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MODELS OF STATIC GEOLOGIC SYSTEMS                                    211






















               Fig. 11.4. The -plog p function plotted against p in (1) natural and (2) decimal logarithmic scales.
                        N
                        X
                  I ¼      p log p                                              (11.3)
                            i     i
                        i¼1
               Thus, the information I is the logarithm of probability of the general state, with
             the reverse sign, weighted with respect to every state of the system. The information
             may be recorded also as a mathematical expectancy:

                  I ¼ M½  log p Š                                               (11.4)
                               i
               If the states of the system have different probabilities, the information, by the
             different communications, will not be equal. The fullest information is borne by the
             communications about events, which are the least probable, a priori. The entropy of
             a system increases with increasing indefiniteness of the system. In a fully definite
             system (of which everything is known or which has the highest orderliness), the
             entropy equals zero. Chaotic state, disorderliness, lack of sorting, heterogeneity, or
             indefiniteness of the state increase the entropy of the system.
                Consequently, magnitude of entropy, which expresses the degree of heterogeneity
             or indefiniteness, may be used in geologic studies and graphic representations of
             heterogeneity of various geologic systems. For example, zones with characteristically
             high entropy (low information capacity) (i.e., zones where different facies are mixed
             in approximately equal proportions) in facies maps will differ from areas occupied
             by limited number of facies with high information capacity (smaller entropy). In the
             case of a zone containing one facies only, the entropy of the system is equal to zero
             and the information is at a maximum.
                Relative entropy is the ratio of determined entropy to the maximum entropy,
             obtained for a given number of components,

                                     !
                            N
                           X
                  H r ¼       p log p i  =H max                                 (11.5)
                               i
                           i¼1
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