Changes

  | isbn    = 0891816607

  | isbn    = 0891816607

}}

}}

A basic tool for analysis and display of spatial geological data is the contour map. A contour map displays variation of a geological variable, such as thickness, depth, or [[porosity]], over an area of interest with contour lines of equal value. Often, one or more contoured maps form the basis of detailed analysis of potential or actual reservoirs and are used to estimate volumes of fluids contained within pore spaces of the geological feature of interest. These studies require that maps be graphically presentable and that values underlying the graphic representation of the surface be reliable and reproducible. Errors inherent in mathematical estimation procedures must be understood so that reliability of values (volumes, percentages, and so on) obtained from these maps can be estimated.

A basic tool for analysis and display of spatial geological data is the [[contour]] map. A contour map displays variation of a geological variable, such as thickness, depth, or [[porosity]], over an area of interest with contour lines of equal value. Often, one or more contoured maps form the basis of detailed analysis of potential or actual reservoirs and are used to estimate volumes of fluids contained within pore spaces of the geological feature of interest. These studies require that maps be graphically presentable and that values underlying the graphic representation of the surface be reliable and reproducible. Errors inherent in mathematical estimation procedures must be understood so that reliability of values (volumes, percentages, and so on) obtained from these maps can be estimated.

Shapes of geological surfaces are complex and not readily approximated by simple mathematical functions because they result from a multitude of interacting processes that vary at different spatial scales. Ideally, spatial data should be examined with a spatial sample of regular geometric design. These designs can capture the range of variation exhibited by most spatial phenomena. However, such designs are, for all practical purposes, impossible for most geological work, although in some instances recent developments in satellite imagery allow their economic implementation. In most cases, subsurface geological features are sparsely sampled relative to their complexity and the samples are highly biased to geophysical and/or geological anomalies. Therefore, values of a variable across an area of interest must be estimated by interpolating from a sparse, irregular control point set.

Shapes of geological surfaces are complex and not readily approximated by simple mathematical functions because they result from a multitude of interacting processes that vary at different spatial scales. Ideally, spatial data should be examined with a spatial sample of regular geometric design. These designs can capture the range of variation exhibited by most spatial phenomena. However, such designs are, for all practical purposes, impossible for most geological work, although in some instances recent developments in satellite imagery allow their economic implementation. In most cases, subsurface geological features are sparsely sampled relative to their complexity and the samples are highly biased to geophysical and/or geological anomalies. Therefore, values of a variable across an area of interest must be estimated by interpolating from a sparse, irregular control point set.

[[file:introduction-to-contouring-geological-data-with-a-computer_fig6.png|300px|thumb|{{figure number|6}}A13 × 13 grid showing the relationship between grid nodes and control points for the Davis<ref name=pt08r6 /> data set.]]

[[file:introduction-to-contouring-geological-data-with-a-computer_fig6.png|300px|thumb|{{figure number|6}}A13 × 13 grid showing the relationship between grid nodes and control points for the Davis<ref name=pt08r6 /> data set.]]

Rectangular gridding, in contrast to triangulation, first uses data at measured control points to interpolate values to a set of grid nodes at a predefined spacing. These values are then used to estimate positions of contours crossing each grid rectangle. The complete surface is assembled from contiguous grid rectangles. For most geological applications, grid squares are used rather than the more general rectangle. Interpolation and contouring of an irregularly spaced control point set on a rectangular grid requires many decisions from the geologist.

Rectangular gridding, in contrast to triangulation, first uses data at measured control points to interpolate values to a set of grid nodes at a predefined spacing. These values are then used to estimate positions of [[contour]]s crossing each grid rectangle. The complete surface is assembled from contiguous grid rectangles. For most geological applications, grid squares are used rather than the more general rectangle. Interpolation and contouring of an irregularly spaced control point set on a rectangular grid requires many decisions from the geologist.

To obtain a contoured surface representation by a rectangular gridding method, the geologist must decide on a grid spacing, a search criterion, and the method with which to interpolate control point data to grid nodes as well as a suitable contour interval. Most commercial mapping packages include a variety of options for spacing, search criterion, and method. These decisions require an understanding of the relationship between control point density/distribution and the texture of the surface.

To obtain a contoured surface representation by a rectangular gridding method, the geologist must decide on a grid spacing, a search criterion, and the method with which to interpolate control point data to grid nodes as well as a suitable contour interval. Most commercial mapping packages include a variety of options for spacing, search criterion, and method. These decisions require an understanding of the relationship between control point density/distribution and the texture of the surface.