Taken to extremes, every map contains an infinite number of points within its map area. Because it is impractical to sample or estimate the value of any variable at an infinite number of points within the map area, we define a grid to describe locations where estimates will be calculated for use in the contouring process.
A grid is formed by arranging a set of values into a regularly spaced array, commonly a square or rectangle, although other grid forms may also used. The locations of the values represent the geographic locations in the area to be mapped and contoured (Jones, et al., 1986). For example, well spacing and known geology might influence your decision to calculate porosity every 450 feet in the north-south direction, and every 300 feet in the east-west direction. By specifying a regular interval of columns (every 450 feet in the north-south
direction) and rows (every 300 feet in the east-west direction), you have, in effect, created a grid.
Grid nodes are formed by the intersection of each column with a row. The area enclosed by adjacent grid nodes is called a grid cell (three nodes for a triangular arrangement, or more commonly, four nodes for a square arrangement).
Because the sample data represent discrete points, a grid should be designed to reflect the average spacing between the wells, and designed such that the individual data points lie as closely as possible to a grid node.
GRID SPACING
The grid interval controls the detail that can be seen in the map. No features smaller than the interval are retained. To accurately define a feature, it must cover two to three grid intervals; thus the cell should be small enough to show the required detail of the feature. However, there is a trade-off involving grid size.
Large grid cells produce quick maps with low resolution, and a course
appearance. While small grid cells may produce a finer appearance with better resolution, they also tend to increase the size of the data set, thus leading to longer computer processing time; furthermore a fine grid often imparts gridding artifacts that show up in the resulting map (Jones, et al., 1986).
A rule of thumb says that the grid interval should be specified so that a given grid cell contains no more than one sample point. A useful approach is to estimate, by eye, the average well spacing, and use it as the grid interval, rounded to an even increment (e.g., 200 rather than 196.7).
GRIDS AND GRIDDING
Within the realm of geostatistics, you will often discover that seemingly similar words have quite different meanings. In this case, the word “gridding” should not be considered as just a grammatical variation on the word “grid.”
Gridding is the process of estimating the value of an attribute from isolated points onto a regularly spaced mesh, called a grid (as described above). The attribute‟s values are estimated at each grid node.
Interpolation And Contouring
The objective of contouring is to visually describe or delineate the form of a surface. The surface may represent a structural surface, such as depth to the top of a reservoir, or may represent the magnitude of a petrophysical property, such as porosity. Contour lines, strictly speaking, are isolines of elevation. However, geologists are rather casual about their use of terminology, and usually call any isoline a contour, whether it depicts elevation, porosity, thickness, composition, or other property.
Contour maps are a type of three-dimensional graph or diagram, compressed onto a flat, two-dimensional representation. The X-and Y-axes usually
correspond to the geographical coordinates east-west and north-south. The Z-axis typically represents the value of the attribute, for example: elevation with respect to sea level, or porosity, thickness, or some other quantity (Davis, 1986).
Contour lines connect points of equal value on a map, and the space between two successive contour lines contains only points falling within the interval defined by the contour lines. It is not possible to know the value of the surface at every possible location, nor can we measure its value at every point we might wish to choose. Thus, the purpose of contouring is to summarize large volumes of data and to depict its three-dimensional spatial distribution on a 2-D paper surface. We use contour maps to represent the value of the property at unsampled locations (Davis, 1986; Jones, et al., 1986).
The Interpolation Process
The mapping (interpolation) and contouring process involves four basic steps.
According to Jones, et al. (1986), the four mapping and contouring steps are:
1. Identifying the area and the attribute to be mapped (Figure 1 , Location and values of control points within the mapping area, North Cowden Field, West Texas);
Figure 1
2. Designing the grid over the area (Figure 2 , Grid design superimposed on the control points);
Figure 2
3. Calculating the values to be assigned at each grid node (Figure 3, Upper left quadrant of the grid shown in Figure 2.
Figure 3
The values represent interpolated values at the grid nodes.These values are used to create the contours shown in Figure 4);
4. Using the estimated grid node values to draw contours (Figure 4 , Contour map of porosity, created from the contol points in Figure 1 and the grid mesh values shown in Figure 3).
Figure 4
To illustrate these steps, we will use porosity measurements from the previously mentioned West Texas data set.
TRADITIONAL INTERPOLATION METHODS