Statistical comparison of variogram-based inversion methods for conditioning to indirect data

Abstract

This study compared the performance of five variogram-based calibration approaches for five different geological problems. The geostatistical calibration methods studied were the sequential spectral turning band method (S-STBM), gradual deformation (GD), iterative spatial resampling (ISR), phase annealing (PA), and fast Fourier transform moving average simulated annealing (FFTMA-SA). The first two problems aimed to produce continuous and categorical simulations with known theoretical distributions. The other two problems were hydrogeological and aimed to calibrate the conductivity field to the pressure heads and travel time between wells. The final problem sought to generate non-Gaussian fields that exhibit spatial directional asymmetry. Two methods, S-STBM and FFTMA-SA, obtained good calibration results for all five problems, with S-STBM being the best overall, particularly for the categorical scenarios. The other methods, GD, ISR, and PA, exhibited a more variable performance. ISR did not properly calibrate simulations for the majority of the problems owing to slow convergence. PA adequately calibrated the five problems, but for the first two, the statistical distributions of the calibrated realizations departed significantly from the theoretical distributions. Similarly, GD exhibited slow convergence for the second problem, which resulted in significant differences compared with the known theoretical distributions. Because the S-STBM constructs the calibrated field directly, it avoids the difficulty encountered by the other calibration methods of having to begin from an unfavorable initial state. The examples clearly illustrate that the choice of the calibration algorithm is significant for some inversion problems.