Hamiltonian Monte Carlo AVA Inversion

Markov chain Monte Carlo algorithms are employed for accurate uncertainty appraisals in non-linear amplitude versus angle (AVA) inversions. The downside of these algorithms is the considerable number of samples needed to achieve stable posterior estimations. To overcome this issue, we implement a Hamiltonian Monte Carlo (HMC) AVA inversion algorithm for the estimation of elastic properties and associated uncertainties from pre-stack data using a 1D convolutional forward operator based on the Zoeppritz equations. HMC uses an artificial system in which a model is viewed as a particle moving along a trajectory in an extended space. In this context, the inclusion of the derivatives information of the misfit function into the sampling framework allows for long-distance moves with high probabilities of acceptance from the current position towards a new independent model. We adopt a simple Gaussian a-priori distribution that allows for an analytical inclusion of geostatistical constraints into the prior model. We also propose a strategy that replaces the numerical computation of the Jacobian with a matrix operator analytically derived from a linearization of the Zoeppritz equations. Synthetic and field data inversions demonstrate that HMC is a very promising approach to cast the non-linear AVA inversion into a solid Bayesian framework