The influence of resolution on scale-dependent clustering in fracture spacing data

Abstract

It is a common practice to analyze fracture spacing data collected from scanlines and wells at various resolutions for the purposes of aquifer and reservoir characterization. However, the influence of resolution on such analyses is not well-studied. Lacunarity is a parameter that is used for multiscale analysis of spatial data. In quantitative terms, at any given scale, it is a function of the mean and variance of the distribution of masses captured by a gliding a window of that scale (size) across any pattern of interest. We have described the application of lacunarity for delineating differences between scale-dependent clustering attributes of data collected at different resolutions along a scanline. Specifically, we considered data collected at different resolutions from two outcrop exposures, a pavement and a cliff section, of the Cretaceous turbititic sandstones of the Chatsworth Formation widely exposed in southern California. For each scanline, we analyzed data from low-resolution aerial or ground photographs and high-resolution ground measurements for scale-dependent clustering attributes. High-resolution data show larger values of scale-dependent lacunarity than their respective low-resolution counterparts. We further performed a bootstrap analysis for each data set to test for the significance of such clustering differences. We started with generating 300 realizations for each data set and then ran lacunarity analysis on them. It was seen that lacunarity for higher resolution data set lay significantly outside the upper 90th percentile values, thus proving that higher resolution data are distinctly different from random and fractures are clustered. We have therefore postulated that lower resolution data capture fracture zones that had relatively uniform spacing, whereas higher resolution data capture thin and short splay joints and sheared joints that contribute to fracture clustering. Such findings have important implications in terms of understanding organization of fractures in fracture corridors, which in turn is critical for modeling and upscaling exercises.