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Spatial correlation of permeability in cross‐stratified sediment with hierarchical architecture
Author(s) -
Ritzi Robert W.,
Dai Zhenxue,
Dominic David F.,
Rubin Yoram N.
Publication year - 2004
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2003wr002420
Subject(s) - variogram , permeability (electromagnetism) , spatial correlation , geology , exponential function , mathematics , statistics , hierarchy , spatial variability , soil science , geometry , mathematical analysis , kriging , chemistry , biochemistry , membrane , economics , market economy
Cross‐stratified deposits can give rise to a hierarchy of permeability modes, across scales, corresponding to a hierarchy of sedimentary unit types. The shape of the sample semivariogram for permeability can be largely controlled by the shape of the cross‐transition probabilities of unit types having the greatest contrast in permeability. The shape of those cross‐transition probabilities can be, in turn, largely determined by the variance of the lengths of those unit types. A sufficient condition for an exponential‐like semivariogram is the repeated occurrence of unit types having both a contrast in permeability and a large length variance. These relationships are shown through writing the identities for spatial correlation of permeability in a hierarchical and multimodal form and as a function of the transition probabilities for the sedimentary unit types. These relationships are also illustrated through analyzing data representing cross‐stratified sediments within a point bar deposit.