The new approach makes use of concepts from the field of computational geometry to drive the search in a high dimensional parameter space. The practicality of any inversion method, of this type, is heavily dependent on the number of times the forward problem must be solved, as is required each time the predictions from a proposed model are compared to the observed data. A powerful feature of the new approach is that it has the potential to vastly reduce the number of times the forward problem needs to be solved, compared to previous methods, and yet still find models with high data fit. The self-adaptive nature of the algorithm is illustrated in Figure 7. Here a simple two parameter problem is considered.
Lighter shades indicate better data fit.
The object is to find the model or region of models containing the highest data fit. Figure 7b shows the initial 100 samples and their corresponding neighbourhood regions used by the new algorithm. In this case the neighbourhood of the global maximum has been identified as well as most secondary maxima. The samples concentrate in regions of high data fit and have located the global minimum of the multi-peaked surface.