Changes

[[file:using-and-improving-surface-models-built-by-computer_fig2.png|thumb|300px|{{figure number|2}}Cross section showing the output from filtering being constrained between models built by shifting the initial surface model up and down slightly.]]

[[file:using-and-improving-surface-models-built-by-computer_fig2.png|thumb|300px|{{figure number|2}}Cross section showing the output from filtering being constrained between models built by shifting the initial surface model up and down slightly.]]

A common problem with computer-generated surface models are surface structures that are not supported by data. That is, the structures are by-products of the surface-modeling algorithm. Filters such as least squares, biharmonic, laplacian, and others can be applied to existing surface models to remove these unsupported structures. Data should be honored while filtering so that data values continue to fall on the correct side of contours.

A common problem with computer-generated surface models are surface structures that are not supported by data. That is, the structures are by-products of the surface-modeling algorithm. Filters such as least squares, biharmonic, laplacian, and others can be applied to existing surface models to remove these unsupported structures. Data should be honored while filtering so that data values continue to fall on the correct side of [[contour]]s.

Sometimes undesired contour wobbles are caused by data. For example, shot point values for a seismic line that parallels strike and whose shot point z values fluctuate about a contour value will cause contours to wobble through the data. This wobble is due to noise in the seismic data and is usually undesirable. Many filter programs allow surface models other than the one being filtered to act as upper and lower constraints within which the resultant surface model must stay. By shifting the original surface model up and down by small amounts (magnitude of the wobbles) and using these new surfaces to constrain filtering, a smoother model that still honors surface form can be created ([[:file:using-and-improving-surface-models-built-by-computer_fig2.png|Figure 2]]).

Sometimes undesired contour wobbles are caused by data. For example, shot point values for a seismic line that parallels strike and whose shot point z values fluctuate about a contour value will cause contours to wobble through the data. This wobble is due to noise in the seismic data and is usually undesirable. Many filter programs allow surface models other than the one being filtered to act as upper and lower constraints within which the resultant surface model must stay. By shifting the original surface model up and down by small amounts (magnitude of the wobbles) and using these new surfaces to constrain filtering, a smoother model that still honors surface form can be created ([[:file:using-and-improving-surface-models-built-by-computer_fig2.png|Figure 2]]).

====Regional trend assist====

====Regional trend assist====

This technique is sometimes used when the surface is tilted, projection up and down dip is desired, and algorithms that project slope do not produce acceptable results ([[:file:using-and-improving-surface-models-built-by-computer_fig3.png|Figure 3]]). The general steps are (1) build a first- or second-order trend surface through the data, (2) back interpolate from the trend surface a ''z'' value at each data location, (3) subtract the back interpolated values from the original data creating difference values, (4) build a surface model of the difference, and (5) add the difference surface to the trend surface.

This technique is sometimes used when the surface is tilted, projection up and down [[dip]] is desired, and algorithms that project slope do not produce acceptable results ([[:file:using-and-improving-surface-models-built-by-computer_fig3.png|Figure 3]]). The general steps are (1) build a first- or second-order trend surface through the data, (2) back interpolate from the trend surface a ''z'' value at each data location, (3) subtract the back interpolated values from the original data creating difference values, (4) build a surface model of the difference, and (5) add the difference surface to the trend surface.

[[file:using-and-improving-surface-models-built-by-computer_fig4.png|300px|thumb|{{figure number|4}}Cross sections through the same data. (a) The surface model does not honor the data. (b) Surface is shifted to data by modeling the error between the data and the original surface and then adding the original and error models.]]

[[file:using-and-improving-surface-models-built-by-computer_fig4.png|300px|thumb|{{figure number|4}}Cross sections through the same data. (a) The surface model does not honor the data. (b) Surface is shifted to data by modeling the error between the data and the original surface and then adding the original and error models.]]

===Digitize and model hand-drawn contours===

===Digitize and model hand-drawn contours===

Often too few data are available to build an acceptable surface model or to support the detailed shape of a geologist's interpretation. If this problem exists over most of the map area, then editing the output model or using dummy points is not feasible. Instead, hand-drawn maps should be used. Contours from hand-drawn maps are digitized and used as input for the surface modeling algorithms. Some algorithms are specifically designed for digitized contours. If one of these is not available, there are usually specific parameter settings that make point-modeling algorithms effective for modeling digitized contours.

