Markov Chain Analysis of Carbonate Rocks: Applications, Limitations, and Implications as Exemplified by the Pennsylvanian System in Southern Nevada

摘要

Markov chain analysis may be used as a technique for evaluating the presence of determinism ("memory") in a sequence of physical events. Application to the vertical facies changes found in the Pennsylvanian carbonate sequences of southern Nevada shows that (1) the interval examined in the Arrow Canyon Range (1846 ft, miogeosynclinal, Bird Spring Group) has a chi-square value of 167.41, indicating "memory" present; (2) the Callville Formation at Frenchman Mountain (1055 ft, shelf) yields a chi-square of 26.40, also indicating the presence of "memory"; and (3) the Callville at Azure Ridge (779 ft, shelf) yields a chi-square of 15.02, indicating no "memory." All of these values were obtained with recognition of four facies with multistory relationships. Investigation of potential sources of error shows that consistency from studied section to studied section in choice of number of facies, evaluation of facies changes, and whether multistory or unit facies are recognized is essential if results are to be compared. The presence of covered intervals, while detrimental, does not obscure results where less than 20 percent of the total number of facies units are labeled covered.