Finding acceptable models in nonlinear inverse problems using a neighbourhood algorithm

A recently proposed new class of direct search method is applied to the pro blem of mapping out the region of data-acceptable models (sets of unknowns) in a finite-dimensional nonlinear inverse problem. A model is defined to b e data acceptable if its fit to the observed data is better than some presc ribed level. The neighbourhood algorithm (NA) can be used to generate ensem bles of models which preferentially sample the data-acceptable regions of p arameter space. Simple transformations of a data misfit criterion are propo sed to assist in this task. Some numerical experiments are presented which are motivated by highly nonlinear geophysical inverse problems. In these ca ses 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 s hown how the NA can concentrate sampling in multiple acceptable regions sim ultaneously.