Often too few data are available to build an acceptable surface model or to support the detailed shape of a geologist's interpretation. If this problem exists over most of the map area, then editing the output model or using dummy points is not feasible. Instead, hand-drawn maps should be used. [[Contour]]s from hand-drawn maps are digitized and used as input for the surface modeling algorithms. Some algorithms are specifically designed for digitized contours. If one of these is not available, there are usually specific parameter settings that make point-modeling algorithms effective for modeling digitized contours.

==Intersecting surface techniques==

==Intersecting surface techniques==

===Baselap and truncation===

===Baselap and truncation===

For computer mapping, the term ''baselap'' can be defined as the abrupt termination of a higher surface (usually depositional) against a lower surface. A similar definition could be used for ''truncation''—the abrupt termination of a lower surface against a higher surface (usually an unconformity).

For computer mapping, the term ''baselap'' can be defined as the abrupt termination of a higher surface (usually depositional) against a lower surface. A similar definition could be used for ''truncation''—the abrupt termination of a lower surface against a higher surface (usually an [[unconformity]]).

Most computer mapping systems build a surface model using only data for that surface. When one surface laps onto or truncates another, the initial surface models will almost always cross ([[:file:using-and-improving-surface-models-built-by-computer_fig8.png|Figure 8]]). This is expected and must be corrected. The following discussion describes methods for handling baselap and truncation in a grid-based mapping system.

Most computer mapping systems build a surface model using only data for that surface. When one surface laps onto or truncates another, the initial surface models will almost always cross ([[:file:using-and-improving-surface-models-built-by-computer_fig8.png|Figure 8]]). This is expected and must be corrected. The following discussion describes methods for handling baselap and truncation in a grid-based mapping system.

====Baselap====

====Baselap====

Baselap can be achieved in several ways. To baselap one grid onto another for the purpose of cross section display and volumetrics work, the elevation ''z'' values at each grid node are compared and the maximum value is retained in a new grid. This makes the two grids coincident in the area where the upper grid is missing due to base lap ([[:file:using-and-improving-surface-models-built-by-computer_fig9.png|Figure 9]]).

Baselap can be achieved in several ways. To baselap one grid onto another for the purpose of [[cross section]] display and volumetrics work, the elevation ''z'' values at each grid node are compared and the maximum value is retained in a new grid. This makes the two grids coincident in the area where the upper grid is missing due to base lap ([[:file:using-and-improving-surface-models-built-by-computer_fig9.png|Figure 9]]).

Contour maps of baselapping surfaces should have no contours in areas of baselap because the surface does not exist there. To baselap one grid onto another for map display, the elevation z values at each grid node are compared and the value of the baselapping grid is set to missing if lower or kept if higher than the other grid ([[:file:using-and-improving-surface-models-built-by-computer_fig9.png|Figure 9]]).

Contour maps of baselapping surfaces should have no contours in areas of baselap because the surface does not exist there. To baselap one grid onto another for map display, the elevation z values at each grid node are compared and the value of the baselapping grid is set to missing if lower or kept if higher than the other grid ([[:file:using-and-improving-surface-models-built-by-computer_fig9.png|Figure 9]]).

====Truncation====

====Truncation====

With only a few modifications, the approach used for baselap can be applied to truncation. For cross section and volumetrics work, the two grids are compared and the minimum is kept as the new truncated grid. For contour display, the grids are compared and the values of the truncated grid are set to missing if higher or kept if lower than the other grid. The intersection grid for subcrop display is built just as it was for baselap.

With only a few modifications, the approach used for baselap can be applied to truncation. For [[cross section]] and volumetrics work, the two grids are compared and the minimum is kept as the new truncated grid. For [[contour]] display, the grids are compared and the values of the truncated grid are set to missing if higher or kept if lower than the other grid. The intersection grid for subcrop display is built just as it was for baselap.

