Cross-section diagrams in Cross-section diagrams in 3 Dimentions 3 Dimentions (Chapter 7 Cont.)(Chapter 7 Cont.)

Fence DiagramsFence Diagrams

In petroleum exploration, the development of a prospect In petroleum exploration, the development of a prospect is a three-dimensional problem. One of the drawbacks of is a three-dimensional problem. One of the drawbacks of cross sections is that they are limited to two dimensions. cross sections is that they are limited to two dimensions. How can we illustrate the three-dimensional geology of How can we illustrate the three-dimensional geology of an area? an area? The most common type of diagram showing geological The most common type of diagram showing geological relationships in three dimensions is a fence diagram (relationships in three dimensions is a fence diagram (Figure 1). Fence diagrams consist of a three-). Fence diagrams consist of a three-dimensional network of geological cross sections drawn dimensional network of geological cross sections drawn in two dimensions. The diagram is built on a map base in two dimensions. The diagram is built on a map base which is seen in plan view.which is seen in plan view.

Figure 01Figure 01

Fence DiagramsFence Diagrams

In constructing a fence diagram, the plane of the map In constructing a fence diagram, the plane of the map base corresponds to the chosen datum plane, and the base corresponds to the chosen datum plane, and the well location on the map is taken to be the point where well location on the map is taken to be the point where the well intersects the datum plane. The wells are hung the well intersects the datum plane. The wells are hung on the datum and then individual cross section panels on the datum and then individual cross section panels are filled in, beginning at the front of the diagram. are filled in, beginning at the front of the diagram. In fence diagrams, one must consider the overall In fence diagrams, one must consider the overall orientation of the figure, bearing in mind that panels orientation of the figure, bearing in mind that panels oriented parallel to the viewing direction will appear only oriented parallel to the viewing direction will appear only as straight lines. Such panels are usually omitted from as straight lines. Such panels are usually omitted from the diagram. If important panels are not displayed to the the diagram. If important panels are not displayed to the best advantage, the viewing direction can be changed best advantage, the viewing direction can be changed so that the features of interest are presented in the most so that the features of interest are presented in the most effective way. effective way.

Fence DiagramsFence Diagrams

Front panels sometimes obscure parts of rear Front panels sometimes obscure parts of rear panels in fence diagrams. Where two panels panels in fence diagrams. Where two panels overlap, the correlations on the front panel are overlap, the correlations on the front panel are drawn in with solid lines and highlighted with drawn in with solid lines and highlighted with colors, while the correlations on the overlapped colors, while the correlations on the overlapped part of the rear panel are simply dashed in. part of the rear panel are simply dashed in.

When the vertical scale is too large or the When the vertical scale is too large or the spacing of sections is too close, very large spacing of sections is too close, very large parts of the rear panels may be obscured (parts of the rear panels may be obscured (Figure 2). ).

Figure 02Figure 02

Fence DiagramsFence Diagrams Usually, this problem can be minimized if the vertical Usually, this problem can be minimized if the vertical scale and the panel spacing are carefully chosen. scale and the panel spacing are carefully chosen. However, it is not always possible to change the scale However, it is not always possible to change the scale or spacing without losing important details illustrated or spacing without losing important details illustrated by the diagram. In such a case, one can construct an by the diagram. In such a case, one can construct an isometric projection of the fence diagram ( isometric projection of the fence diagram ( Figure 4 Figure 4 , , oonly lines parallel to the North-South and East-West nly lines parallel to the North-South and East-West axes are undistortedaxes are undistorted). ). The map base in an isometric projection is shown as if The map base in an isometric projection is shown as if it was turned at an angle and tilted toward the viewer. it was turned at an angle and tilted toward the viewer. The conversion is actually a transformation from The conversion is actually a transformation from orthogonal to nonorthogonal axes. A rectangular map orthogonal to nonorthogonal axes. A rectangular map base will become a parallelogram in an isometric base will become a parallelogram in an isometric projection ( projection ( Figure 3 and and Figure 4Figure 4). ).

• All lines that were parallel to the original horizontal and vertical axes remain parallel to the corresponding new axes, and the scale along these lines also remains unchanged. However, lines which were not parallel to the original axes will be distorted. Points along such lines must be transferred onto the projection by coordinates relative to the new axes. A grid system is helpful in this process.

Figure 03Figure 03

Figure 04Figure 04

Block DiagramsBlock Diagrams

• Along with the fence diagram, another type of diagram illustrating three- dimensional geological relationships is a block diagram (Figure 5).

• This type of figure is a two-dimensional representation of a rectangular block. Two intersecting cross sections often form the sides of the block; the top of the block shows either a mapped surface or relief on the uppermost geological boundary shown in the cross sections. The block may be rotated to achieve the most effective viewing angle, and it may be drawn with or without the use of perspective.

Figure 05Figure 05

Block DiagramsBlock Diagrams

• Isometric block diagrams do not employ perspective. opposite sides of the block remain parallel, making the distant end of the diagram appear to be larger (Figure 6 , Figure 7, and Figure 8).

The top of this type of block diagram may be given any degree of tilt toward the viewer.

Figure 06Figure 06

Figure 07Figure 07

Figure 08Figure 08

• A large amount of tilt emphasizes features on the top surface of the block; a smaller degree of tilt brings out details on the sides of the block. Scales along the x, y, and z axes need not be equal.

• The scale along the sides of the figure (y) is sometimes chosen to be smaller than the scale across the front and back edges (x), thus creating an illusion of perspective.

• Perspective can be used in constructing block diagrams (Figure 9).

Figure 09Figure 09

In perspective blocks, all parallel lines with a component in the y direction converge to a vanishing point on the horizon.

Sets of parallel lines with different orientations converge to different vanishing points.

The cross section on the front face of the block is usually left undistorted by perspective. It is possible both to rotate the block about the z axis or to display it at different elevations relative to the horizon. Again, the choice of block orientation is made to emphasize the important features of the diagram.