Subsurface structural maps are stored as spatially referenced numeric grids. The spatial sampling density of these grids is a critical parameter in the mapping process because the sampling and aliasing that occurs when transforming from original data sources during the gridding process controls the information content and aesthetics of the final map. New results from upscaling experiments and sampling theory indicate that it is possible to specify gridding parameters that remove noise while retaining key geologic structure — an optimized generalization procedure. Furthermore, geologic structure may exist at multiple scales. Sampling theory can again be applied, in a multiscale curvature analysis, to yield structure at a range of scales via decomposition of a gridded surface. These products can be analyzed further for indications of short-wavelength, high-curvature features that may correspond to fault or fracture zones, and long-wavelength, prospect, and field-scale structure. These results combine to inform a discussion on sampling, smoothing, and geologic information, as well as provide a quantitative alternative to rules of thumb for grid sampling that balance signal and noise in standard mapping schemes.