A significant problem in automatic interpolation procedures is that of honoring data points exactly. When maps of subsurface structures are made by computer, contours can pass on the wrong side of well data points or, where the well log depth is the same as the contour, not pass through them. They will be misplaced a varying amount depending on the grid size employed during interpolation. Honoring the data points can be guaranteed only if the rectangular or triangular grid base has as some proportion of its nodes the wells themselves. Therefore, the concept of a variable size grid is introduced using either rectangles or triangles, with the cell size decreasing in areas of closely clustered boreholes. By using locally defined functions it is possible to maintain a continu us surface over the whole map area and create a faithful representation of the structures in the map. FELIX, a minicomputer mapping and analysis system, is one system used to interpolate the subsurface structure of an oil field where the wells are distributed unevenly over the test area. In the triangular case in this system, it seems likely that little time need be spent searching for optimal triangular networks and a relatively simple algorithm is substituted.

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