RandomFields (version 3.0.35)

Tbm: Turning Bands method

Description

The Turning Bands method is a simulation method for stationary, isotropic random fields in any dimension and defined on arbitrary points or arbitrary grids. It performs a multidimensional simulation by superposing lower-dimensional fields. In fact, the Turning Bands method is called with the Turning Bands model, see RMtbm. For details see RMtbm.

Usage

RPtbm(phi, fulldim, reduceddim, layers, lines,
      linessimufactor, linesimustep, center, points)

Arguments

phi

object of class RMmodel; specifies the covariance function to be simulated; a univariate stationary isotropic covariance model (see RFgetModelNames(type="positive definite",

fulldim

a positive integer. The dimension of the space of the random field to be simulated

reduceddim

a positive integer; less than fulldim. The dimension of the auxiliary hyperplane (most frequently a line, i.e. reduceddim=1 used in the simulation.

layers

a boolean value; for space time model. If TRUE then the turning layers are used whenever a time component is given. If NA the turning layers are used only when the traditional TBM is not applicable. If FALSE then

lines

Number of lines used. Default: 60.

linessimufactor

linessimufactor or linesimustep must be non-negative; if linesimustep is positive then linesimufactor is ignored. If both arguments are naught then points is used (and must be positive

linesimustep

If linesimustep is positive the grid on the line has lag linesimustep. See also linesimufactor. Default: 0.0.

center

Scalar or vector. If not NA, the center is used as the center of the turning bands for fulldim. Otherwise the center is determined automatically such that the line length is minimal. See also points

points

integer. If greater than 0, points gives the number of points simulated on the TBM line, hence must be greater than the minimal number of points given by the size of the simulated field and the two paramters linesimufactor

Value

• RPtbm returns an object of class RMmodel

Details

RPtbm(Turning bands methods; turning layers). It is generally difficult to use the turning bands method (RPtbm) directly in the 2-dimensional space. Instead, 2-dimensional random fields are frequently obtained by simulating a 3-dimensional random field (using RPtbm) and taking a 2-dimensional cross-section. 3-dimensional RPtbm allows multiplicative models; in case of anisotropy the anisotropy matrices must be multiples of the first matrix or the anisotropy matrix consists of a time component only (i.e. all components are zero except the very last one). RPtbm allows for arbitrary points, and arbitrary grids (arbitrary number of points in each direction, arbitrary grid length for each direction).

Note: Both the precision and the simulation time depend heavily on linesimustep and linesimufactor. For covariance models with larger values of the scale parameter, linesimufactor=2 is too small.

The turning layers are used for the simulations with time component. Here, if the model is a multiplicative covariance function then the product may contain matrices with pure time component. All the other matrices must be equal up to a factor and the temporal part of the anisotropy matrix (right column) may contain only zeros, except the very last entry.

References

• Lantuejoul, C. (2002)Geostatistical Simulation: Models and Algorithms.Springer.
• Matheron, G. (1973). The intrinsic random functions and their applications.Adv. Appl. Probab.,5, 439-468.

See Also

RMtbm, RP, RPspectral

Examples

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again
model <- RPtbm(RMstable(s=1, alpha=1.8))
x <- seq(-3,3,0.1)
z <- RFsimulate(model=model, x=x, y=x)
plot(z)

model <- RPtbm(RMexp(Aniso=matrix(nc=2, rep(1,4))))
z <- RFsimulate(model=model, x=x, y=x)
plot(z)
FinalizeExample()