tips for variogram modeling

Variogram Estimation

Types of variogramThe variogram most common that are implemented in softwares are:

Exponential

Spherical

Gaussian

Types of variogram• The nugget can be modelled as a variogram and it can be combined with

another variogram• An example is: Exponetial Variogram + Nugget Variogram

0

0.25

0.5

0.75

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0

0.25

0.5

0.75

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0

0.25

0.5

0.75

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Sill

Geostatistical works in a normalized space.

The data are transformed in a way to have mean =0 and variance =1

Thus the sill has to be 1 because where there is not correlation we have the maximum variance

The sill can be bigger than 1 when we have few data or there is a trend or a cyclicity

Variogram Estimation Parameters

Rule of thumb: an efficient (for CPU) Search radius has to be 2 times the correlation length

If petrophysical property are simulated after facies the search radius has to be less than

facies correlation (the facies variogram have to be calculated first)

Variogram Estimation Parameters

the optimal Lag distance allows to have enough couples of data in each bin to have a reasonable estimation of variance

the most important bins are the first ones

in vertical direction we have a lot of data and we can use the cell thickness

Variogram Estimation Parameters Lag distance

if we have a lot of data the Lag distance does not affect the variogram estimation

Variogram Estimation Parameters

Lag distance27 wells

if we have a poor data set, we have more possibility to understand the variogram with a large Lag distance

Variogram Estimation Parameters

The Lag tolerance has to be at least 50%

Increasing the Lag tolerance could help for understanding the variogram (loosing detail)

Variogram Estimation Parameters

Tolerance angle (combined with Band with) is used to estimate variogram along a specified direction. The tolerance impact on the accuracy of the angle estimation.

The accuracy you can have is strongly dependent on the number of data

Variogram Estimation Parameters

A large Band width and Tolerance angle =90 allow to estimate an isotropic variogram

Variogram Estimation Parameters

Thickness

Thickness specifies a tolerance in vertical direction

Nugget is affected by the thickness