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Abstract

Help the student understand how an experimental indicator variogram is calculated.

The example used is inspired from the cross-sections used by Cox et al, AAPG94-22, and reproduced in Fig. 47. In order to make hand-calculations possible, the size of the image was reduced (Fig. 1).

  1. It is assumed that 3 “wells” have been drilled in the image of Fig. 1, respectively along the left edge, in the middle and along the right edge of the image. Calculate the proportion of each facies along the well of your choice.

  2. Calculate the indicator variogram of the facies of your choice along the well selected in question 1.

  3. Fig. 2 shows the variograms calculated on the 3 wells for the 4 facies. Do you observe the same behaviour from one well to another? Why? Fig. 3 shows the vertical and horizontal variograms calculated over the whole image of Fig. 1. Compare the two and comment the main differences and similarities.

  4. Figs. 4 and 5 (to be discussed later in the course) represent the cross-variograms and transition probability functions calculated for the whole image of Fig. 1. What extra information is brought by these functions?

Understand how conditional simulation algorithms work. Understand how experimental variograms are calculated on continuous parameters.

A throw of a dice generates a uniformly distributed random variable taking the values 1, 2, 3, 4, 5 or 6.

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