R: Spectral turning bands method

Spectral {RandomFields} | R Documentation

## 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 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((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 kπ/`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 nth 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 then`RandomFields` tries to find a good choice for `sigma` itself. Default: `0`.

### Value

`RPspectral` returns an object of class `RMmodel`

### Author(s)

Martin Schlather, schlather@math.uni-mannheim.de

### 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)

[Package RandomFields version 3.1.50 Index]