Uncertainty estimation for amplitude variation with offset (AVO) inversion

This paper uses a Bayesian approach for inverting seismic amplitude versus offset (AVO) data to provide estimates and uncertainties of the viscoelastic physical parameters at an interface. The inversion is based on Gibbs' sampling approach to determine properties of the posterior probability distribution (PPD), such as the posterior mean, maximum a posteriori (MAP) estimate, marginal probability distributions, and covariances. The Bayesian formulation represents a fully nonlinear inversion; the results are compared to those of standard linearized inversion. The nonlinear and linearized approaches are applied to synthetic test cases which consider AVO inversion for shallow marine environments with both unconsolidated and consolidated seabeds. The result of neglecting attenuation in the seabed is investigated, and the effects of data factors such as independent and systematic errors and the range of incident angles are considered. The Bayesian approach is also applied to estimate the physical parameters and uncertainties from AVO data collected at two sites along a seismic line in the Baltic Sea with differing sediment types; it clearly identifies the distinct seabed compositions. Data uncertainties (independent and systematic) required for this analysis are estimated using a maximum-likelihood approach.