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. |