Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 2 3/4 1995 10.5194/npg-2-158-1995 http://www.nonlin-processes-geophys.net/2/158/1995/ http://www.nonlin-processes-geophys.net/2/158/1995/npg-2-158-1995.html http://www.nonlin-processes-geophys.net/2/158/1995/npg-2-158-1995.pdf 158 177 0000-00-00 Organisation of joints and faults from 1-cm to 100-km scales revealed by optimized anisotropic wavelet coefficient method and multifractal analysis G. Ouillon D. Sornette C. Castaing Institut de Géodynamique, CNRS URA 1279, Rue A. Einstein, Sophia Antipolis, 06560 Vabonne, France BRGM, Avenue de Concyr, Orléans-La Source (Loiret), B.P.6009, 45060 Orléans Cedex 2, France Laboratoire de Physique de la Matiére Condensée, CNRS URA 190, Université de Nice-Sophia Antipolis, B.P.70 Parc Valrose, 06108 Nice Cedex 2, France The classical method of statistical physics deduces the macroscopic behaviour of a system from the organization and interactions of its microscopical constituents. This kind of problem can often be solved using procedures deduced from the Renormalization Group Theory, but in some cases, the basic microscopic rail are unknown and one has to deal only with the intrinsic geometry. The wavelet analysis concept appears to be particularly adapted to this kind of situation as it highlights details of a set at a given analyzed scale. As fractures and faults generally define highly anisotropic fields, we defined a new renormalization procedure based on the use of anisotropic wavelets. This approach consists of finding an optimum filter will maximizes wavelet coefficients at each point of the fie] Its intrinsic definition allows us to compute a rose diagram of the main structural directions present in t field at every scale. Scaling properties are determine using a multifractal box-counting analysis improved take account of samples with irregular geometry and finite size. In addition, we present histograms of fault length distribution. Our main observation is that different geometries and scaling laws hold for different rang of scales, separated by boundaries that correlate well with thicknesses of lithological units that constitute the continental crust. At scales involving the deformation of the crystalline crust, we find that faulting displays some singularities similar to those commonly observed in Diffusion- Limited Aggregation processes.