RMfbm: Variogram Model of Fractal Brownian Motion
In RandomFields: Simulation and Analysis of Random Fields

Description Usage Arguments Details Value References See Also Examples

RMfbm is an intrinsically stationary isotropic variogram model. The corresponding centered semi-variogram only depends on the distance r ≥ 0 between two points and is given by

γ(r) = r^α

where 0 < α ≤ 2.
By now, the model is implemented for dimensions up to 3.
For a generalized model see also RMgenfbm.

1	RMfbm(alpha, var, scale, Aniso, proj)

`alpha`	numeric in (0,2]; refers to the fractal dimension of the process
`var,scale,Aniso,proj`	optional arguments; same meaning for any `RMmodel`. If not passed, the above variogram remains unmodified.

The variogram is unbounded and belongs to a non-stationary process with stationary increments. For α=1 and scale=2 we get a variogram corresponding to a standard Brownian Motion.

For 0 < α < 2 the quantity H=α/2 is called Hurst index and determines the fractal dimension D of the corresponding Gaussian sample paths

D = d + 1 - H

where d is the dimension of the random field (see Chiles and Delfiner, 1999, p. 89).

RMfbm returns an object of class RMmodel.

Chiles, J.-P. and P. Delfiner (1999) Geostatistics. Modeling Spatial Uncertainty. New York, Chichester: John Wiley & Sons.
Stein, M.L. (2002) Fast and exact simulation of fractional Brownian surfaces. J. Comput. Graph. Statist. 11, 587–599.

RMgenfbm, RMmodel, RFsimulate, RFfit.

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

model <- RMfbm(alpha=1)
x <- seq(0, 10, 0.02)
plot(model)
plot(RFsimulate(model, x=x))

Loading required package: sp
Loading required package: RandomFieldsUtils

Attaching package: 'RandomFields'

The following object is masked from 'package:RandomFieldsUtils':

    RFoptions

The following objects are masked from 'package:base':

    abs, acosh, asin, asinh, atan, atan2, atanh, cos, cosh, exp, expm1,
    floor, gamma, lgamma, log, log1p, log2, logb, max, min, round, sin,
    sinh, sqrt, tan, tanh, trunc

NULL
NOTE: simulation is performed with fixed random seed 0.
Set 'RFoptions(seed=NA)' to make the seed arbitrary.
New output format of RFsimulate: S4 object of class 'RFsp';
for a bare, but faster array format use 'RFoptions(spConform=FALSE)'.