Experimental Variogram
Experimental variogram is an estimated value of the variogram based on sampling. In the
common method of plotting experimental variograms, the distance axes separating two points are
divided into successive intervals, similar to a histogram. As an exploitation analysis tool, the
experimental variogram has the disadvantage that the graph depends on the selection of intervals
and is influenced by the averaging method. Included in the definition of an experimental
variogram are:
1. Scales
Experimental variogram is a graph that is usually used more in geostatistical
applications to investigate the uncertainty. This experimental contains information about
the fluctuation of the scale variable.
2. Close to Center
The behavior of the variogram at small distances determines whether the spatial
function appears continuous and smooth. Meanwhile, the behavior of the experimental
variogram at the center (at short distances) indicates the degree of smoothness function.
3. Large-Scale Behavior
The behavior of the variogram at distances proportional to the area size
determines whether the function is a stationary function.
As a function, the experimental variogram will stabilize a value around it, namely the sill. As a
stationary function, the sill obtained will describe the length of the scale. (Kitanidis, 1997).
The hypothesis used to determine the variogram is based on the nature of intrinsic
stationarity, the estimate of the experimental variogram is at a distanceh is :
N (h )
1 2
2 γ^ ( h )= ∑
N ( h ) i=1
[ Z ( s i +h ) −z ( si ) ]
While the semivariogram is half of the quantity γ ( h ). The semivariogram can be used to measure
spatial correlation in the form of the variance of different observations at location s+h and 𝑠 .
(Cressie, 1993)
experimental semivariogram estimate at distance h , can be written as follows:
N (h )
1 2
^γ ( h )= ∑
2 N ( h ) i=1
[ Z ( s i +h ) −z ( si ) ]
Where : γ ¿h) = (semi) variogram for a given direction and distance h
h = 1d, 2d, 3d, 4d (d = distance between samples)
z(si) = price (data) at point si
z(si+h) = data at a point h from si
N(h) = number of data pairs.
As an example of gold content data (in ppm) along a vein with a sampling distance (d) every 2
m:
Experimental variogram is an estimated value of the variogram based on sampling. In the
common method of plotting experimental variograms, the distance axes separating two points are
divided into successive intervals, similar to a histogram. As an exploitation analysis tool, the
experimental variogram has the disadvantage that the graph depends on the selection of intervals
and is influenced by the averaging method. Included in the definition of an experimental
variogram are:
1. Scales
Experimental variogram is a graph that is usually used more in geostatistical
applications to investigate the uncertainty. This experimental contains information about
the fluctuation of the scale variable.
2. Close to Center
The behavior of the variogram at small distances determines whether the spatial
function appears continuous and smooth. Meanwhile, the behavior of the experimental
variogram at the center (at short distances) indicates the degree of smoothness function.
3. Large-Scale Behavior
The behavior of the variogram at distances proportional to the area size
determines whether the function is a stationary function.
As a function, the experimental variogram will stabilize a value around it, namely the sill. As a
stationary function, the sill obtained will describe the length of the scale. (Kitanidis, 1997).
The hypothesis used to determine the variogram is based on the nature of intrinsic
stationarity, the estimate of the experimental variogram is at a distanceh is :
N (h )
1 2
2 γ^ ( h )= ∑
N ( h ) i=1
[ Z ( s i +h ) −z ( si ) ]
While the semivariogram is half of the quantity γ ( h ). The semivariogram can be used to measure
spatial correlation in the form of the variance of different observations at location s+h and 𝑠 .
(Cressie, 1993)
experimental semivariogram estimate at distance h , can be written as follows:
N (h )
1 2
^γ ( h )= ∑
2 N ( h ) i=1
[ Z ( s i +h ) −z ( si ) ]
Where : γ ¿h) = (semi) variogram for a given direction and distance h
h = 1d, 2d, 3d, 4d (d = distance between samples)
z(si) = price (data) at point si
z(si+h) = data at a point h from si
N(h) = number of data pairs.
As an example of gold content data (in ppm) along a vein with a sampling distance (d) every 2
m:
