Statistical Rock Physics and Bayesian Classification – Are Marginal Distributions Important?

The importance and impact of the way marginal (unconditional) distributions are considered in statistical rock physics and Bayesian classification of inverted seismic data was analyzed. Two scenarios were compared, one assuming perfect knowledge of the probability density functions and perfect and unbiased sampling; and another one where an unclassified group is included, with a given distribution in order to account for imperfections in the data, models, and estimation techniques. Using a dataset from a clastic Palaeocen field in the North Sea, it was shown that assuming the first scenario (perfectly known distributions) leads to probabilistic volumetric estimations of hydrocarbon saturated sands at least 3 times bigger than in the second case where an unclassified group is included. For the sake of further downstream engineering and facilities analyses, it is straightforward to realize the impact of such over-predictions in the estimation of P10, P50 and P90 volumes of hydrocarbons in place.