Fractional Lévy motion as a model for spatial variability in sedimentary rock

Scott Painter, Lincoln Paterson

Research output: Contribution to journalArticlepeer-review

84 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)2857-2860
Number of pages4
JournalGeophysical Research Letters
Volume21
Issue number25
DOIs
StatePublished - Dec 15 1994
Externally publishedYes

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