The goal of this exercise is to show how a 3D model is fitted to an anisotropic experimental variogram.
The example used is from Chu et al. (1994). This paper shows (in its Fig. 7) experimental porosity variograms calculated in the North-South, East-West, and vertical directions. The data are from an Amoco west-Texas carbonate field of Permian age.
The experimental variograms were calculated from the well data in their strati-graphic coordinates, within a layer of thickness ranging from 11 to 27 m. A total of 4697 elementary porosity-log data were available in 90 wells. Experimental variograms are displayed in Fig. 2-26. The model fitted by Chu et al. is shown in Fig. 2-26. A screen copy of the spreadsheet used is shown in Figs. E1-1. Thanks to this spreadsheet, it is possible to evaluate the impact of a parameter change on the variogram model, and thus to better understand the meaning of each parameter. A particular point to discuss is the use of a shortrange model to represent the nugget effect of the lateral variograms, without impacting the vertical variogram fit.
The goal of this exercise is to evaluate the impact of the variogram choice on the results of an elementary kriging system.
We assume that we work in 2D, and that the value of a variable z at a data point x0 is kriged using the values at four data points located in the neighborhood of xo (Figs. E2-1).