The simulation of groundwater flow velocity random fields by the method of partitioning and randomization of the spectrum

Due to the heterogeneity of aquifers, groundwater flow velocity fields can be viewed as vector random fields (v.r.f.). For the application of Monte Carlo methods to investigate problems of pollutant transport, the efficient generation of v.r.f. with prescribed covariance structure is an important task. The subject of this paper is the simulation of v.r.f. with a given spectral tensor. We adopt a method that combines two principles: spectral domain partitioning and spectrum randomization (SDP/SR). The SR principle allows to reproduce exactly the covariance structure of the v.r.f., which is of particular importance for Monte Carlo simulation, such as random walk particle tracking. Following this methodology, replicates of the v.r.f. can be generated using a cosine series. Once the coefficients of the series were determined, the v.r.f. can be computed at any point of its domain by mere evaluation of the cosine terms. The method does not require a computational grid and is computationally more efficient than, e.g., Gaussian conditioning.