In the past decade and a half, Monte Carlo (MC) methods ( Hammersley & Handscomb 1964) have enjoyed a resurgence in popularity amongst geophysicists, particularly in application to inverse problems. Numerical techniques, receiver functions, waveform inversion. It is shown that the new algorithm produces a sophisticated type of ‘self-adaptive’ search behaviour, which to our knowledge has not been demonstrated in any previous technique of this kind. This is known to be a non-linear problem, where linearized inversion techniques suffer from a strong dependence on the starting solution. The new direct search algorithm is illustrated with an application to a synthetic problem involving the inversion of receiver functions for crustal seismic structure. It is also shown how Voronoi cells can be used to enhance any existing direct search algorithm, by intermittently replacing the forward modelling calculations with nearest neighbour calculations. In this way all difficulties associated with the scaling of a data misfit function are avoided, and any combination of data fit criteria can be used. The algorithm is conceptually simple, requires just two ‘tuning parameters’, and makes use of only the rank of a data fit criterion rather than the numerical value. These are nearest neighbour regions defined under a suitable distance norm. The new search algorithm makes use of the geometrical constructs known as Voronoi cells to derive the search in parameter space. (A related paper deals with the quantitative appraisal of the ensemble.) The objective here is to find an ensemble of models that preferentially sample the good data-fitting regions of parameter space, rather than seeking a single optimal model. It falls into the same class of method as simulated annealing and genetic algorithms, which are commonly used for global optimization problems.

This paper presents a new derivative-free search method for finding models of acceptable data fit in a multidimensional parameter space.

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