Hierarchical Bayesian Inversion of Time-Lapse Seismic Data with Different Acquisition Geometries

We describe a methodology for inferring the change in subsurface model parameters from time-lapse seismic data within a hierarchical Bayesian framework, where the time-lapse and baseline surveys may have different acquisition geometries. Conventional methods for processing time-lapse data with differing acquisition geometries involve inverting the baseline and time-lapse datasets separately and subtracting the inverted models; however, such methods do not correctly account for differing model uncertainty between surveys due to differences in illumination and observational noise. Within the hierarchical Bayesian setting, the solution to the time-lapse inverse problem is given by the marginal maximum a posteriori (MAP) estimate of the time-lapse change, which seeks the most probable time-lapse change over all probable baseline models described by the data. We present a framework for computing the marginal MAP estimate using the expectation-maximization (E-M) algorithm, which iteratively performs sequential estimation of the time-lapse change and the baseline model. Our algorithm is validated numerically on synthetic data simulated from the Marmousi model (with a time-lapse perturbation), where the hierarchical Bayesian estimates significantly outperform conventional time-lapse inversion results.