A generalized FFTMA approach for simulating multivariate non-Gaussian random fields with spatial asymmetry

Many environmental sites are the result of complex geological phenomena influenced by physical, chemical, biological, or anthropogenic activities. These intricate relationships are often modeled using multivariate Gaussian random fields, where variables exhibit correlations. However, in recent decades, it has been shown that environmental and geological variables, such as precipitation, concentrations, or mining deposit fields, can exhibit non-Gaussian spatial structures. This paper proposes a stochastic methodology to simulate non-Gaussian random fields with spatial asymmetry using a symmetric nonlinear model of coregionalization (N-LMC). This approach accounts for direct- and cross-spatial statistics of variables that can exhibit spatial correlation, rank asymmetry, i.e., low and high values demonstrate different spatial dependence structures, or directional asymmetry, i.e., spatial dependence structures vary across different directions. Our approach utilizes a family of multivariate Gaussian random fields with an N-LMC model sampled according to a specific rule to generate multivariate non-Gaussian random fields. We developed the methodology to address varying spatial structures between variables, where some may exhibit non-Gaussian dependencies while others behave in a Gaussian manner. Guidelines are provided to identify the presence of multivariate spatial asymmetries. Pseudo-admissible N-LMCs are employed, referring to N-LMCs that are not strictly admissible but can be approximated through spectral decomposition by replacing negative eigenvalues with zero. This approximation is implemented using a multivariate spectral geostatistical simulation method, the Generalized Fast Fourier Transform Moving Average (GFFTMA) algorithm. A series of synthetic examples is presented to illustrate the capabilities of the proposed approach. In addition, a case study on the concentration fields of two contaminants is provided to demonstrate the future research direction of the methodology.