Optimising Overdetermined Non-linear Inverse Problems

Many geophysical problems are both non-linear and overdetermined (ie there are more data points than model parameters). A common strategy is to apply linear least-squares inversion iteratively. Although each observed datapoint contributes towards the solution, not all do so in a positive manner - some (because of the nonlinearity of the problem) make the parameter change values very poor estimates of the correct values. This paper examines strategies for producing optimised results based on using only subsets of the observed data. Conventional approaches, such as the use of the data resolution matrix, are tested and found to give poor results. The method is demonstrated using different gravity models.