Fitting variograms

Overview

Fitting theoretical variograms to empirical observations is an important modeling step to ensure valid mathematical models of geospatial continuity. Given an empirical variogram, the following function can be used to fit models:

GeoStatsFunctions.fit — Function

fit(F, f, algo=WeightedLeastSquares(); kwargs...)

Fit theoretical geostatistical function of type F to empirical function f using algorithm algo.

Optionally fix theoretical parameters like range, sill and nugget in the kwargs.

Examples

julia> fit(SphericalVariogram, g)
julia> fit(ExponentialVariogram, g)
julia> fit(ExponentialVariogram, g, sill=1.0)
julia> fit(ExponentialVariogram, g, maxsill=1.0)
julia> fit(GaussianVariogram, g, WeightedLeastSquares())

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fit(Fs, f, algo=WeightedLeastSquares(); kwargs...)

Fit theoretical geostatistical functions of types Fs to empirical function f using algorithm algo and return the one with minimum error.

Examples

julia> fit([SphericalVariogram, ExponentialVariogram], g)

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fit(F, f, weightfun; kwargs...)

Convenience method that forwards the weighting function weightfun to the WeightedLeastSquares algorithm.

Examples

fit(SphericalVariogram, g, h -> exp(-h))
fit(Variogram, g, h -> exp(-h/100))

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fit(Variogram, g, algo=WeightedLeastSquares(); kwargs...)

Fit all stationary Variogram models to empirical variogram g using algorithm algo and return the one with minimum error.

Examples

julia> fit(Variogram, g)
julia> fit(Variogram, g, WeightedLeastSquares())

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Example

# sinusoidal data
𝒟 = georef((Z=[sin(i/2) + sin(j/2) for i in 1:50, j in 1:50],))

# empirical variogram
g = EmpiricalVariogram(𝒟, :Z, maxlag = 25u"m")

varioplot(g)

We can fit specific models to the empirical variogram:

γ = GeoStatsFunctions.fit(SineHoleVariogram, g)

varioplot(g)
varioplot!(γ, maxlag = 25u"m")
Mke.current_figure()

or let the framework find the model with minimum error:

γ = GeoStatsFunctions.fit(Variogram, g)

varioplot(g)
varioplot!(γ, maxlag = 25u"m")
Mke.current_figure()

which should be a SineHoleVariogram given that the synthetic data of this example is sinusoidal.

Optionally, we can specify a weighting function to give different weights to the lags:

γ = GeoStatsFunctions.fit(SineHoleVariogram, g, h -> 1 / h^2)

varioplot(g)
varioplot!(γ, maxlag = 25u"m")
Mke.current_figure()

Methods

Weighted least squares

GeoStatsFunctions.WeightedLeastSquares — Type

WeightedLeastSquares()
WeightedLeastSquares(w)

Fit theoretical variogram using weighted least squares with weighting function w (e.g. h -> 1/h). If no weighting function is provided, bin counts of empirical variogram are normalized and used as weights.

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