Model representation and visualization
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In earth modeling, a surface corresponding to a layer boundary is usually represented by a set of triangles, the size and shape of which vary depending on the complexity of the reflector geometry. Shown in Figure 9.0-4 are four surfaces associated with layer boundaries included in an earth model. Also included in Figure 9.0-4 are the representations of these surfaces by triangulation.
A velocity-depth model usually is represented either in the form of a gridded or tessellated volume. Gridding means dividing the whole volume into a set of 3-D cells of equal size with appropriate dimensions in the inline, crossline, and depth directions. Tessellation means dividing the volume associated with each layer into a set of tetrahedra, the size and shape of which depend on the geometry of layer boundaries (Figure 9.0-5). In a tessellated velocity-depth model, a velocity and a gradient, if available from sonic logs, are assigned to each corner of the tetrahedra.
A velocity-depth model is represented either in gridded or tessellated form depending on the application that needs it as input. For instance, ray tracing in coherency inversion and prestack depth migration may be performed using gridded or tessellated models. On the other hand, wave extrapolation in 3-D poststack depth migration based on finite-difference schemes is performed conveniently using gridded models.
Images of layer boundaries included in an earth model in depth can be converted to a physical model using various image construction techniques. Figure 9.0-6 shows the four surfaces that represent the layer boundaries from the earth model as in Figure 9.0-4 and the slabs that represent the layers of the earth model created by laser lithography.
In areas with complex structures, we often have to deal with mulitvalued depth surfaces. For instance, salt overhangs associated with diapirism and imbricate structures associated with overthrusting cause a surface to fold onto itself. Shown in Figure 9.0-7 is an earth model that comprises a complex diapiric structure. The top-salt boundary is represented by the multivalued yellow surface and the base-salt boundary is represented by the pink surface. The surfaces that represent the layer boundaries within the overburden must be attached to the top-salt boundary surface without any gaps so as to form individual volumes associated with each layer. Figure 9.0-8a shows the solid-model representation of the earth model in Figure 9.0-7. When expanded, the solid model shows the individual volumes associated with the layers included in the earth model (Figure 9.0-8b).
Isolate the salt mass from the model as shown in Figure 9.0-9 to examine the complexity of the salt diapir. The multivalued surface that represents the top-salt boundary is shown in Figure 9.0-10a. The triangulated mesh for this surface is shown in Figure 9.0-10b with an enlarged view in Figure 9.0-11.
- Introduction to earth modeling in depth
- Inversion methods for data modeling
- Inversion procedures for earth modeling
- Velocity-depth ambiguity