The Rock Model - Reservoir Model Design - page 36

Fig. 2.22 The raw data
for a variogram model:
a systematic change in
variance between data
points with increasing
distance between those
points

g

Lag (distance)

Fig. 2.23
A semivariogram model
fitted to the points in
Fig. 2.22

Sill

g

Range

Nugget

Lag (distance)

model (Fig. 2.23 ) and it is this model which may
be used as input to geostatistical packages during
parameter modelling.
A semivariogram model has three defining
features:
￿

Now recall the definition of the sill, from
Isaaks and Srivastava ( 1989 ), quoted at the start
of this section. In simpler terms, the sill is the
point at which the semivariogram function is
equal to the variance, and the key measure for
reservoir modelling is the range - the distance at
which pairs of data points no longer bear any
relationship to each other. A large range means
that data points remain correlated over a large
area, i.e. they are more homogeneously spread;
a small range means the parameters are highly
variable over

the sill , which is a constant value that may

be approached for widely-spaced pairs and
approximates the variance;

ʳ

￿ the range , which is the distance at which the

sill is reached, and

￿ the nugget , which is the extrapolated ʳ value

at zero separation. short distances i.e. they are