A new algorithm for joint stochastic inversion of well logs and multiple-angle stacks of migrated 3D prestack seismic data is based on a Bayesian statistical search criterion implemented with fast Markov-chain Monte Carlo updates. It enforces a priori measures of spatial correlation as well as geometric structural and stratigraphic embedding. Results consist of spatial distributions of elastic properties with a vertical resolution intermediate between that of seismic-amplitude data and well logs. In addition, the algorithm provides quantitative estimates of nonuniqueness based on statistical distribution of multiple spatial realizations derived from random initial models. It is also possible to estimate lithology and petrophysical properties such as porosity by enforcing multidimensional statistical correlations between elastic and petrophysical properties sampled from well logs. Results are described from the successful application of the inversion algorithm to the high-resolution characterization of hydrocarbon-producing units of a deepwater reservoir in the central Gulf of Mexico. Sensitivity analyses of resolution and non-uniqueness at blind-well locations corroborate the reliable estimation of elastic and petrophysical properties. Estimated distributions of lithology and elastic properties are influenced only marginally by the choice of inversion parameters and the assumed measures of spatial correlation.