Bayesian Anisotropic Dix Inversion

We present a Bayesian method for anisotropic Dix inversion and illustrate it with a synthetic 1D example. The method consists of two sequential constrained Dix type inversions, in which the first step solves for interval NMO velocity using the Bayesian Dix inversion developed by Buland et al. (2011). We then input the posterior distribution from this first step into the second where we solve for the interval anisotropy parameter η . For the second inversion we define data and model vector that enable us to use the same linearized operator used in the first step, and thus obtain the posterior solution by the same explicit analytical expressions. Because of this, the Bayesian anisotropic Dix inversion is computationally fast and does not require stochastic simulation.