ABSTRACT

Statistical analysis was performed on 414 metres (1357 ft) of core from the Mission Canyon and Charles Formations of the central Williston Basin of North Dakota. Carbonate and sulfate lithologies from the Ratcliffe, Frobisher-Alida, and Tilston intervals were sampled and examined for the presence of cyclicity. Binary (presence-absence) data were collected for 50 lithologic components. Similarity measures were calculated using the phi association coefficient. Unweighted pair-group mean clustering was performed on the similarity matrices. The significance of clusters was tested using chi-square related 99 per cent and 95 per cent confidence levels. Clusters significant at the 99 per cent level have distinct lithologic identities and are interpreted as lithofacies. Lithofacies were used as the mutually exclusive states required by numerical analysis of cyclicity. Iterative, simultaneous use of embedded Markov chain and mutual substitutability analyses was followed by examination of relative entropy patterns.

Markov property was determined to be present in each of the three wells studied. Two or more pairs of states were found to be mutually substitutable in each well. In all wells, patterns of Markov dependencies were resolved into two cycles. In NDGS 793, one type of cycle is formed by oolitic packstones and grainstones, the other by more restricted marine facies which include dolomitic mudstone, bedded sulfate, and intraclastic and microfossiliferous wackestones. In NDGS 1262, one group of 5 cyclic facies are echinoderm wackestones, packstones, and grainstones; the other cycle type is composed of restricted marine facies including oolitic facies, dolomitic mudstone, sulfates, and ostracod and calcisphere-bearing wackestones. The differences between the two types of cyclicity identified in NDGS 7207 are less easily recognized than in the other wells. One set of transitions contains relatively more restricted marine facies but both include the brachiopod-echinoderm facies.

Entropy patterns for all wells suggest that cyclicity in the central Williston Basin is symmetrical. No conclusions can be drawn from the depth distribution of lithofacies in NDGS 7207. The stratigraphic distribution of lithofacies forming cycles in wells 793 and 1262 shows a clear and abrupt change from the more restricted marine facies in the upper portion of the cored interval, to the echinoderm-bearing carbonates or oolitic facies. This indicates abrupt rather than gradual introduction of more evaporative facies and control of upper and lower cyclicity by separately operating depositional mechanisms.