Finding acceptable models in nonlinear inverse problems using a neighbourhood algorithm

A recently proposed new class of direct search method is applied to the problem of mapping out the region of data-acceptable models (sets of unknowns) in a finite-dimensional nonlinear inverse problem. A model is defined to be data acceptable if its fit to the observed data is better than some prescribed level. The neighbourhood algorithm (NA) can be used to generate ensembles of models which preferentially sample the data-acceptable regions of parameter space. Simple transformations of a data misfit criterion are proposed to assist in this task. Some numerical experiments are presented which are motivated by highly nonlinear geophysical inverse problems. In these cases it is shown how the NA can be used to map out the main features of data-acceptable regions in both high-and low-dimensional problems. It is also shown how the NA can concentrate sampling in multiple acceptable regions simultaneously.