The intrinsic random functions and their applications

Matheron, G.

doi:10.2307/1425829

Cited by 1,203 publications

(440 citation statements)

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“…In test problems 1 and 2, the synthetic T fields were generated as unconditional random fields using the two-dimensional random field generator TUBA (Zimmerman and Wilson, [1990]; see also work by Mantoglou and Wilson [1982] and Matheron [1973]). In test problems 3 and 4 the initial field was also generated using TUBA, but additional discrete modifications were made to each.…”

Section: Description Of the Four Test Problemsmentioning

confidence: 99%

A comparison of seven geostatistically based inverse approaches to estimate transmissivities for modeling advective transport by groundwater flow

Zimmerman¹,

Marsily²,

Gotway³

et al. 1998

Water Resources Research

291

180

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Abstract. This paper describes the first major attempt to compare seven different inverse approaches for identifying aquifer transmissivity. The ultimate objective was to determine which of several geostatistical inverse techniques is better suited for making probabilistic forecasts of the potential transport of solutes in an aquifer where spatial variability and uncertainty in hydrogeologic properties are significant. Seven geostatistical methods (fast Fourier transform (FF), fractal simulation (FS), linearized cokriging (LC), linearized semianalytical (LS), maximum likelihood (ML), pilot point (PP), and sequential self-calibration (SS)) were compared on four synthetic data sets. Each data set had specific features meeting (or not) classical assumptions about stationarity, amenability to a geostatistical description, etc. The comparison of the outcome of the methods is based on the prediction of travel times and travel paths taken by conservative solutes migrating in the aquifer for a distance of 5 km. Four of the methods, LS, ML, PP, and SS, were identified as being approximately equivalent for the specific problems considered. The magnitude of the variance of the transmissivity fields, which went as high as 10 times the generally accepted range for linearized approaches, was not a problem for the linearized methods when applied to stationary fields; that is, their inverse solutions and travel time predictions were as accurate as those of the nonlinear methods. Nonstationarity of the "true" transmissivity field, or the presence of "anomalies" such as high-permeability fracture zones was, however, more of a problem for the linearized methods. The importance of the proper selection of the semivariogram of the 1og•0 (T) field (or the ability of the method to optimize this variogram iteratively) was found to have a significant impact on the accuracy and precision of the travel time predictions. Use of additional transient information from pumping tests did not result in major changes in the outcome. While the methods differ in their underlying theory, and the codes developed to implement the theories were limited to varying degrees, the most important factor for achieving a successful solution was the time and experience devoted by the user of the method. •2Stanford University, Stanford, California.•3Duke Engineering and Services, Inc., Austin, Texas.•4University of Arizona, Tucson.•Slnstitut Franqais du Pftrole, Rueil-Malmaison, France.•6University of California, Berkeley.Copyright 1998 by the American Geophysical Union. Paper number 98WR00003.0043-1397/98/98WR-00003509.00 tion, or performance assessment of planned waste disposal projects, it is no longer enough to determine the "best estimate" of the distribution in space of the aquifer parameters. A measure of the uncertainty associated with this estimation is also needed. Geostatistical techniques are ideally suited to filling this role. Basically, geostatistics fits a "structural model" to the data, reflecting their spatial variability. Then, both "best estim...

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Section: Description Of the Four Test Problemsmentioning

confidence: 99%

A comparison of seven geostatistically based inverse approaches to estimate transmissivities for modeling advective transport by groundwater flow

Zimmerman¹,

Marsily²,

Gotway³

et al. 1998

Water Resources Research

291

180

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“…This section discusses how the concept of variogram can be modified to accommodate three-dimensional data. The space-depth covariogram and the space-depth generalized covariance function can be treated in a similar way (Serra, 1982;Matheron, 1973).…”

Section: Geostatistical Interpolationmentioning

confidence: 99%

Spatial interaction of methylene blue stained soil pores

2001

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In this paper, we compare different types of patterns that emerge when applying methylene blue dye as a tracer on soils to detect preferential flow paths as a result of large cracks. Patterns on channels, vughs and cracks are analyzed with the J-function and with indicator variograms. By means of a combined analysis, we obtained a better understanding of the patterns as well as some clear indications for precision agriculture management. The study is illustrated with methylene blue patterns obtained at two locations at four succeeding depths in the Netherlands.

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“…The local analysis of the regularity performed by wavelets and their properties of local approximation (see [16,15]) can give ground to a justification of this hope. Several numerical experiments have been done for the one-dimensional Burgers equation (see for instance [11,21,221). A recent extension to Korteweg de Vries equation has also been implemented ( [18]).…”

Section: Nonlinear Evolution Equationsmentioning

confidence: 99%

“…In typical scenes, the highlighted pixels represent only a few percent of the original 512 x 480 array (see Table 2 To determine which of the highlighted pixels actually represent vias or contacts, a video subimage from the original (or enhanced original) scene, about the same size as the vias or contacts, is extracted and correlated with a nominal template of the desired element. In this research, correlation 221 Linear and non-linear decomposition of images using Gabor wavelets } was usually performed by a trained neural net (connected in the backpropagation mode) [8].…”

mentioning

confidence: 99%

Probabilistic and Stochastic Methods in Analysis, with Applications

Byrnes¹

1992

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The intrinsic random functions and their applications

Cited by 1,203 publications

References 3 publications

A comparison of seven geostatistically based inverse approaches to estimate transmissivities for modeling advective transport by groundwater flow

A comparison of seven geostatistically based inverse approaches to estimate transmissivities for modeling advective transport by groundwater flow

Spatial interaction of methylene blue stained soil pores

Probabilistic and Stochastic Methods in Analysis, with Applications

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