honours control points (Mallet, 1992). A structural module provides various workflows to model different structural frameworks.

The conceptual model illustrated here, builds from the constructed 2.5-D maps described above to a 3D model in 4 steps: 1) construction of cross-sections in a CAD environment; 2) integration of 2.5-D CAD map and 2D cross-sections through data transformation to the gOcad geological modelling format; 3) surface interpolation based on the geological property of the 2.5-D map elements, 2D cross-sections and subsurface borehole data; 4) Verifications and corrections of inter-surface distances through gridded tangential inter-surface measurements. The conceptual 3-D model construction scheme is described through a series of frames (F1 to F37) found in the computer animated model (Figure 7 ÐF1-F37). The model represents the eastern portion of the Moose Mountain structural culmination, in the vicinity of Canyon Creek and Moose Dome Creek, which are situated in the centre part of the 2.5-D map illustrated in the animation found at Figure 3.

Construction of cross-sections in a CAD environment

The initial phase of construction of a model consists in compiling all available data in a common reference frame. This is best done using a CAD program, which also provides the tools to perform interactive 2.5-D point and line editing of elements derived from the field and photogrammetric mapping described above. In the case presented here this editing was performed with Bentley Microstation SETM. The first dataset illustrated consists of a DEM (Figure 5 - F1), over which a detailed geological map (Marcil, in preparation) of all formation boundaries and structural features was draped in the CAD and then converted to the gOcad format (F2 to F3). More detailed work consisting of oblique photogrammetry-derived boundaries could be added at this stage in complex or rugged areas. Each line on F2-F3 is thus the ground trace of geological unit boundaries or faults positionned in 3-D.

The CAD environment is also ideal to construct a series of cross-sections to extrapolate the subsurface geometry of geological horizons, following classic empirical geology rules such as conservation of area (Dahlstrom, 1969, Groshong, 1999). Parallel cross-sections can be quickly compared and edited using the selective "display depth" of the CAD software, along rotated views aligned with the orthogonal axis to each cross-section. Parallel copy of curved stratigraphic contact lines along set distances in the cross-section plane also provide quick tools to depict parallel strata of known stratigraphic thickness (e.g. 'copy parallel' tool of Microstation). The series of regularly spaced parallel cross-sections is used to guide the construction of 3D surfaces from ground mapped geological contacts (F4 to F11). The position of geological contacts in the sub-surface along the cross-sections was projected downplunge, from surface positions and orientations of geological boundaries, using known stratigraphic thickness. The next step would be to balance the sections; only the rough sketch stage is illustrated here. Additional constraints, like geophysical and drilling data would also be included at this stage.

Integration of 2.5-D map and 2D cross-sections into gOcad

Because data are transfered between two very different software (from Microstation to gOcad), geological contacts need to be validated in 2.5-D, by visually inspecting their position relative to a draped orthophoto of the terrain (Figure 7, F12 to F15). If discrepancies are found, the geologist goes back to the CAD to validate the linework against the orthophotos or verifies the data transfer procedure. This can be a very time consuming task but allows for a more precise geological model.

Surface interpolation to connect the 2.5-D map model, 2D cross-sections and subsurface borehole data

Once the geological model is carefully inspected and contacts validated, the geological surfaces construction is performed (F16 To F19). A mean plane representing a geological horizon or a fault surface was created with a surface construction tool. Using the constraints imposed by the positions of the ground level and cross-section curvi-linear and multi-segmented geological boundaries, DSI is imposed to the plane that become a surface that honours all field data (F20).

Once the surface validation is performed, the TIN is then cut by the newly built geological surfaces and a property colour is attributed to each parcelled ground area for visualisation purpose (F21 to F25).

Although gOcad can interpolate three-dimensional surfaces, users have to supervise closely these surface constructions (F16 to F19). To verify the surfaces interpolated from the field and cross-section data, an algorithm that measures orthogonal distances between surfaces was programmed. In this manner, anomalies in stratigraphic thickness can be quickly verified by draping coloured contours of the stratigraphic thickness of a unit over its upper or lower boundaries (F26 to F29). Successive iterations then follow to find either a source of error, given that most surface boundaries should be sub-parallel in this geological setting, or to validate the existence of a real stratigraphic anomaly.

The final phase of the model construction consists in moving from a surface construction and intersection mode to a volumetric mode. This is done by constructing a voxet that represent a 3-D spaced grid of voxels which can be filled with a geological property value for geophysical or other modelling (F30 to 34). Cross-sections can then be quickly produced in the voxet (F35 to F37). Anomalies such as important variations in unit thicknesses observed in the block diagram, are quickly recognized as construction errors due to lack of constraints or operator guidance, and thus attest to the strength of the visualization method and to some weaknesses in the surfaces construction, which are obviously not sub-parallel contrary to their real world equivalent.