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Estimating parameters and uncertainty in geophysical inversion: A new approach using the Neighbourhood Algorithm

The neighbourhood algorithm (NA) is a recently proposed direct search (i.e. derivative free) approach to nonlinear inversion which is finding increasing numbers of applications from problems in earthquake seismology to production uncertainty quantification in oil reservoirs. An inverse problem occurs whenever data only indirectly constrain some physical, chemical or parameters of interest. For example when seismic data, collected at the Earth’s surface is used to constrain structure at depth. Inverse problems occur in many areas of the physical and mathematical sciences. The NA is applicable in cases where the relationship between unknowns and observations is highly nonlinear and simple derivative calculations are undesirable, or impossible. NA is in the same class of technique as Genetic Algorithms (GA) and Simulated Annealing (SA), which are often associated with global optimization. The NA makes use of simple geometrical concepts, and requires just two tuning parameters, but has been shown to produce a sophisticated ‘self-adaptive’ search behaviour in multi-dimensional parameter spaces. It also allows a fully nonlinear estimation of uncertainty in unknowns arising from noise, or other uncertainties, in the data.