Geoscience Reference
In-Depth Information
mean lag,
PN
is the number of pairs, and
GE
is the variogram estimator. We
can now plot the classical variogram estimator (variogram versus mean
separation distance), together with the population variance:
plot(DE,GE,'.' )
var_z = var(z);
b = [0 max(DE)];
c = [var_z var_z];
hold on
plot(b,c, '--r')
yl = 1.1 * max(GE);
ylim([0 yl])
xlabel('Averaged distance between observations')
ylabel('Averaged semivariance')
hold off
h e variogram in Figure 7.20 exhibits a typical pattern of behavior. Values
are low at small separation distances (near the origin), they increase with
increasing distance until reaching a plateau (
sill
), which is close to the
population variance. h is indicates that the spatial process is correlated over
short distances but there is no spatial dependency over longer distances. h e
extent of the spatial dependency is called the
range
and is dei ned as the
separation distance at which the variogram reaches the sill.
h e
variogram model
is a parametric curve i tted to the variogram
estimator. h is is similar to frequency distribution i tting (see Section 3.5),
where the frequency distribution is modeled by a distribution type and its
parameters (e.g., a normal distribution with its mean and variance). For
theoretical reasons, only functions with certain properties should be used
as variogram models. Common
authorized models
are the spherical, the
exponential, and the linear model (more models can be found in the relevant
published literature).
Spherical model:
Exponential model: