Spectral turning bands method
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 Ξ for a given covariance function C(h). For x in R^d, the field
Y(x)=√{2} cos(<V,x> + 2 pi U)
with V ~ Ξ and U ~ Ufo((0,1)) is a random field with covariance function C(h). A scaled superposition of many independent realizations of Y gives a Gaussian field according 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.
RPspectral(phi, boxcox, sp_lines, sp_grid, prop_factor, sigma)
phi |
object of class |
boxcox |
the one or two parameters of the box cox transformation.
If not given, the globally defined parameters are used.
See |
sp_lines |
Number of lines used (in total for all additive components of the covariance function). Default: |
sp_grid |
Logical.
The angle of the lines is random if
Default: |
prop_factor |
positive real value.
Sometimes, the spectral density must be sampled by MCMC.
Let p be the average rejection rate. Then
the chain is sampled every nth point where
n = |log(p)| * Default: |
sigma |
real. Considered if the Metropolis
algorithm is used. It gives the standard deviation of the
multivariate normal distribution of the proposing
distribution.
If Default: |
RPspectral returns an object of class
RMmodel.
Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
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.
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)
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