Geostatistical analysis of an experimental stratigraphy

Abstract

[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.

Equivalent hydraulic conductivity of an experimental stratigraphy: Implications for basin‐scale flow simulations

“…The procedure of image scale‐up and the subsequent upscaling analysis to compute the equivalent conductivity is summarized in Figure 3. More detailed discussions on the experimental stratigraphy and the construction of the basin‐scale conductivity map are given by Zhang et al [2005b].…”

Two-scale modeling of solute transport in an experimental stratigraphy

“…Since the end-member conductivities used to create the map are those of unconsolidated sand and clay (Zhang et al, 2005b), such an assumption is considered reasonable. Comparing the velocity magnitude ðv ¼ jṽjÞ of both models (Figs.…”

“…Discussions and conclusions are then presented, followed by future research directions. k max and k min are the integral scales along the major and minor statistical axis, respectively, obtained from re-scaling those estimated for the subregions (Zhang et al, 2005b). Due to small bedding angle and the lateral flow condition, k max approximates k (integral scale along mean flow direction); k min approximates vertical integral scale.…”

“…Zhang et al, 2005a), motivates an analysis based on a high-resolution, fully heterogeneous hydraulic conductivity map, created from an experimental stratigraphy (Zhang et al, 2005b). The conductivity map is unique compared to other synthetic data: the heterogeneity pattern corresponds to physical sedimentation that is statistically inhomogeneous.…”

“…For representative subregions, Zhang et al (2005b) calculates the experimental lnK variograms and estimates the (anisotropic) integral scales. For the HSM, Zhang et al (2006) computes an equivalent conductivity (K * ) for each unit via up-scaling.…”