FRACTIONAL LEVY MOTION AS A MODEL FOR SPATIAL VARIABILITY IN SEDIMENTARY-ROCK

A new approach to the modeling of spatial variability in sedimentary formations is introduced. This approach avoids the assumption of Gaussian behavior. Specifically, borehole measurements of physical properties of sedimentary rock from contrasting geological settings are shown to have a statistical character consistent with fractional Levy motion. Successive increments in the measurement sequences are accurately modeled as having Levy-stable distributions. The Levy parameters are similar for boreholes in the same sedimentary basin, but vary from basin to basin. Thinly bedded formations have smaller values for the Levy index, suggesting that the Levy index may be a useful measure of heterogeneity. The measurement sequences are also statistically self-similar and have long-range negative dependence among the increments (antipersistence). In addition to reproducing the statistical properties of well logs, the new model also mimics the most striking visual features of sedimentary formations.