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

Abstract

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. Copyright 2009 by the American Geophysical Union.