Simulating Nonhomogeneous Non-Gaussian Field by Using Iterative Rank-Dependent Reordering versus Translation Process-Based Procedure

Table 1

Definition of the cases (see [12]).

Case	Prescribed autocorrelation function for homogeneous cases (1 to 4) or autocovariance function for nonhomogeneous cases (5 to 8)	Distribution type and notes
		Beta distribution	Lognormal distribution
1		p = 4, q = 2. For Cases 1 to 4, . The field is defined for x within 0 to 2 and discretized using Δx = 0.02.; For Cases 5 to 8, , , . The mean and the standard deviation is given by the autocovariance function. The field is defined for x within 0 to 1 and discretized using Δx = 0.01	, β = 1. For Cases 1 to 4, α = −0.7707 and δ = −0.7628. The field is defined for x within 0 to 2 and discretized using Δx = 0.02.; For Cases 5 to 8, α(xj) and δ(xj) could be obtained by solving , . The mean and the variance is given by the autocovariance function. The field is defined for x within 0 to 1 and discretized using Δx = 0.01
2
3
4
5
6
7
8