Efficient simulation of multivariate three-dimensional cross-correlated random fields conditioning on non-lattice measurement data

It is challenging to simulate large-scale or fine-resolution multivariate three-dimensional (3D) cross-correlated conditional random fields because of computational issues such as inverting, storing Cholesky decomposition large correlation matrices. Recently, an efficient univariate 3D field simulation method was developed based on the separability assumption autocorrelation functions in vertical and horizontal directions. The allows for Kronecker-product derivations matrices thus does not need invert store Moreover, it can handle non-lattice data (e.g., all soundings measure one soil property there exists missing at some depths soundings). may be more common see multiple properties soundings) practical site investigations. However, proposed applicable cannot directly account cross-correlation among different variables purpose current paper extend previous accommodate data. extended still takes advantage avoid mathematical operation A simulated example adopted illustrate effectiveness method.