A Bayesian methodology is described for designing experiments or surveys that will optimally complement all previously available information. This methodology uses strong prior information to linearize the problem, and to guide the design toward maximally reducing forecast uncertainties in the interpretation of the future experiment. The prior information could possibly be correlated among model parameters or the observation noise. With no prior information this approach reduces to the fast recursive implementation of the D-optimality criterion. Synthetic geophysical tomography examples are used to illustrate the benefits of this approach. The dependence of the design on the model representation is also discussed.
The locations of seismic events are used to infer reservoir properties and to guide future production activity, as well as to determine and understand the stress field. Thus, locating seismic events with uncertainty quantification remains an important problem. Using Bayesian analysis, a joint probability density function of all event locations was constructed from prior information about picking errors in kinematic data and explicitly quantified velocity model uncertainty. Simultaneous location of all seismic events captured the absolute event locations and the relative locations of some events with respect to others, along with their associated uncertainties. We found that the influence of an uncertain velocity model on location uncertainty under many realistic scenarios can be significantly reduced by jointly locating events. Many quantities of interest that are estimated from multiple event locations, such as fault sizes and fracture spacing or orientation, can be better estimated in practice using the proposed approach.
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