Quantifying lateral heterogeneities in fluvio‐deltaic sediments using three‐dimensional reflection seismic data: Offshore Gulf of Mexico

Deshpande, Anil; Flemings, Peter B.; Huang, Jie

doi:10.1029/97jb01143

Cited by 14 publications

(18 citation statements)

References 45 publications

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“…They concluded that the fluvial sediments (with high‐amplitude channels trending north‐northwest) in one horizontal plane were consistent with FBM with H ≈ 0.4 to 0.65 in roughly the direction of channels (along dip) and H ≈ 0.05 transverse to the channels (along strike). Deshpande et al [1997] found less striking evidence of horizontal anisotropy in the deltaic sediments, with different H values of 0.26 versus 0.4. All of their vertical data was in the FBM range, with H ≈ 0.3 to 0.5.…”

Section: Operator‐scaling Random Fieldsmentioning

confidence: 77%

Aquifer operator scaling and the effect on solute mixing and dispersion

Benson

Meerschaert

Baeumer

et al. 2006

Water Resources Research

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[1] Since aquifer parameters may have statistical dependence structures that are present across a huge range of scales, the concepts of fractional Brownian motion (fBm) have been used in both analytic and numerical stochastic settings. Most previous models have used isotropic scaling characterized by a single scalar Hurst coefficient. Any real-world anisotropy has been handled by an elliptical stretching random K field. We define a d-dimensional extension of fBm in which the fractional-order integration may take on different orders in the d primary (possibly nonorthogonal) scaling directions, and the degree of connectivity and long-range dependence is freely assigned via a probability measure on the unit sphere. This approach accounts for the different scaling found in the vertical versus horizontal directions in sedimentary aquifers and allows very general degrees of continuity of K in certain directions. It also allows for the representation of fracture networks in a continuum setting: The eigenvectors of the scaling matrix describe the primary fracture scaling directions, and discrete weights of fractional integration represent fracture continuity that may be limited to a small number of directions. In a numerical experiment, the motion of solutes through 2-D ''operator-fractional'' Gaussian fields depends very much on transverse Hurst coefficients. Transverse scaling in the range of fractional Gaussian noise engenders greater plume mixing and a transition to a Fickian regime. Higher orders of integration, in the range of fractional Brownian motion, are associated with thicker layering of aquifer sediments and more preferential, unmixed transport. Therefore direct representation of the unique directional scaling properties of an aquifer is important for realistic simulation of transport.

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Section: Operator‐scaling Random Fieldsmentioning

confidence: 77%

Aquifer operator scaling and the effect on solute mixing and dispersion

Benson

Meerschaert

Baeumer

et al. 2006

Water Resources Research

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“…Following [11][12][13][14][15][16][17][18][19][20][21], statistical scaling of moments of velocity is investigated through the analysis of directional sample structure functions, i.e., qth-order statistical moments of absolute increments…”

Section: Scaling Of Statisticsmentioning

confidence: 99%

“…Indeed, the statistics of hydrological properties in aquifers and reservoirs exhibit dependences on various characteristic length scales, e.g., measurement volume and resolution, scale of observation, spatial correlation, and size of the sampled domain [10]. Scaling analyses of statistical moments of hydraulic conductivity and permeability data have been presented in many works, including [11][12][13][14][15][16][17][18][19][20]. In all these studies, measurement volumes are associated with a support scale ranging from the millimeter to the meter and data sets are collected on domains at the field (kilometer) or laboratory (decimeter to meter) scale.…”

Section: Introductionmentioning

confidence: 99%

“…Similar to [11][12][13][14][15][16][17][18][19][20][21], we do so by relying on the analysis of sample structure functions of order q > 0 of such increments. We then compare the scaling behaviors observed for static (i.e., local porosity and surface area) and dynamic (i.e., Lagrangian velocity) quantities, evaluated on the same rock samples.…”

Section: Introductionmentioning

confidence: 99%

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Statistical scaling of pore-scale Lagrangian velocities in natural porous media

et al. 2014

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We investigate the scaling behavior of sample statistics of pore-scale Lagrangian velocities in two different rock samples, Bentheimer sandstone and Estaillades limestone. The samples are imaged using x-ray computer tomography with micron-scale resolution. The scaling analysis relies on the study of the way qth-order sample structure functions (statistical moments of order q of absolute increments) of Lagrangian velocities depend on separation distances, or lags, traveled along the mean flow direction. In the sandstone block, sample structure functions of all orders exhibit a power-law scaling within a clearly identifiable intermediate range of lags. Sample structure functions associated with the limestone block display two diverse power-law regimes, which we infer to be related to two overlapping spatially correlated structures. In both rocks and for all orders q, we observe linear relationships between logarithmic structure functions of successive orders at all lags (a phenomenon that is typically known as extended power scaling, or extended self-similarity). The scaling behavior of Lagrangian velocities is compared with the one exhibited by porosity and specific surface area, which constitute two key pore-scale geometric observables. The statistical scaling of the local velocity field reflects the behavior of these geometric observables, with the occurrence of power-law-scaling regimes within the same range of lags for sample structure functions of Lagrangian velocity, porosity, and specific surface area.

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“…Porosity logs from 15 wells drilled in a deltaic environment in the Gulf of Mexico give a spectral slope of 1.4 with a standard deviation of 0.2 [ Pelletier and Turcotte , 1996]. However, within the same basin, vertical geophysical well logs of a multifacies sand/shale deposit from a fluvial/deltaic system give a spectral slope ranging from 1.4 to 2.1 [ Deshpande et al , 1997], higher than the other data and falling outside the range of 1/ f noise.…”

Section: Discussionmentioning

confidence: 99%

Geostatistical analysis of an experimental stratigraphy

Zhang

Person

Paola

et al. 2005

Water Resources Research

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[1] A high-resolution stratigraphic image of a flume-generated deposit was scaled up to sedimentary basin dimensions where a natural log hydraulic conductivity (ln(K)) was assigned to each pixel on the basis of gray scale and conductivity end-members. The synthetic ln(K) map has mean, variance, and frequency distributions that are comparable to a natural alluvial fan deposit. A geostatistical analysis was conducted on selected regions of this map containing fluvial, fluvial/floodplain, shoreline, turbidite, and deepwater sedimentary facies. Experimental ln(K) variograms were computed along the major and minor statistical axes and horizontal and vertical coordinate axes. Exponential and power law variogram models were fit to obtain an integral scale and Hausdorff measure, respectively. We conclude that the shape of the experimental variogram depends on the problem size in relation to the size of the local-scale heterogeneity. At a given problem scale, multilevel correlation structure is a result of constructing variogram with data pairs of mixed facies types. In multiscale sedimentary systems, stationary correlation structure may occur at separate scales, each corresponding to a particular hierarchy; the integral scale fitted thus becomes dependent on the problem size. The Hausdorff measure obtained has a range comparable to natural geological deposits. It increases from nonstratified to stratified deposits with an approximate cutoff of 0.15. It also increases as the number of facies incorporated in a problem increases. This implies that fractal characteristic of sedimentary rocks is both depositional process-dependent and problem-scale-dependent.

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Quantifying lateral heterogeneities in fluvio‐deltaic sediments using three‐dimensional reflection seismic data: Offshore Gulf of Mexico

Cited by 14 publications

References 45 publications

Aquifer operator scaling and the effect on solute mixing and dispersion

Aquifer operator scaling and the effect on solute mixing and dispersion

Statistical scaling of pore-scale Lagrangian velocities in natural porous media

Geostatistical analysis of an experimental stratigraphy

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