RandomFields (version 3.1.16)

Spectral: Spectral turning bands method

Description

The spectral turning bands method is a simulation method for stationary Gaussian random fields (Mantoglou and Wilson, 1982). It makes use of Bochners's theorem and the corresponding spectral measure $\Xi$ for a given covariance function $C(h)$. For $x in R^d$, the field $$Y(x)= \sqrt{2} cos( + 2 \pi U)$$ with $V ~ \Xi $ and $U ~ Ufo((O,1))$ is a random field with covariance function $C(h)$. A scaled superposition of many independent realizations of $Y$ gives a Gaussian field, acoording to the central limit theorem. For details see Lantuejoul (2002). The standard method allows for the simulation of 2-dimensional random fields defined on arbitrary points or arbitrary grids.

Usage

RPspectral(phi, boxcox, sp_lines, sp_grid, prop_factor, sigma)

Arguments

phi

object of class RMmodel; specifies the covariance model to be simulated.

boxcox

the one or two parameters of the box cox transformation. If not given, the globally defined parameters are used. see RFboxcox for Details.

sp_lines

Number of lines used (in total for all additive components of the covariance function).

Default: 2500.

sp_grid

Logical. The angle of the lines is random if grid=FALSE, and $k\pi/$sp_lines for $k$ in 1:sp_lines, otherwise. This argument is only considered if the spectral measure, not the density is used. Default: TRUE.

prop_factor

positive real value. Sometimes, the spectral density must be samples by MCMC. Let $p$ the average rejection rate. Then the chain is sampled every $n$th point where $n = |log(p)| *$prop_factor

Default: 50.

sigma

real. Considered if the Metropolis algorithm is used. It gives the standard deviation of the multivariate normal distribution of the proposing distribution. If sigma is not positive thenRandomFields tries to find a good choice for sigma itself. Default: 0.

Value

RPspectral returns an object of class RMmodel

References

• Lantuejoul, C. (2002) Geostatistical Simulation: Models and Algorithms. Springer.
• Mantoglou, A. and J. L. Wilson (1982), The Turning Bands Method for simulation of random fields using line generation by a spectral method. Water Resour. Res., 18(5), 1379-1394.

See Also

Gaussian, RP, RPtbm.

Examples

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again

model <- RPspectral(RMmatern(nu=1))
y <- x <- seq(0,10, len=400)
z <- RFsimulate(model, x, y, n=2)
plot(z)