  We present a new method of data clustering applied to earthquake catalogs,
with the goal of reconstructing the seismically active part of fault networks.
We first use an original method to separate clustered events from uncorrelated
seismicity using the distribution of volumes of tetrahedra defined by closest
neighbor events in the original and randomized seismic catalogs. The spatial
disorder of the complex geometry of fault networks is then taken into account
by defining faults as probabilistic anisotropic kernels, whose structures are
motivated by properties of discontinuous tectonic deformation and previous
empirical observations of the geometry of faults and of earthquake clusters at
many spatial and temporal scales. Combining this a priori knowledge with
information theoretical arguments, we propose the Gaussian mixture approach
implemented in an Expectation-Maximization (EM) procedure. A cross-validation
scheme is then used and allows the determination of the number of kernels that
should be used to provide an optimal data clustering of the catalog. This
three-steps approach is applied to a high quality relocated catalog of the
seismicity following the 1986 Mount Lewis ($M_l=5.7$) event in California and
reveals that events cluster along planar patches of about 2 km$^2$, i.e.
comparable to the size of the main event. The finite thickness of those
clusters (about 290 m) suggests that events do not occur on well-defined
euclidean fault core surfaces, but rather that the damage zone surrounding
faults may be seismically active at depth. Finally, we propose a connection
between our methodology and multi-scale spatial analysis, based on the
derivation of spatial fractal dimension of about 1.8 for the set of hypocenters
in the Mnt Lewis area, consistent with recent observations on relocated
catalogs.
