Improved Monte Carlo 1D-Inversion of vertical electrical sounding and time-domain electromagnetic data

This work deals with a robust and reliable global search inversion tool for vertical electrical sounding (VES) and time-domain electromagnetic (TDEM) data, able to take into account the data quality and the dimensionality of the problem. The approach is an importance sampling method that exploits a scale property of the solution to move the random population of models closer to the solution. We obtain a more efficient sampling of the model parameter space with respect to a pure Monte Carlo method. The application of the scale properties overcomes some of the problems encountered when using optimization methods (e.g., simulated annealing), which are based on transition probability rules barely related to the specific problem or that require tuning of control parameters or training procedures (e.g., neural networks). Furthermore, the scale properties reduce the bias related to the initial definition of the boundaries of the model parameter space. A statistical test that accounts for the data uncertainties and the degrees of freedom of the problem is adopted to draw inference on the results. Synthetic and field data show that the algorithm is able to concentrate the sampling in high probability density zones of the model parameter space and to supply a reliable picture of the non-uniqueness and equivalence problems.