Geologic characteristics of hole-effect Variograms calculated from lithology-indicator variables

Variograms calculated from binary variables, such as from two lithologies, tend to show sinusoidal forms with decreasing amplitudes for increasing lag distances. This cyclicity is observed often when analyzing drill-hole data for rock sequences with alternating lithologies, and the variograms are thus labeled hole-effect variograms. Such variograms show a variety of forms: (1) Low to moderate variation in lithologic-body dimensions causes variograms to have strong cyclicity with decaying amplitude. (2) Variograms with one or more peaks and troughs usually result from a binary variable for which lithologies are about equally abundant but possibly large variations exist in the size of lithologic bodies. (3) Variograms show poor cyclicity if one lithology has highly variable body sizes and the other has moderately variable body dimensions. (4) Variograms that attain a plateau at short lag distances represent extremely high or low sandstone fraction, high variability in size of the most abundant lithology, and low variability in the other Information about the dimensions of lithologic bodies makes it possible to approximate characteristics of the variogram of the lithology variable without numerous wells. Conversely, a hole-effect variogram of lithology may be used to estimate lithologic dimensions.