Built-in

IDW(var₁=>param₁, var₂=>param₂, ...)

Inverse distance weighting estimation solver.

Parameters

• neighbors - Number of neighbors (default to all the data)
• distance - A distance defined in Distances.jl (default to Euclidean())
• power - Power of the distances (default to 1)

References

Shepard 1968. A two-dimensional interpolation function for irregularly-spaced data.

LWR(var₁=>param₁, var₂=>param₂, ...)

Locally weighted regression estimation solver.

Parameters

• neighbors - Number of neighbors (default to all the data)
• distance - A distance from Distances.jl (default to Euclidean())
• weightfun - Weighting function (default to exp(-3*h^2/2))

References

• Stone 1977. Consistent non-parametric regression.
• Cleveland 1979. Robust locally weighted regression and smoothing scatterplots.
• Cleveland & Grosse 1991. Computational methods for local regression.

Kriging(var₁=>param₁, var₂=>param₂, ...)

A polyalgorithm Kriging estimation solver.

Each pair var=>param specifies the KrigingParam param for the Kriging variable var. In order to avoid boilerplate code, the constructor expects pairs of Symbol and NamedTuple instead.

Parameters

• variogram - Variogram model (default to GaussianVariogram())
• mean - Simple Kriging mean
• degree - Universal Kriging degree
• drifts - External Drift Kriging drift functions

Latter options override former options. For example, by specifying drifts, the user is telling the algorithm to ignore degree and mean. If no option is specified, Ordinary Kriging is used by default with the variogram only.

• minneighbors - Minimum number of neighbors (default to 1)
• maxneighbors - Maximum number of neighbors (default to nothing)
• neighborhood - Search neighborhood (default to nothing)
• distance - Distance used to find nearest neighbors (default to Euclidean())

The maxneighbors option can be used to perform approximate Kriging with a subset of data points per estimation location. If maxneighbors is set to nothing, global Kriging is performed. Two neighborhood search methods are available depending on the value of neighborhood:

• If a neighborhood is provided, local Kriging is performed by sliding the neighborhood in the domain.

• If neighborhood is not provided, the Kriging system is built using maxneighbors nearest neighbors according to a distance.

Examples

Solve the variable :var₁ with Simple Kriging by specifying the mean, and the variable :var₂ with Universal Kriging by specifying the degree and the variogram model.

julia> Kriging(
  :var₁ => (mean=1.,),
  :var₂ => (degree=1, variogram=SphericalVariogram(range=20.))
)

Solve all variables of the problem with the default parameters (i.e. Ordinary Kriging with unit Gaussian variogram):

julia> Kriging()

LUGS(var₁=>param₁, var₂=>param₂, ...)

LU Gaussian simulation.

Parameters

• variogram - Theoretical variogram (default to GaussianVariogram())
• mean - Mean of unconditional simulation (default to 0)
• mapping - Data mapping method (default to NearestMapping())
• factorization - Factorization method (default to cholesky)

Joint parameters

• correlation - correlation coefficient between two covariates (default to 0).

Global parameters

• rng - random number generator (default to Random.GLOBAL_RNG)

Examples

Simulate two variables var₁ and var₂ independently:

julia> LUGS(:var₁ => (variogram=SphericalVariogram(),mean=10.),
            :var₂ => (variogram=GaussianVariogram(),))

Simulate two correlated variables var₁ and var₂ with correlation 0.7:

julia> LUGS(:var₁ => (variogram=SphericalVariogram(),mean=10.),
            :var₂ => (variogram=GaussianVariogram(),),
            (:var₁,:var₂) => (correlation=0.7,))

References

• Alabert 1987. The practice of fast conditional simulations through the LU decomposition of the covariance matrix

• Oliver 2003. Gaussian cosimulation: modeling of the cross-covariance

FFTGS(var₁=>param₁, var₂=>param₂, ...)

FFT Gaussian simulation.

Parameters

• variogram - theoretical variogram (default to GaussianVariogram())
• mean - mean of Gaussian field (default to 0)

In the case of conditional simulation, the following parameters can be passed to the underlying Kriging solver:

• minneighbors - Minimum number of neighbors (default to 1)
• maxneighbors - Maximum number of neighbors (default to 10)
• neighborhood - Search neighborhood (default to nothing)
• distance - Distance used to find nearest neighbors (default to Euclidean())

Global parameters

• threads - number of threads in FFT (default to all physical cores)
• rng - random number generator (default to Random.GLOBAL_RNG)

References

• Gutjahr 1997. General joint conditional simulations using a fast Fourier transform method

• Gómez-Hernández, J. & Srivastava, R. 2021. One Step at a Time: The Origins of Sequential Simulation and Beyond

SGS(var₁=>param₁, var₂=>param₂, ...)

Sequential Gaussian simulation.

Parameters

• variogram - Variogram model (default to GaussianVariogram())
• mean - mean for simple Kriging (default to 0.0)
• path - Simulation path (default to LinearPath())
• minneighbors - Minimum number of neighbors (default to 1)
• maxneighbors - Maximum number of neighbors (default to 10)
• neighborhood - Search neighborhood (default to nothing)
• distance - Distance used to find nearest neighbors (default to Euclidean())
• mapping - Data mapping method (default to NearestMapping())

For each location in the simulation path, a maximum number of neighbors maxneighbors is used to fit a Gaussian distribution. The neighbors are searched according to a neighborhood.

Global parameters

• rng - random number generator (default to Random.GLOBAL_RNG)

References

• Gomez-Hernandez & Journel 1993. Joint Sequential Simulation of MultiGaussian Fields

SPDEGS(var₁=>param₁, var₂=>param₂, ...)

SPDE Gaussian simulation.

Parameters

• sill - Sill or total variance (default to 1.0)
• range - Range or correlation length (default to 1.0)

References

• Lindgren et al. 2011. An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach

CookieCutter(master, others)

A cookie-cutter simulation solver.

Parameters

• master - Master simulation solver (a.k.a. facies solver)
• others - Solvers for each value of the master realization

Examples

Simulate lithofacies with image quilting and fill porosity values with LU Gaussian simulation:

julia> f  = IQ(:facies => (TI=IMG, template=(30,30,1)))
julia> p₀ = LUGS(:poro => (variogram=SphericalVariogram(range=10.),))
julia> p₁ = LUGS(:poro => (variogram=SphericalVariogram(range=20.),))
julia> CookieCutter(f, Dict(0=>p₀, 1=>p₁))

PointwiseLearn(model)

A learning solver that converts geospatial data to a tabular format with features (and possibly labels) for each point, and then solves the problem with classical statistical learning model.

Parameters

• model - Learning model implementing the MLJModelInterface.jl.

References

• Hoffimann et al. 2020. Geostatistical Learning: Challenges and Opportunities