## GEOSTATS:cross variogram

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• Dear all.. I have some question about cross variogram analysis.. in geoscience data integration scheme, for the purpose of the evaluation of quantitative
Message 1 of 2 , May 4, 1999
Dear all..

I have some question about cross variogram analysis..

in geoscience data integration scheme,
for the purpose of the evaluation of quantitative spatial influences of
each data layer to integrated layer.
if I perform cross variogram analysis with respect to
classified data, not continous data,
(ex) class 1 : 0 ~ 10 , class 2 : 10 ~ 11 etc..
control variable : integrated layer , target variable : each input
layer)
is it reasonable ? or is it useless ?
I wonder whether application to the classified data of cross variogram
is valid, or not..
also,if the grid cell size is 30m * 30m,
what is the reasonable unit lag interval w.r.t. sampling space?

If anyone has cross variogram fortran codes,

Thank you..

best regards,

nowook..

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• I am not sure that I have fully understood your question but I would recommend performing an indicator transform of your data before starting the (cross)
Message 2 of 2 , May 5, 1999
I am not sure that I have fully understood your question
but I would recommend performing an indicator transform of
your data before starting the (cross) variogram analysis.
For each class, you can define an indicator of occurrence
of that class at any location u; e.g. for your classes
1 (0-10) and 2 (10-20):
I(u;c_1)=1 if 0 < z(u) <= 10, and I(u;c_1)=0 otherwise
I(u;c_2)=1 if 10 < z(u) <= 20, and I(u;c_2)=0 otherwise

Then, you compute a semivariogram of these indicators:
g(h,c_1) = (1/2N(h)) sum_alpha=1^N(h) [i(u_alpha;c_1)-i(u_alpha+h;c_1)]^2
or cross semivariogram
g(h,c_1,c_2) = (1/2N(h)) sum_alpha=1^N(h)
[i(u_alpha;c_1)-i(u_alpha+h;c_1)] x
[i(u_alpha;c_2)-i(u_alpha+h;c_2)]

The indicator variogram (=twice the value of the semivariogram 2g(h,c_1))
measures how often two locations a vector h apart belong to c_1
and another category. The smaller 2g(h,c_1), the better the spatial
connectivity of the class c_1. The cross variogram (2g(h,c_1,c_2))
measures the transition frequency between c_1 and c_2.

Cross indicator semivariograms can be computed using the public-domain
http://www.ualberta.ca/~smpe/people/clayton/software.html
Examples of class indicator variograms can be found in the paper:
Goovaerts, P. 1996.
Stochastic simulation of categorical variables using a classification
algorithm and simulated annealing.
Mathematical Geology, 28(7):909--921.

There is also a research report (SCRF 94 paper) that you can download
from my webpage.

If you want to invest more time in the use of
indicator variograms to detect different types
of processes (e.g. mosaic, diffusion-type..), two
references are:
Rivoirard (1993). Relations between the indicators related to a
regionalized variable. In: Soares, A. (Ed.), Geostatistics Tr\'oia '92,
Kluwer Academic Publishers, Dordrecht, pp. 273--284.

Webster R, Boag B (1992) Geostatistical analysis of cyst nematodes
in soil. J. Soil Sci. 43: 583--595

Regards,

Pierre

<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

________ ________
| \ / | Pierre Goovaerts
|_ \ / _| Assistant professor
__|________\/________|__ Dept of Civil & Environmental Engineering
| | The University of Michigan
| M I C H I G A N | EWRE Building, Room 117
|________________________| Ann Arbor, Michigan, 48109-2125, U.S.A
_| |_\ /_| |_
| |\ /| | E-mail: goovaert@...
|________| \/ |________| Phone: (734) 936-0141
Fax: (734) 763-2275
http://www-personal.engin.umich.edu/~goovaert/

<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

On Wed, 5 May 1999, nowook park wrote:

> Dear all..
>
> I have some question about cross variogram analysis..
>
> in geoscience data integration scheme,
> for the purpose of the evaluation of quantitative spatial influences of
> each data layer to integrated layer.
> if I perform cross variogram analysis with respect to
> classified data, not continous data,
> (ex) class 1 : 0 ~ 10 , class 2 : 10 ~ 11 etc..
> control variable : integrated layer , target variable : each input
> layer)
> is it reasonable ? or is it useless ?
> I wonder whether application to the classified data of cross variogram
> is valid, or not..
> also,if the grid cell size is 30m * 30m,
> what is the reasonable unit lag interval w.r.t. sampling space?
>
> If anyone has cross variogram fortran codes,
>
> Thank you..
>
> best regards,
>
> nowook..
>
>
> --
> *To post a message to the list, send it to ai-geostats@....
> *As a general service to list users, please remember to post a summary
> of any useful responses to your questions.
> *To unsubscribe, send email to majordomo@... with no subject and
> "unsubscribe ai-geostats" in the message body.
> DO NOT SEND Subscribe/Unsubscribe requests to the list!
>

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