Optimal nonlinear bayesian experimental design: An application to amplitude versus offset experiments, Geophys

S U M M A R Y When designing an experiment, the aim is usually to find the design which minimizes expected post-experimental uncertainties on the model parameters. Classical methods for experimental design are shown to fail in nonlinear problems because they incorporate linearized design criteria. A more fundamental criterion is introduced which, in principle, can be used to design any nonlinear problem. The criterion is entropy-based and depends on the calculation of marginal probability distributions. In turn, this requires the numerical calculation of integrals for which we use Monte Carlo sampling. The choice of discretization in the parameter/data space strongly influences the number of samples required. Thus, the only practical limitation for this technique appears to be computational power. A synthetic experiment with an oscillatory, highly nonlinear parameter-data relationship and a simple seismic amplitude versus offset (AVO) experiment are used to demonstrate the method. Interestingly, in our AVO example, although overly coarse discretizations lead to incorrect evaluation of the entropy, the optimal design remains unchanged. Key words: Bayesian, design, experimental, inversion, nonlinear, survey. I N T RO D U C T I O N Finding an optimal geometry, or design, of a practical experiment often means finding the design which maximizes the expected postexperimental information of particular model parameters of interest. This is equivalent to minimizing the expected post-experimental uncertainties in those model parameters. Thus, experimental design requires an understanding of the relationship between data and postexperimental model parameter uncertainties Consider a linearized problem in which the forward problem of estimating data d given a model parameter vector m, and the associated inverse problem solution are, respectively, where G m 0 is a matrix of derivatives of d with respect to m calculated at a reference model m 0 , matrix L is defined in eq