## 1259GEOSTATS: Linear Model of Coregionalization

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• Jun 1 4:10 PM
Dear all,

I am looking for the "ultimate" truth about the Linear Model of
Coregionalization!

I want to model the variograms of variable A and B, and the
cross-variogram of variables A-B. The variogram and cross-
variogram models cannot be built independently from one
another (Issaks & Srivastava, 1989; Goovaerts, 1997).
This is where the Linear Model of Coregionalization comes
into play: any basic model that is included in the cross-
variogram model must be included in all the variogram
models (ibid.).
I have a program for calculating variogram and cross-
variogram models that can handle only one basic model for
each (cross-) variogram, i.e. no nested structures are allowed.
From the above description of the Linear Model of
Coregionalization does it now follow that

Question 1:
if I use e.g. a spherical model for the cross-variogram of
variables A-B, I have to use a spherical model for both, the
variogram of variable A and the variogram of variable B?
And further:

Question 2:
The ranges of both variogram models and the range of the cross-
variogram model have to be identical?

Question 3:
What are the consequences of violating the Linear Model of
Coregionalization? Some people seem to think that it is o.k.
to ignore the Linear Model of Coregionalization as long as
they appear to get reasonable results from their analysis.

The reason for my confusion comes from the fact that I have
seen both cases in the literature:
people using the same variogram models and the same ranges
for their variograms and cross-variograms, and
people (non-geostatisticans?) using different models (e.g.
an exponential model for variogram A, a spherical model
for variogram B, and a Gaussian model for the cross-
variogram A-B) with different ranges.

I would really appreciate any comments that could
shed some light on this (for me) confusing topic!

Thanks for your help and have a nice day!

Gerhard

--

******************************************************************
| Gerhard Hunner |
|----------------------------------------------------------------|
| Ph.D. candidate |
| Geostatistics, GIS, Remote Sensing |
|----------------------------------------------------------------|
| GIS and Remote Sensing Program |
| Department of Forest Sciences |
| Fort Collins, CO 80523 |
| USA |
| Tel.: (970) 221-1826 |
| Fax: (970) 491-6754 |
| Email: gerhard@... |
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