===Combining baselap, truncation, and conformity===

===Combining baselap, truncation, and conformity===

In projects involving more than two surfaces, the techniques for baselap, truncation, and conformity are often used in combination ([[:file:using-and-improving-surface-models-built-by-computer_fig12.png|Figure 12]]). The following rules are used to order the techniques:

In projects involving more than two surfaces, the techniques for baselap, truncation, and conformity are often used in combination ([[:file:using-and-improving-surface-models-built-by-computer_fig12.png|Figure 12]]). The following rules are used to order the techniques:

* On a hand-drawn cross section showing all surface relationships, identify the unconformities.

* On a hand-drawn [[cross section]] showing all surface relationships, identify the [[Unconformity|unconformities]].

* Identify the sequences of conformable surfaces.

* Identify the sequences of conformable surfaces.

* Select a control surface (the surface that builds the best grid) for each sequence.

* Select a control surface (the surface that builds the best grid) for each sequence.

===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 ([[: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.

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 [[Unconformity|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.

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.

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===

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]]).

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 section]]s, 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.

===Combined methods===

===Combined methods===

==Volumetrics==

==Volumetrics==

Estimates of volumes are normally calculated between two structure surfaces, above a fluid contact, or sometimes below another fluid contact.

Estimates of volumes are normally calculated between two structure surfaces, above a [[Fluid contacts|fluid contact]], or sometimes below another fluid contact.

===The volumetrics algorithm===

===The volumetrics algorithm===

Following is a brief description of the range of volume calculation techniques used. This discussion uses a grid-based system, although similar procedures could apply to triangulated or other systems. The discussion assumes that volumes are calculated within a bounding area (polygon).

Following is a brief description of the range of volume calculation techniques used. This discussion uses a grid-based system, although similar procedures could apply to triangulated or other systems. The discussion assumes that volumes are calculated within a bounding area (polygon).

====Volume by point count====

====Volume by point count====

This approach assumes that each grid cell extends from a base up to a flat top, which is the grid node's value, and that the node is in the center of the cell. If the center of the cell is inside the polygon, it is counted; if it is outside, it is not ([[:file:using-and-improving-surface-models-built-by-computer_fig18.png|Figure 18]]).

This approach assumes that each grid cell extends from a base up to a flat top, which is the grid node's value, and that the node is in the center of the cell. If the center of the cell is inside the polygon, it is counted; if it is outside, it is not ([[:file:using-and-improving-surface-models-built-by-computer_fig18.png|Figure 18]]).

====Volume by simple plane fits====

====Volume by simple plane fits====

Grid nodes occupy corners of grid cells, and a line is drawn diagonally across a cell dividing it into two triangles. The value at each corner of the triangle is known; therefore, a flat plane can be fit through these points. The base above which volumes are to be calculated is also a plane, and its value is known. Since the dimensions of the sides of the triangular prism are known from the grid increments, all of the information needed to calculate the prism's volume is available. The volume of all triangle prisms totally inside the polygon are calculated and summed. Any prisms partially within the polygon are subdivided into smaller prisms with the values at the corners of the smaller prisms linearly interpolated from the three original triangle corners. The volumes of these partial values are calculated, summed, and added to the volume of prisms totally within the polygon ([[:file:using-and-improving-surface-models-built-by-computer_fig19.png|Figure 19]]).

Grid nodes occupy corners of grid cells, and a line is drawn diagonally across a cell dividing it into two triangles. The value at each corner of the triangle is known; therefore, a flat plane can be fit through these points. The base above which volumes are to be calculated is also a plane, and its value is known. Since the dimensions of the sides of the triangular prism are known from the grid increments, all of the information needed to calculate the prism's volume is available. The volume of all triangle prisms totally inside the polygon are calculated and summed. Any prisms partially within the polygon are subdivided into smaller prisms with the values at the corners of the smaller prisms linearly interpolated from the three original triangle corners. The volumes of these partial values are calculated, summed, and added to the volume of prisms totally within the polygon ([[:file:using-and-improving-surface-models-built-by-computer_fig19.png|Figure 19]]).

