Geoscience Reference
In-Depth Information
is the right-hand-side vector. To obtain the weights and the Lagrange
multiplier the matrix
G_mod
is inverted:
h e kriging variance is given by
For our calculations using MATLAB we need the matrix of coei cients
derived from the distance matrix
D
and a variogram model.
D
was calculated
in the variography section above and we use the exponential variogram
model with a nugget, sill, and range from the previous section:
G_mod = (nugget + sill*(1 - exp(-3*D/range))).*(D>0);
We then take the number of observations and add a column and row vector
of all values of one to the
G_mod
matrix and a zero in the lower let corner:
n = length(x);
G_mod(:,n+1) = 1;
G_mod(n+1,:) = 1;
G_mod(n+1,n+1) = 0;
h e
G_mod
matrix now has to be inverted:
G_inv = inv(G_mod);
A grid with the locations of the unknown values is needed. Here we use a
grid cell size of i ve within a quadratic area ranging from 0 to 200 in
x
and
y
directions. h e coordinates are created in matrix form by:
R = 0 : 5 : 200;
[Xg1,Xg2] = meshgrid(R,R);
and converted to vectors by:
Xg = reshape(Xg1,[],1);
