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Fractional Lévy motion as a model for spatial variability in sedimentary rock
Author(s) -
Painter Scott,
Paterson Lincoln
Publication year - 1994
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/94gl02035
Subject(s) - geology , sedimentary rock , structural basin , borehole , sedimentary depositional environment , sedimentary basin , gaussian , geomorphology , paleontology , physics , quantum mechanics
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 Lévy motion. Successive increments in the measurement sequences are accurately modeled as having Lévy‐stable distributions. The Lévy parameters are similar for boreholes in the same sedimentary basin, but vary from basin to basin. Thinly bedded formations have smaller values for the Lévy index, suggesting that the Lévy 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.