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==Faults ==

==Faults ==

Few programs automatically identify faults based on input data; therefore, an interpretation of the presence and position of faults must be made prior to computer mapping. Once the fault interpretation has been made, several techniques exist for incorporating them into a surface model. Some commonly used methods are described here.

Few programs automatically identify faults based on input data; therefore, an interpretation of the presence and position of faults must be made prior to computer mapping. Once the fault interpretation has been made, several techniques exist for incorporating them into a surface model. Some commonly used methods are described here.

===Fault block===

===Fault block===

The fault block or polygon technique uses polygons to isolate fault blocks. Typically, several sides of the enclosing polygon are faults, while some are lines (zero throw faults) used to close the polygon. Digitized contours and data points for the surface inside the polygons are used to build that fault block's surface model. A separate model is built for each of the surface's fault blocks. To create a contour map, each of the fault block surface models must be contoured separately with the contours constrained to stay within the fault block's polygon. All of the contours are drawn on the same map along with the fault traces (Figure 13). Similarly, volumes must be calculated on a block-by-block basis and summed for the unit.

The fault block or polygon technique uses polygons to isolate fault blocks. Typically, several sides of the enclosing polygon are faults, while some are lines (zero throw faults) used to close the polygon. Digitized contours and data points for the surface inside the polygons are used to build that fault block's surface model. A separate model is built for each of the surface's fault blocks. To create a contour map, each of the fault block surface models must be contoured separately with the contours constrained to stay within the fault block's polygon. All of the contours are drawn on the same map along with the fault traces ([[:file:using-and-improving-surface-models-built-by-computer_fig13.png|Figure 13]]). Similarly, volumes must be calculated on a block-by-block basis and summed for the unit.

 

[[file:using-and-improving-surface-models-built-by-computer_fig13.png|thumb|{{figure number|13}}Separate surface models are built for each fault block. (a, b, and c) The surface for each fault block is allowed to extend past faults defining the block edge. (d) When displayed, contours are constrained to inside the fault block polygon and all models are displayed on the same map. (After <ref name=pt08r11 />.)]]

Special care must be taken when constructing a fault block surface near sides of polygons that do not represent faults. Since these portions of the polygons have been drawn across unfaulted surfaces, grid node values should change smoothly across these polygon lines.

Special care must be taken when constructing a fault block surface near sides of polygons that do not represent faults. Since these portions of the polygons have been drawn across unfaulted surfaces, grid node values should change smoothly across these polygon lines.

Fault gaps imply nonvertical faults, and traces with gaps would be expected to shift position from one surface to the next. Since digitizing polygons requires significant effort, the same set of polygons is often used for all surfaces (vertical faults). It is important to understand how a vertical assumption affects unit volumes.

Fault gaps imply nonvertical faults, and traces with gaps would be expected to shift position from one surface to the next. Since digitizing polygons requires significant effort, the same set of polygons is often used for all surfaces (vertical faults). It is important to understand how a vertical assumption affects unit volumes.

===Fault plane===

===Fault plane===

The fault plane technique is used to model surfaces cut by nonvertical faults when enough data are available to model fault faces and structural surfaces on either side of those faults. Separate models are built for each surface on each side of each fault and for each fault plane. Baselap (maximum) and truncation (minimum) operations are used to prevent surface models from projecting through faults that bound them and to merge faults that intersect one another properly (Figure 14). The faults are treated as if they were unconformities and the surfaces between faults as if they were sequences, thus the previously described techniques apply. For more than a few faults (three or four), the ordering of the operations becomes complex. Both normal and reverse faults can be modeled.

The fault plane technique is used to model surfaces cut by nonvertical faults when enough data are available to model fault faces and structural surfaces on either side of those faults. Separate models are built for each surface on each side of each fault and for each fault plane. Baselap (maximum) and truncation (minimum) operations are used to prevent surface models from projecting through faults that bound them and to merge faults that intersect one another properly ([[:file:using-and-improving-surface-models-built-by-computer_fig14.png|Figure 14]]). The faults are treated as if they were unconformities and the surfaces between faults as if they were sequences, thus the previously described techniques apply. For more than a few faults (three or four), the ordering of the operations becomes complex. Both normal and reverse faults can be modeled.

[[file:using-and-improving-surface-models-built-by-computer_fig14.png|thumb|{{figure number|14}}Surface models are constructed for the faults and for each surface on each side of each fault. Operations between surface models prevent them from projecting past one another.]]

If this technique is used, then creating displays and volumes for a surface or zone requires careful manipulation of a large number of surface models. This is because each surface is represented by a suite of surface models, one for each fault block. Also, much care is required to model surfaces cut by faults that fade out in the map area.

If this technique is used, then creating displays and volumes for a surface or zone requires careful manipulation of a large number of surface models. This is because each surface is represented by a suite of surface models, one for each fault block. Also, much care is required to model surfaces cut by faults that fade out in the map area.

[[file:using-and-improving-surface-models-built-by-computer_fig15.png|left|thumb|{{figure number|15}}Faults act as barriers beyond which data cannot be seen from the location for which a surface value is being calculated. (a) A grid node (indicated by +) to the west of fault A can only see data in the hatchured area. (b) A grid node farther to the south of fault A can see more data, thus the surface smoothly changes form around the fault ends.<ref name=pt08r11 />]]

===Fault trace===

===Fault trace===

The fault trace technique uses fault trace locations and a faulted surface modeling algorithm to build continuous faulted surface models. The algorithm prevents data on one side of a fault from being used when assigning values to the surface model on the other side of the fault (line-of-sight method) (Figure 15). This technique is used by a large number of mapping programs.