====Volume by mathematical fit and integration====

====Volume by mathematical fit and integration====

Political boundaries, [[porosity]] cutoffs, or other types of constraints must also be incorporated into the calculation. In some systems, these are incorporated into the model before going into the volumetrics program. In others, they are handeled automatically by the program.

Political boundaries, [[porosity]] cutoffs, or other types of constraints must also be incorporated into the calculation. In some systems, these are incorporated into the model before going into the volumetrics program. In others, they are handeled automatically by the program.

===Modeling and volume calculation in a thickness domain===

===Modeling and volume calculation in a thickness domain===

There are many considerations when building each of these surface models.

There are many considerations when building each of these surface models.

====Building the GR model====

====Building the GR model====

Once constructed, the base of volume model is subtracted from the top of volume model, creating the gross rock thickness model. This model is positive where thickness exists and either zero or negative where it does not. The negatives in this case are desired as they allow clear definition of the reservoir edge (zero line).

Once constructed, the base of volume model is subtracted from the top of volume model, creating the gross rock thickness model. This model is positive where thickness exists and either zero or negative where it does not. The negatives in this case are desired as they allow clear definition of the reservoir edge (zero line).

====Other variables for volumetrics====

====Other variables for volumetrics====

Often porosity and water saturation (and sometimes net to gross ratio) are input as constants representing the average value over the area of interest. Otherwise the variables are entered as surface models. Creating these surface models is complex and can be done in many ways. One of the most common is to digitize a hand-drawn map and build a model. Another is to build a model from well data. During model construction and use, certain issues must be considered:

Often porosity and water saturation (and sometimes net to gross ratio) are input as constants representing the average value over the area of interest. Otherwise the variables are entered as surface models. Creating these surface models is complex and can be done in many ways. One of the most common is to digitize a hand-drawn map and build a model. Another is to build a model from well data. During model construction and use, certain issues must be considered:

* Incomplete information caused by partial penetration, eroded top, faulting, and so on is often encountered. When this happens, the value of net to gross ratio or any other parameter being modeled will only represent the portion of the rock unit present. [[:file:using-and-improving-surface-models-built-by-computer_fig24.png|Figure 24]] demonstrates this problem for a partially penetrating well. The N: G for the middle well is 0.875 (or 3.5/4), while for the left and right wells, which fully penetrate the unit, the N: G is 0.55. Clearly the partial unit value does not correctly represent the “true” unit value. If the missing portion was pay, then the N: G would be 0.95 [(3.5 + 6)/10]. If the missing portion was nonpay, then the N: G would be 0.35 (3.5/10). The true N: G lies somewhere between these two limits. Special techniques must be used to model incomplete data (<xref ref-type="bibr" rid="pt08r11">Jones et al., 1986</xref>).

* Incomplete information caused by partial penetration, eroded top, faulting, and so on is often encountered. When this happens, the value of net to gross ratio or any other parameter being modeled will only represent the portion of the rock unit present. [[:file:using-and-improving-surface-models-built-by-computer_fig24.png|Figure 24]] demonstrates this problem for a partially penetrating well. The N: G for the middle well is 0.875 (or 3.5/4), while for the left and right wells, which fully penetrate the unit, the N: G is 0.55. Clearly the partial unit value does not correctly represent the “true” unit value. If the missing portion was pay, then the N: G would be 0.95 [(3.5 + 6)/10]. If the missing portion was nonpay, then the N: G would be 0.35 (3.5/10). The true N: G lies somewhere between these two limits. Special techniques must be used to model incomplete data.<ref name=pt08r11 />

* Modeling water saturation using standard algorithms and well data generally does not produce acceptable results. This is because the amount of water in the oil or gas portion of the reservoir is dependent upon porosity, [[permeability]], height above fluid contact, and other factors. Generally several engineering functions (J-curves) that relate porosity, height above fluid contact, and water saturation are used to convert structure top, structure base, fluid contact, and porosity models to a water saturation model (<xref ref-type="bibr" rid="pt08r9">Hamilton and Jones, 1992</xref>). The resulting model can be adjusted to honor the existing water saturation data at wells.

