66.Exponential Model of Variogram
Экспоненциальная
где а – эффективный радиус корреляции (range). На этом расстоянии значение вариограммы достигает 95% плато. Экспоненциальная модель достигает плато асимптотически.
Во всех моделях c – плато (sill) – может быть только положительным.
67.Gaussian Model of Variogram
Gaussian model - where c0 is the nugget effect. c0+c1 is the sill. The range is 3a. This model describes a random field that is considered to be too smooth and possesses the peculiar property that Z(s) can be predicted without error for any s on the plane.
68. Cubic Model of Variogram
69 Kriging Method
What is Kriging?
Optimal interpolation based on regression against observed z
values of surrounding data points, weighted according to spatial
covariance values. Usually, the result of kriging is the expected value (“kriging mean”) and variance (“kriging variance”) computed for every point within a region. Practically,
this is done on a fine enough grid
Some advantages of kriging:
- Helps to compensate for the effects of data clustering, assigning
individual points within a cluster less weight than isolated
data points (or, treating clusters more like single points)
- Gives estimate of estimation error (kriging variance), along with
estimate of the variable, Z, itself (but error map is basically a
scaled version of a map of distance to nearest data point, so
not that unique)
- Availability of estimation error provides basis for stochastic
simulation of possible realizations of Z(u)
Usually, the result of kriging is the expected value (“kriging mean”) and variance
(“kriging variance”) computed for every point within a region. Practically,
this is done on a fine enough grid
The System of Kriging’s Equations
matrix of the Kriging System Equations
72. Ordinary krigin
73. Stoip calculation
74. Example(Empirical Variogram)
