Geoscience Reference
In-Depth Information
where
c
0
is the nugget ef ect.
We can even combine variogram models, e.g., two spherical models with
dif erent ranges and sills. h ese combinations are called
nested models
. During
variogram modeling the components of a nested model are regarded as
spatial structures that should be interpreted as being the results of geological
processes. Before we discuss further aspects of variogram modeling let us
just i t some models to our data. We begin with a spherical model with no
nugget ef ect, and then add an exponential model and a linear model, both
with nugget variances:
plot(DE,GE,'o','MarkerFaceColor',[.6 .6 .6])
var_z = var(z);
b = [0 max(DE)];
c = [var_z var_z];
hold on
plot(b,c,'--r')
xlim(b)
yl = 1.1*max(GE);
ylim([0 yl])
% Spherical model with nugget
nugget = 0;
sill = 0.803;
range = 45.9;
lags = 0:max(DE);
Gsph = nugget + (sill*(1.5*lags/range - 0.5*(lags/...
range).^3).*(lags<=range) + sill*(lags>range));
plot(lags,Gsph,':g')
% Exponential model with nugget
nugget = 0.0239;
sill = 0.78;
range = 45;
Gexp = nugget + sill*(1 - exp(-3*lags/range));
plot(lags,Gexp,'-.b')
% Linear model with nugget
nugget = 0.153;
slope = 0.0203;
Glin = nugget + slope*lags;
plot(lags,Glin,'-m')
xlabel('Distance between observations')
ylabel('Semivariance')
legend('Variogram estimator','Population variance',...
'Sperical model','Exponential model','Linear model')
hold off
