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

Abstract

[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,

Optimization of model parameters and experimental designs with the Optimal Experimental Design Toolbox (v1.0) exemplified by sedimentation in salt marshes

“…These asymptotic properties were first proved by Jennrich (1969) for the ordinary least squares estimator and also discussed in Malinvaud (1970) and Wu (1981). In White (1980), these properties were proved for the weighted least squares estimator and for the generalized least squares estimator in White and Domowitz (1984).…”

Optimised Sequential Experimental Design for Geoelectrical Resistivity Monitoring Surveys

“…It is important to distinguish between iterative optimal design techniques for non-linear problems, which are often described as "sequential" (Guest and Curtis, 2009), and sequential experimental design methods which depend explicitly on previous data. In these methods, it is assumed that there is a set of available experiments that may be conducted.…”

“…However, there is considerable interest in using resistivity imaging in a monitoring context as well as for one-off surveys. This raises the possibility that information from previous images could be used to guide the design of future surveys, a process known as sequential experimental design (Guest and Curtis, 2009). Although the optimal design of geoelectrical surveys depends only very weakly on the resistivity structure of the subsurface (Wilkinson et al 2012b), it would still be possible to focus the resolution of future surveys on regions of the subsurface that have been identified in previous images as being of interest (i.e.…”

Recent advances in optimized geophysical survey design

“…Nonprobabilistic methods ͑which do not explicitly consider the prior probability distribution͒ have also been used ͑e.g., Maurer and Boerner 1998a;Curtis, 1999aCurtis, , 1999bStummer et al, 2004;Coles and Morgan, 2009͒. Truly nonlinearized design methods that optimize the objective function in equation 13 have been developed in geophysical problems only relatively recently ͑van den Berg et al, 2003Berg et al, , 2005Curtis, 2004b;Winterfors and Curtis, 2008;Guest andCurtis, 2009, 2010͒.…”

“…Algorithms for nonlinear problems are generally computationally expensive and thus have been restricted to fairly specific problems that can be parameterized with relatively few ͑ϳ10͒ parameters. Examples include designing surface seismic receiver density or data-processing strategies for optimal amplitude variation with offset/amplitude variation with angle ͑AVO/AVA͒ analysis ͑van den Berg et al, 2003Berg et al, , 2005Guest andCurtis 2009, 2010͒ or designing optimal receiver locations for earthquake or microseismic monitoring surveys ͑Winterfors and Curtis, 2008͒. Hyperparameterization methods, recently applied in linearized geophysical problems ͑Ajo-Franklin, 2009͒, are being extended successfully to fully nonlinear design methods applicable for full 2D or 3D seismic surveys ͑Guest and Curtis, 2010͒.…”