Optimal Survey Design Using the Point Spread Function Measure of Resolution

An objective in survey design is to determine optimal survey parameters, such as the position of sources/receivers and possibly frequencies in EM experiments, that would provide ‘better’ model resolution in a region of interest. We pose survey design as an inverse problem by maximizing a resolution measure, the point spread function. The point spread function quantifies how an impulse in thetruemodelisobservedintheinversionresultand, hence, the goal is to adjust the survey parameters so that the point spread function is as delta-like as possible. This problem is solved as a nonlinear optimization problem with constraints on the parameters. Due to the highly nonlinear nature of the problem we examine two approaches for its solution. The first is a local, (Newton) strategy that use a primal interior point method to incorporate bounds on the parameters;the second is global method, simulated annealing. This paper primarily concentrates on the problem formulation and we illustrate our methodology through application to a ray-based tomography example.