Dear Sir or Madam,

I have a question about the routine 'vario.pgs'. This routine is based on the paper 'A pairwise likelihood approach for the empirical estimation of the underlying variograms in the plurigaussian models' by N. Desassis et al.

Within the plurigaussian model, 'vario.pgs' estimates model parameters for the underlying Gaussian random fields, based a truncation map and a facies field. I am concentrating on the case of two bivariate Gaussian random fields.

I have first defined a grid:

N=50

db=db.create(flag.grid=T,nx=c(N,N),x0=c(0,0),ndim=2).

I have also defined a truncation map with its associated proportions:

rule=rule.create(c("S","T","F1","F3","F2"))

props=c(0.1096, 0.3816, 0.5088)

I have read in the facies field fac.

I then added it to the data base db:

vec_f=as.vector(fac)

db=db.add(db,vec_f)

The data based looks like this:

[i]Data Base Characteristics

=========================

Data Base Summary

-----------------

File is organized as a regular grid

Space dimension = 2

Number of fields = 4

Maximum Number of attributes = 4

Total number of samples = 2500

Grid characteristics:

Origin : 0.000 0.000

Mesh : 1.000 1.000

Number : 50 50

Angles : 0.000 0.000

Variables

---------

Field = 1 - Name = rank - Locator = rank

Field = 2 - Name = x1 - Locator = x1

Field = 3 - Name = x2 - Locator = x2

Field = 4 - Name = V1 - Locator = z1

I executed the command:

vario=vario.pgs(db,rule=rule,props=props,calcul='vg')

Because my truncation rule is made for two realizations of Gaussian random fields, I was expecting 'vario' to contain output for two models. However, 'vario' only contains meaningful output for one variable:

Variogram characteristics

=========================

Number of variable(s) = 2

Number of direction(s) = 1

Space dimension = 2

Direction 1

-----------

Number of lags = 10

Direction coefficients = ( 1.000 0.000)

Direction angles (degrees) = ( 0.000)

Tolerance on direction = 90.000000 (deg)

Calculation lag = 3.46482

For variable 1

Referenced value (variance,...) = 1.000

Rank Npairs Distance Value

0 9702.000 1.205 0.085

1 90586.000 3.797 0.364

2 156406.000 7.148 0.674

3 208942.000 10.533 0.796

4 248084.000 13.899 0.800

5 280526.000 17.323 0.783

6 301658.000 20.794 0.762

7 291970.000 24.227 0.749

8 306378.000 27.687 0.835

9 272540.000 31.169 0.950

Between variables 2 and 1

Referenced value (covariance,...) = 0.000

Rank Npairs Distance Value

0 9702.000 1.205 0.000

1 90586.000 3.797 0.000

2 156406.000 7.148 0.000

3 208942.000 10.533 0.000

4 248084.000 13.899 0.000

5 280526.000 17.323 0.000

6 301658.000 20.794 0.000

7 291970.000 24.227 0.000

8 306378.000 27.687 0.000

9 272540.000 31.169 0.000

For variable 2

Referenced value (variance,...) = 1.000

Rank Npairs Distance Value

0 9702.000 1.205 0.000

1 90586.000 3.797 0.000

2 156406.000 7.148 0.000

3 208942.000 10.533 0.000

4 248084.000 13.899 0.000

5 280526.000 17.323 0.000

6 301658.000 20.794 0.000

7 291970.000 24.227 0.000

8 306378.000 27.687 0.000

9 272540.000 31.169 0.000

How is this possible?

How should I format my input to obtain models for the underlying GRFs using 'vario.pgs'?

Many thanks indeed!

Marise Westbroek