The fault trace technique uses fault trace locations and a faulted surface modeling algorithm to build continuous faulted surface models. The algorithm prevents data on one side of a fault from being used when assigning values to the surface model on the other side of the fault (line-of-sight method) ([[:file:using-and-improving-surface-models-built-by-computer_fig15.png|Figure 15]]). This technique is used by a large number of mapping programs.

 

[[file:using-and-improving-surface-models-built-by-computer_fig15.png|thumb|{{figure number|15}}Faults act as barriers beyond which data cannot be seen from the location for which a surface value is being calculated. (a) A grid node (indicated by +) to the west of fault A can only see data in the hatchured area. (b) A grid node farther to the south of fault A can see more data, thus the surface smoothly changes form around the fault ends. (After <ref name=pt08r11 />.)]]

For normal faults, the traces usually enclose an area called the ''fault gap''. The gap represents the area where the structure surface is missing. Nodes in this area are typically set to missing, although they are sometimes assigned values representative of the fault plane. Traces that do not have gaps imply vertical faults and therefore will not change position from surface to surface. Traces for nonvertical faults should shift from surface to surface, and those for significant throws will show a gap in map view.

For normal faults, the traces usually enclose an area called the ''fault gap''. The gap represents the area where the structure surface is missing. Nodes in this area are typically set to missing, although they are sometimes assigned values representative of the fault plane. Traces that do not have gaps imply vertical faults and therefore will not change position from surface to surface. Traces for nonvertical faults should shift from surface to surface, and those for significant throws will show a gap in map view.

Contouring, cross section, volumetrics, and other surface display and manipulation algorithms must be modified to use fault traces. When modified, these algorithms do not use surface model values from one side of a fault for contouring and volume calculations on the other side of the fault.

Contouring, cross section, volumetrics, and other surface display and manipulation algorithms must be modified to use fault traces. When modified, these algorithms do not use surface model values from one side of a fault for contouring and volume calculations on the other side of the fault.

===Vertical separation===

===Vertical separation===

Surface-modeling algorithms that use a fault's vertical separation (see <ref name=pt08r21>Tearpock, D. J., Bischke, R. E., 1991, Applied Subsurface Geological Mapping: Englewood Cliffs, NJ, Prentice Hall.</ref>, for definition) can use data from one side of a fault when building a surface model on the other side of the same fault. This is because data on the opposite side of a fault are adjusted by that fault's separation before being used to calculate the surface's value.

Surface-modeling algorithms that use a fault's vertical separation (see <ref name=pt08r21>Tearpock, D. J., Bischke, R. E., 1991, Applied Subsurface Geological Mapping: Englewood Cliffs, NJ, Prentice Hall.</ref>, for definition) can use data from one side of a fault when building a surface model on the other side of the same fault. This is because data on the opposite side of a fault are adjusted by that fault's separation before being used to calculate the surface's value.

Vertical separation modeling is usually handled either by (1) building a separation model for each fault and adjusting all the data at once or (2) adjusting each data point for vertical separation at the time it is used for surface modeling. In the first approach, a vertical separation model is built for each fault. All of the separation models for faults that affect a particular surface are added together. Data for that surface are shifted by the total separation at each location, moving them to their prefault position. A surface model is constructed using the adjusted data, and the total vertical separation model is then subtracted from the unfaulted surface model, creating the final faulted surface model (Figure 16).

Vertical separation modeling is usually handled either by (1) building a separation model for each fault and adjusting all the data at once or (2) adjusting each data point for vertical separation at the time it is used for surface modeling. In the first approach, a vertical separation model is built for each fault. All of the separation models for faults that affect a particular surface are added together. Data for that surface are shifted by the total separation at each location, moving them to their prefault position. A surface model is constructed using the adjusted data, and the total vertical separation model is then subtracted from the unfaulted surface model, creating the final faulted surface model ([[:file:using-and-improving-surface-models-built-by-computer_fig16.png|Figure 16]]).

 

[[file:using-and-improving-surface-models-built-by-computer_fig16.png|thumb|{{figure number|16}}(a) Surface model built with no fault constraints. (b) Model of vertical separation. (c) Unfaulted structure model built after removing vertical separation from data. (d) Faulted structure model built by subtracting separation model from unfaulted structure model. (After <ref name=pt08r11 />.)]]

The second approach is similar to the fault trace method in that it alters the use of a data point on the opposite side of a fault. However, instead of not using the point, it adjusts the point's z value by the vertical separation of the faults that lie between the point and the node being calculated (Figure 17).

[[file:using-and-improving-surface-models-built-by-computer_fig17.png|thumb|left|{{figure number|17}}The data value is adjusted by the separation of faults crossed by the line connecting the data point and the location for which an estimate is being made.]]

[[file:using-and-improving-surface-models-built-by-computer_fig17.png|thumb|{{figure number|17}}The data value is adjusted by the separation of faults crossed by the line connecting the data point and the location for which an estimate is being made.]]

The second approach is similar to the fault trace method in that it alters the use of a data point on the opposite side of a fault. However, instead of not using the point, it adjusts the point's z value by the vertical separation of the faults that lie between the point and the node being calculated ([[:file:using-and-improving-surface-models-built-by-computer_fig17.png|Figure 17]]).

Once constructed, cross sections, contour maps, volumes, and so on are commonly generated from these models using algorithms similar to those used for fault trace models. There are other methods for modeling with vertical separation, but regardless of which method is used, they all require significantly more information about faults than other fault-modeling methods. Often much of this information is not available. When this happens, most of these programs will “degenerate” to working as the fault trace method does.

Once constructed, cross sections, contour maps, volumes, and so on are commonly generated from these models using algorithms similar to those used for fault trace models. There are other methods for modeling with vertical separation, but regardless of which method is used, they all require significantly more information about faults than other fault-modeling methods. Often much of this information is not available. When this happens, most of these programs will “degenerate” to working as the fault trace method does.