QUANTIFYING THE SPATIAL HETEROGENEITY OF ATTRIBUTES IN SANDSTONES WITH POINT PATTERN ANALYSIS

Sandstone petrographic studies yield qualitative descriptions or scalar statistics of, e.g., modal composition of QFL and porosity, and grain size distribution (GSD). However, two sandstones with identical modal composition and/or GSD may differ significantly in the spatial distribution of these attributes. The differences, called spatial heterogeneity, contain critical clues on both depositional and diagenetic processes and is often described qualitatively. Quantifying the spatial heterogeneity of sandstones is challenged by its discrete multicomponent solid nature and scale-dependent patterns. A process-based spatial homogeneity is defined—a sandstone is homogeneous if it can be generated by a random process. Such process can be repeated numerous times to produce a stack of random patterns through Monte Carlo simulation by maintaining the same grain count and observation area. These patterns can be averaged to form a reference. Then, the degree of spatial heterogeneity of a sandstone is quantified as the deviation from this reference. Two statistics, Clark-Evans’ R and Hopkins-Skellem’s A, are used to characterize the spatial distribution of a point attribute in a sandstone into a single value, where all grains are represented by their centroid points with assigned coordinates in the study area. The statistic value of the observed sandstone is then compared to the mean and standard deviation of simulated random patterns to produce a p-value and a z-score. The p-value indicates the probability of a random process generating the observed pattern. The z-score, termed the Heterogeneity Index (HI), measures the type and degree of spatial heterogeneity: 0 for random, negative values for clustered, and positive values for regular patterns. The absolute value of HI indicates the degree of heterogeneity of a pattern. Tests on 2-D simulated patterns and the thin section of a lacustrine wave-dominated deltaic sandstone indicate that HI is an effective quantitative measurement of spatial heterogeneity of patterns of compositional and textural attributes and potentially linked with sedimentary processes. However, HI may be greatly affected by the area percentage (i.e. grain size) of an attribute. The effect and the spatial correlations of paired attributes are the focus of our current research.