[1] In experimental design, the main aim is to minimize postexperimental uncertainty on parameters by maximizing relevant information collected in a data set. Using an entropy-based method constructed on a Bayesian framework, it is possible to design experiments for highly nonlinear problems. However, the method is computationally infeasible for design spaces with even a few dimensions. We introduce an iteratively constructive method that reduces the computational demand by introducing one new datum at a time for the design. The method reduces the multidimensional design space to a single-dimensional space at each iteration by fixing the experimental setup of the previous iteration. Both a synthetic experiment using a highly nonlinear parameter-data relationship and a seismic amplitude versus offset (AVO) experiment are used to illustrate that the results produced by the iteratively constructive method closely match the results of a global design method at a fraction of the computational cost. This work thus extends the class of iterative design methods to nonlinear problems and makes fully nonlinear design methods applicable to higher dimensional real-world problems.Citation: Guest, T., and A. Curtis (2009), Iteratively constructive sequential design of experiments and surveys with nonlinear parameter-data relationships,

When processing data, a principal aim is to maximize information inferred from a data set by minimizing the expected postprocessing uncertainties on parameters of interest. Nonlinear statistical experimental design ͑SED͒ methods can be used to find optimal trace profiles for processing amplitude-variation-with-angle ͑AVA͒ surveys that account for all prior petrophysical information about the target reservoir. Optimal selections change as prior knowledge of rock parameters and reservoir fluid content changes, and which of the prior parameters have the greatest effect on selected traces can be assessed. The results show that optimal profiles are far more sensitive to prior information about reservoir porosity than to information about saturating fluid properties. By applying ray-tracing methods, AVA results can be used to design optimal processing profiles from seismic data sets for multiple targets, each with different prior-model uncertainties.

S U M M A R YThe principal aim of performing a survey or experiment is to maximize the desired information within a data set by minimizing the post-survey uncertainty on the ranges of the model parameter values. Using Bayesian, non-linear, statistical experimental design (SED) methods we show how industrial scale amplitude variations with offset (AVO) surveys can be constructed to maximize the information content contained in AVO crossplots, the principal source of petrophysical information from seismic surveys. The design method allows offset dependent errors, previously not allowed in non-linear geoscientific SED methods. The method is applied to a single common-midpoint gather. The results show that the optimal design is highly dependent on the ranges of the model parameter values when a low number of receivers is being used, but that a single optimal design exists for the complete range of parameters once the number of receivers is increased above a threshold value. However, when acquisition and processing costs are considered we find that a design with constant spatial receiver separation survey becomes close to optimal. This explains why regularly-spaced, 2-D seismic surveys have performed so well historically, not only from the point of view of noise attenuation and imaging in which homogeneous data coverage confers distinct advantages, but also to provide data to constrain subsurface petrophysical information.

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