* Modeling water saturation using standard algorithms and well data generally does not produce acceptable results. This is because the amount of water in the oil or gas portion of the reservoir is dependent upon porosity, [[permeability]], height above [[Fluid contacts|fluid contact]], and other factors. Generally several engineering functions (J-curves) that relate porosity, height above fluid contact, and water saturation are used to convert structure top, structure base, fluid contact, and porosity models to a water saturation model.<ref name=pt08r9 /> The resulting model can be adjusted to honor the existing water saturation data at wells.

* Net to gross and sometimes average porosity can change rapidly in the area extending from the point where the base of reservoir encounters the fluid contact to the reservoir edge (wedge zone). If the vertical distribution of net rock is not homogeneous throughout the reservoir, then these variables may change significantly in the wedge zone relative to values where the reservoir is full thickness. Often these changes are ignored. Sometimes the reservoir is separated into subzones, with a full suite of volumetric models constructed for each subzone. Three-dimensional modeling of net and porosity is a more precise solution.

* Net to gross and sometimes average porosity can change rapidly in the area extending from the point where the base of reservoir encounters the fluid contact to the reservoir edge (wedge zone). If the vertical distribution of net rock is not homogeneous throughout the reservoir, then these variables may change significantly in the wedge zone relative to values where the reservoir is full thickness. Often these changes are ignored. Sometimes the reservoir is separated into subzones, with a full suite of volumetric models constructed for each subzone. Three-dimensional modeling of net and porosity is a more precise solution.

* If more than one of the four models input to the HPT equation contain negative values, then additional incorrect volumes could result. This is because these models are multiplied together, and if two have negative values at the same location, the resulting value will be positive, creating a volume where no volume should exist. A commonly used safety measure is to clip porosity, water saturation, and net-to-gross models to a minimum value of zero, eliminating the problem. Zeros in the model often produce a very jagged zero line contour. However, that is preferred rather than significant volume errors. There are techniques for correcting these jagged zero contour lines.

* If more than one of the four models input to the HPT equation contain negative values, then additional incorrect volumes could result. This is because these models are multiplied together, and if two have negative values at the same location, the resulting value will be positive, creating a volume where no volume should exist. A commonly used safety measure is to clip porosity, water saturation, and net-to-gross models to a minimum value of zero, eliminating the problem. Zeros in the model often produce a very jagged zero line contour. However, that is preferred rather than significant volume errors. There are techniques for correcting these jagged zero contour lines.

==Other surface modeling tools==

==Other surface modeling tools==

In addition to algorithms for gridding, contouring, and cross section display, there are many other tools required for effective computer mapping. Whether a grid, triangulated mesh, or other surface model is used, most of these tools are needed. Where appropriate, the term ''surface model'' is used instead of grid to make the descriptions more general. Here is a list of some of those tools:

In addition to algorithms for gridding, contouring, and [[cross section]] display, there are many other tools required for effective computer mapping. Whether a grid, triangulated mesh, or other surface model is used, most of these tools are needed. Where appropriate, the term ''surface model'' is used instead of grid to make the descriptions more general. Here is a list of some of those tools:

* Single data and surface operations—Add, subtract, multiply, and divide by a constant, trigonometric functions, blank max, blank min, clip max, clip min, normalize, dip and azimuth, statistics, rotate, and so on.

* Single data and surface operations—Add, subtract, multiply, and divide by a constant, trigonometric functions, blank max, blank min, clip max, clip min, normalize, dip and [[azimuth]], statistics, rotate, and so on.

* Dual data and surface operations—Add, subtract, multiply, divide, union, intersection, max, min, blank max, blank min, clip max, clip min, and so on.

* Dual data and surface operations—Add, subtract, multiply, divide, union, intersection, max, min, blank max, blank min, clip max, clip min, and so on.

* Polygon blanking—One or more polygons are used to blank or set to another value data or surface values inside or outside the polygons.

* Polygon blanking—One or more polygons are used to blank or set to another value data or surface values inside or outside the polygons.

==See also==

==See also==

* [[Introduction to integrated computer methods]]

* [[Cross section]]

* [[A development geology workstation]]

* [[A development geology workstation]]

* [[Log analysis applications]]

* [[Log analysis applications]]

[[Category:Integrated computer methods]]

[[Category:Integrated computer methods]]