  In this paper we demonstrate a new algorithm for sparse prestack azimuthal
AVO inversion. A novel Euclidean prior model is developed to at once respect
sparseness in the layered earth and smoothness in the model of reflectivity.
Recognizing that methods of artificial intelligence and Bayesian computation
are finding an every increasing role in augmenting the process of
interpretation and analysis of geophysical data, we derive a generalized
matrix-variate model of reflectivity in terms of orthogonal basis functions,
subject to sparse constraints. This supports a direct application of machine
learning methods, in a way that can be mapped back onto the physical principles
known to govern reflection seismology. As a demonstration we present an
application of these methods to the Marcellus shale. Attributes extracted using
the azimuthal inversion are clustered using an unsupervised learning algorithm.
Interpretation of the clusters is performed in the context of the Ruger model
of azimuthal AVO.
