A self-parametrizing partition model approach to tomographic inverse problems
Résumé
Partition modelling is a statistical method for nonlinear regression and classification, and is particularly suited to dealing with spatially variable parameters. Previous applications include disease mapping in medical statistics. Here we extend this method to the seismic tomography problem. The procedure involves a dynamic parametrization for the model which is able to adapt to an uneven spatial distribution of the information on the model parameters contained in the observed data. The approach provides a stable solution with no need for explicit regularization, i.e. there is neither user supplied damping term nor tuning of trade-off parameters. The method is an ensemble inference approach within a Bayesian framework. Many potential solutions are generated, and information is extracted from the ensemble as a whole. In terms of choosing a single model, it is straightforward to perform Monte Carlo integration to produce the expected Earth model. The inherent model averaging process naturally smooths out unwarranted structure in the Earth model, but maintains local discontinuities if well constrained by the data. Calculation of uncertainty estimates is also possible using the ensemble of models, and experiments with synthetic data suggest that they are good representations of the true uncertainty.