An implementation of differential evolution algorithm for inversion of geoelectrical data

• Inversion of geoelectrical data sets obtained by SP and VES measurements
• Global optimization by DE algorithm for parameter estimation
• Implementation of three mutation strategies together with a binomial type crossover
• Uncertainty analysis by SA without cooling based on the Metropolis–Hastings algorithm
• Fast approximate posterior sampling for low-dimensional inverse geophysical problems

Differential evolution (DE), a population-based evolutionary algorithm (EA) has been implemented to invert self-potential (SP) and vertical electrical sounding (VES) data sets. The algorithm uses three operators including mutation, crossover and selection similar to genetic algorithm (GA). Mutation is the most important operator for the success of DE. Three commonly used mutation strategies including DE/best/1 (strategy 1), DE/rand/1 (strategy 2) and DE/rand-to-best/1 (strategy 3) were applied together with a binomial type crossover. Evolution cycle of DE was realized without boundary constraints. For the test studies performed with SP data, in addition to both noise-free and noisy synthetic data sets two field data sets observed over the sulfide ore body in the Malachite mine (Colorado) and over the ore bodies in the Neem-Ka Thana cooper belt (India) were considered. VES test studies were carried out using synthetically produced resistivity data representing a three-layered earth model and a field data set example from Gökçeada (Turkey), which displays a seawater infiltration problem. Mutation strategies mentioned above were also extensively tested on both synthetic and field data sets in consideration. Of these, strategy 1 was found to be the most effective strategy for the parameter estimation by providing less computational cost together with a good accuracy. The solutions obtained by DE for the synthetic cases of SP were quite consistent with particle swarm optimization (PSO) which is a more widely used population-based optimization algorithm than DE in geophysics. Estimated parameters of SP and VES data were also compared with those obtained from Metropolis–Hastings (M–H) sampling algorithm based on simulated annealing (SA) without cooling to clarify uncertainties in the solutions. Comparison to the M–H algorithm shows that DE performs a fast approximate posterior sampling for the case of low-dimensional inverse geophysical problems.

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