Semi-automated component identification of a complex fracture network using a mixture of von Mises distributions: Application to the Ardeche margin (South-East France)

Proposing a quantitative description of fracture main orientations is of prime interest for reservoir modeling. Manual sorting of fracture sets is time consuming and requires individual expertise. Semi automated methods for determination of the number of fracture sets are not developed in structural geology despite complex fracture networks being common. This study aims at demonstrating the input of mixture of von Mises (MvM) distributions to model complex fracture datasets, based on data from the Ardeche margin (7800 km(2) SE France). An appraisal test selects the optimized number of components, without any a priori, by plotting the cumulative weights of MvM components versus concentrations. Estimation of an index of concentration ( I-7(0)) is added to explicitly estimate the angular range around the mean, such that the probability of falling in the interval [mu-I-70/2; mu+I-70/21 is 0.7. Fitting and model selections are discussed on three datasets (fractures from geological maps at 1: 50,000 and 1: 250,000 and lineaments from a digital elevation model (DEM)), for basement and sedimentary cover data analyzed separately. The five component MvM distributions correspond to the best fit models, for all datasets. The modeled components from the geological maps result in six mean orientations F-A to F-F , striking N010-020, N050-060, N090-100, N120, N140-150 and N170-180 respectively. Basement records the 6 trends whereas cover records all of them, except F-g. Except for the N090-100 trend, modeled components from the lineaments are similar to those obtained from the geological maps. Five of the main trends are consistent with fracture trends deduced from field studies. Estimation robustness is validated by the good reproducibility of results from one geological map to the other. The larger dispersion of means for components F-A and F-F attests for the complex loading history of fractures corresponding to these components.