As a rock characteristics heterogeneity measure in a vertical geological cross section the coefficient of relative entropy (Pelto, 1954; Yaglom, Yaglom, 1960; Dementyev, Khitrov, 1966; Ozhgibesov, 1975) was used.
(1),
where КФ - is the coefficient of relative probability entropy (coefficient of facial heterogeneity); n - the number of group intervals of the measured parameter; pi - the probability of the observation result fall within the i-th group interval; N - the number of group intervals of the measured parameter (here N=10, that is why the denominator represented as a common logarithm is equal to 1).
The first extremal case. The petrophysical rock properties parameters´ amplitudes have been studied on the bore well logs.
It goes from the formula (1) that at n = 10 and pi = 0,1 the КФ value is equal to 1. In the calculations we used the logarithm to base 10. The considered case conforms to the maximal heterogeneity of the vertical section of the isochronal stratigraphic range chosen. The number of facial rock types is equal to 10.
The second extremal case. If the vertical section is homogeneous, all the values of amplitudes in the well log fall within the same grouping class. In this case pi = 1, and the КФ value is equal to zero, as log 1 = 0. The number of facial rock types in the vertical section is equal to 1.
Present-day computer technologies allow getting in the shortest time such vertical section heterogeneity complementary information, which is impossible to get in other ways. This heterogeneity can also be mapped.
For the geological section heterogeneity problem solution on the GC, OGC, SP and RC diagrams we applied the computer programs, which allow analyzing and interpreting the well information quickly using standard petrophysical algorithms and also making the relative section entropy map.
The use of the relative entropy coefficient for the evaluation of vertical section lateral variability has an advantage of other ways of mapping of facies reflecting the geological system heterogeneity. This advantage consists in the fact that the number of facial rock types, which are taken into consideration, when lateral variability of the facies evaluated by information measures theoretically unlimitedly (as distinct from the traditional method of drawing facial maps on the basis of lithological triangles).
The КФ value allows coming to the conclusion about facial heterogeneity of the vertical geological section in every well, and also studying the heterogeneity index variability in the studied area on the parameter value, which changes from 0 to 1. When using this extremely formalized information parameter, the lithology on the direct core sample observations should be taken into account, as КФ = 1 for any homogeneous stratum. For example, for homogeneous porous sandstone and homogeneous dense argillite the КФ value will be the same. Rocks are indistinguishable on this formalized characteristic.
With the appearance of special computer programs allowing representing a well log automatically in the form of a discrete series of points and composing a histogram on the basis of these data in the preset number of grouping classes the possibilities of studying vertical and lateral heterogeneity of a geological section by information measures have increased.
The source material presentation and its further computer treatment procedure described here allow solving the problems, which couldn´t be solved earlier because of the labour intensity and duration of measuring and computation operations (Ozhgibesov, 1975).
However, it should be borne in mind that the beginning of the problem solution and the problem definition itself consist in the substantiation and choice of a concrete stratigraphic interval with isochronal (or relative isochronal) boundaries of its bottom and roof. The analysis and final conclusions about the multivariable lithologic-petrophysical heterogeneity of the vertical section and its lateral variability should be made only with due account for (probably, simplified) the three-dimensional lithlogic-petrophysical model of the studied territory.
Gratitude. The authors thank the Geological Department of the Perm University for the support of the participation of creative collective of students and teachers in the projects of the Russian and European Academies of natural History.
The work is submitted to the International scientific conference "Modern science technology", Tenerife, Spain, November, 20-27, 2008, came to the editorial office on 06.09.2008.