covarianceStructure3DNonStat-init: Non stationary covariance structure

In italo-goncalves/geomod3D: Implicit 3D Geological Modeling and Geostatistics

Description

Representation of one structure in a non stationary spatial continuity model.

Usage

covarianceStructure3DNonStat(type = c("gaussian", "exponential", "spherical",
  "cubic", "matern1", "matern2", "cauchy"), contribution, maxrange,
  midrange = maxrange, minrange = midrange, azimuth = 0, dip = 0,
  rake = 0, power = 1, control_points)

Arguments

type	The type of covariance function represented (see below).
contribution	The variance associated with this structure.
maxrange, midrange, minrange	The structure's range in three orthogonal directions, or the three semi-axes of the covariance ellipsoid.
azimuth, dip, rake	Orientation of the covariance ellipsoid in geological coordinates.
power	The power parameter for the covariance functions that feature one.
control_points	A points3DDataFrame object with the coordinates of the non stationary features.

Details

All parameters except power are non stationary, each modeled by its own (stationary, noiseless) GP and using the control points as data. The GPs are initialized with the values provided as data, and by default predict a constant value everywhere. Use the Fit method of the main GP to determine the best value for each parameter at the control points and the stationary covariance model for each.

Covariance functions

The following functions are available for the type parameter. In the equations below, d is the anisotropy-corrected distance between two points and p is the power parameter. Functions marked with an asterisk support modeling with directional data.

gaussian*

exp(-3*d^2)

exponential

exp(-3*d)

spherical

1 - 1.5*d + 0.5*d^3, 0 <= d <= 1

cubic*

1 - 7*d^2 + 35/4*d^3 - 7/2*d^5 + 3/4*d^7, 0 <= d <= 1

matern1*

(1 + 5*d) * exp(-5*d)

matern2*

(1 + 6*d + 12*d^2) * exp(-6*d)

cauchy*

(1 + d^2)^(-p), p > 0

See Also

covarianceStructure3DNonStat-class, covarianceModel3D-class

italo-goncalves/geomod3D documentation built on May 24, 2019, 2:49 p.m.