We have introduced a methodology for quantifying seismic velocity and pore-pressure uncertainty that incorporates information regarding the geologic history of a basin, rock physics, well log, drilling, and seismic data. In particular, our approach relies on linking velocity models to the basin modeling outputs of porosity, mineral volume fractions, and pore pressure through rock-physics models. We account for geologic uncertainty by defining prior probability distributions on lithology-specific porosity compaction model parameters, permeability-porosity model parameters, and heat-flow boundary condition. Monte Carlo basin simulations are performed by sampling the prior uncertainty space. We perform probabilistic calibration of the basin model outputs by defining data likelihood distributions to represent well data uncertainty. Rock physics modeling transforms the basin modeling outputs to give us multiple velocity realizations used to perform multiple depth migrations. We have developed an approximate Bayesian inference framework that uses migration velocity analysis in conjunction with well data for updating velocity and basin modeling uncertainty. We apply our methodology in 2D to a real field case from the Gulf of Mexico; our methodology allows for building a geologic and physical model space for velocity and pore-pressure prediction with reduced uncertainty.