Stochastic Bayesian Algorithm to a Jointly Acoustic Inversion and Wavelet Estimation

de Figueiredo, Leandro Passos (UFSC) | Santos, Marcio (UFSC) | Roisenberg, Mauro (UFSC) | Schwedersky, Guenther (CENPES/PDGP/CMR)



This paper describes how geostatistical inversion based in a Bayesian framework can be modeled and applied on post-stack seismic data, yielding multiple stochastic realizations of acoustic impedance with improved vertical resolution and conditioned to well data. The proposed method is capable to jointly estimate not only the acoustic impedance, but also the wavelet and the uncertainties of the inversion results. The Gaussian assumption for the likelihood models enables to obtain the analytical expressions for the conditioned distributions, which allows sampling from the posterior distribution via Gibbs Algorithm. Here we propose a different convolutional model that simplifies the conditional distributions of the Gibbs algorithm, and discuss in detail how some variables of the stochastic model were defined in a geophysical interpretation. Results of tests on real data are compared with the deterministic Constrained Sparse Spike Inversion and, as expected, clearly show the improvement in the vertical resolution and the conditioning to well data.