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Method of Soil Analysis 1.5 Geostatistics 1.5.1 Introduction 1.5.2 Using Geostatistical Methods. 1 Dec. 2004 D1 Takeshi TOKIDA. 1.5.1 Introduction. True understanding of the spatial variability in the soil map is very limited. Distinct boundary (too continuous or sudden change).
1 Dec. 2004
D1 Takeshi TOKIDA
Geostatistics is used to…
Objective of the study1.5.2 Using Geostaitstical Methods22.214.171.124 Sampling
The analysis of the data depend on the objective of the study and appropriate data collection.
Na values can be used to estimates B content at lower cost.
Assumptions, i.e. stationarity
Experimental variogram (Estimator)
How to create pairs?
Variance is undefined
Between a lag interval, in this case 1.5 to 4.5, a wide range of actual separation distance occurs.
compared with a situation where every sampling pair has the same distance
A large number of pairs are used to calculate a variogram value.
It is generally accepted that
30 or more pairs are sufficient to produce a reasonable sample variogram.
A sample at a location
Impossible to determine the probability distribution at the point!
The joint distribution do not depend on the location.
A stationary Z(x) has the same joint probability distribution for all locations xi and xi+h.
A measure of the distance for which the attribute is spatially correlated.
normalized form of the autocovariance function
We wish to estimate a value at xo using the data values and combining them linearly with the weiths: λi
Z* should be unbiased:
Z* should be best-linear, unbiased estimator.
Our goal is to reduce as much as possible the variance of the estimation error.
First, rewrite the estimation variance
Let’s rewrite the estimation variance in terms of the semivariogram.
We assume intrinsic hypothesis.
From the definition of the semivariogram we know:
We define an objective function φ containing a term with the Lagrange multiplier, 2β.
To solve the optimization problem we set the partial derivatives to zero:
Estimated kriging variance is nearly equal to the actual estimation error.
Isotropic Case, Kriging Matrix.
But we can’t find the values of a given attribute!
λ1=0.107, λ2=0.600, λ3=0.154, λ4=0.140
Note that the weight for point 1 is less than point 4, even though the distance from the estimation site is almost the same.
Directional variogram oriented in 0°& 90°
Length of each ray is equal to the range of the directional variogram.
Anisotropy ratio = major axes / minor axes
Fig. 1.5-12 Based on Anisotropic variogram
Fig. 1.5-13 Based on isotropic variogram