Iteratively constructive sequential design of experiments and surveys with nonlinear parameter‐data relationships

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.