7. Multivariate Grid-Free Geostatistical Simulation of Natural Phenomena

Conventional geostatistical simulation techniques require an upfront definition of the simulation locations – normally a regular grid. If simulation is performed with different simulation locations, previously simulated values may not be reproduced. A two-step grid-free simulation (GFS) approach is proposed to represent a realization as a function of the simulation location coordinates. Unconditional simulations are generated with turning bands, where 1D line simulations are presented as a function of the simulation location by Fourier series simulation (FSS) technique, and later conditioned to the data by dual kriging. The FSS is framed after the linear model of regionalization (LMR). The independent random factors of the LMR and their coefficients are derived by decomposing the covariance function of the line process into a sum of weighted covariances of random factors in cosine form, where weights are Fourier series coefficients of target 1D covariance function. Multivariate modeling is achieved with the linear model of coregionalization. The GFS implementation is demonstrated with a case study.