Calibration of random fields by a sequential spectral turning bands method

Abstract

A new algorithm for calibration of conditional realizations to measured or desired response functions is presented. The Sequential-Spectral Turning Bands Method (S-STBM) builds the field by choosing the phase of each new cosine function such that the observed field response functions become increasingly calibrated. The phase selection has little influence on the spatial correlation structure but can help to meet other objectives. Conditioning by kriging is used in the algorithm main loop to impose exact hard data reproduction. A first case study illustrates the performance of the algorithm for a cyclic and asymmetric field. S-STBM is shown to reproduce similarly or better the directional asymmetry than calibrated realizations obtained by FFTMA-SA. A training image (TI) with connected low values provides the second case study where the target is the reproduction of non-centered third-order spatial moments. A third case study shows the effectiveness of the S-STBM algorithm to calibrate a Gaussian field to tracer tests. Contrary to FFTMA-SA, S-STBM works on irregular grids. Its computational complexity of O(n) and small memory requirement makes it an attractive method for calibration.