Semiautomated component identification of a complex fracture network using a mixture of von Mises distributions: Application to the Ardeche margin (SouthEast France) Abstract   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 (7800xe2x80xafkm2 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 (I70) is added to explicitly estimate the angular range around the mean, such that the probability of falling in the interval xcexbc xe2x80x93 I702; xcexbcxc2xa0xc2xa0I702 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 FA to FF, striking N010xe2x80x93020, N050xe2x80x93060, N090xe2x80x93100, N120, N140xe2x80x93150 and N170180 respectively. Basement records the 6 trends whereas cover records all of them, except FE. Except for the N090100 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 FA and FF attests for the complex loading history of fractures corresponding to these components.

MIXANDMIX: numerical techniques for the computation of empirical spectral distributions of population mixtures The MIXANDMIX (mixtures by Anderson mixing) tool for the computation of the empirical spectral distribution of random matrices generated by mixtures of populations is described. Within the population mixture model the mapping between the population distributions and the limiting spectral distribution can be obtained by solving a set of systems of nonlinear equations, for which an efficient implementation is provided. The contributions include a method for accelerated fixed point convergence, a homotopy continuation strategy to prevent convergence to nonadmissible solutions, a blind nonuniform grid construction for effective distribution support detection and approximation, and a parallel computing architecture. Comparisons are performed with available packages for the single population case and with results obtained by simulation for the more general model implemented here. Results show competitive performance and improved flexibility.