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This paper presents a statistical inversion scheme that aims at the enhancement of layer boundaries in seismic AVA inversion. By employing a Cauchy norm to the gradients of the model parameters we are inverting for, we are able to enforce a sparse distribution of these gradients and thereby achieving sharper boundaries in the inverted data. We include tests of this approach on synthetic data. In addition, we present work carried to also determine facies from the described blocky inversion method.