Nonlinear Inversion by Direct Search Using the Neighbourhood Algorithm

The Neighbourhood Algorithm (NA) was introduced by Sambridge (1999a,b) as a direct search method for nonlinear inversion. This approach is applicable to a wide range of inversion problems, particularly those where the relationship between the observables (data) and the unknowns (a finite set of model parameters) is rather complex, e.g., fitting of seismic waveforms for Earth structure or source parameters. The approach is divided into two stages. In the first, known as the search stage, one samples a multidimensional parameter space for combinations of parameters (models) that provide satisfactory fit to observed data. In the second, known as the appraisal stage, one tries to extract information from the complete ensemble of models collected, e.g., on resolution and trade-offs. The search algorithm is in the same class of techniques as Genetic Algorithms (GA) and Simulated Annealing (SA), in that it uses randomized decisions to drive the search and avoids the need for calculation of derivatives of the data misfit function. These techniques are often associated with global optimization problems. The NA differs from previous techniques in that it requires just two control parameters to be tuned, and the search process is driven by only the rank of models with respect to the data misfit criterion, and not the misfit itself. This allows considerable flexibility because any combination of data-fit criteria, or other information, can be used to rank models. Recently the NA has been applied to hypocenter location (Sambridge and Kennett, 2001) and seismic source characterization (MarsonPidgeon et al., 2000). 2. The Algorithm