## AI-GEOSTATS: Observations with a known standard deviation

Expand Messages
• Dear list I am currently working with spatial interpolation of geophysical data. Each observation is associated with an individual and known standard
Message 1 of 3 , Jan 30, 2003
• 0 Attachment
Dear list

I am currently working with spatial interpolation of geophysical
data. Each observation is associated with an individual and known standard
deviation. How should this infomation be incorporated if I want to use
ordinary kriging for interpolation ?? My idea was the following:

When finding the vector of weights (w) by solving the system of linear
equations A*w=b, I would exchange the zeros in the diagonal of the
A-matrix with the individual observation variances. Does this sound
reasonable ??

Best regards / Venlig hilsen

Søren Lophaven
******************************************************************************
Master of Science in Engineering | Ph.D. student
Informatics and Mathematical Modelling | Building 321, Room 011
Technical University of Denmark | 2800 kgs. Lyngby, Denmark
E-mail: snl@... | http://www.imm.dtu.dk/~snl
Telephone: +45 45253419 |
******************************************************************************

--
* To post a message to the list, send it to ai-geostats@...
* As a general service to the users, please remember to post a summary of any useful responses to your questions.
* To unsubscribe, send an email to majordomo@... with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list
* Support to the list is provided at http://www.ai-geostats.org
• Soeren I presume what you have is a sort of analytical error for each sample? That is, the standard deviation for two samples at the same location around the
Message 2 of 3 , Jan 30, 2003
• 0 Attachment
Soeren

I presume what you have is a sort of 'analytical
error' for each sample? That is, the standard
deviation for two samples at the same location around
the 'true value' at the same location?

In this case, you can put the variance down the
diagonal of your kriging system to obtain optimal
values.

You would need to be careful that the 'analytical
variance' was not greater than the nugget effect of
the semi-variogram model.

The kriging system would be similar to that obtained
when the sample is not treated as a 'point', but
rather as a volume. This results in a lower kriging
variance than using zero on the diagonal, so to
compensate you should probably add the complete
'analytical variance' back on to get realistic
estimation variances.

There seems to be a lot of confusion in the books (and
software) about what happens if you have a significant
replication variance.

Isobel Clark
http://geoecosse.bizland.com/news.html

__________________________________________________
Do You Yahoo!?
Everything you'll ever need on one web page
from News and Sport to Email and Music Charts
http://uk.my.yahoo.com

--
* To post a message to the list, send it to ai-geostats@...
* As a general service to the users, please remember to post a summary of any useful responses to your questions.
* To unsubscribe, send an email to majordomo@... with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list
* Support to the list is provided at http://www.ai-geostats.org
• Soeren That works if your matrix is made up of covariance terms rather than variogram terms. However you should use the variance of the error term instead of
Message 3 of 3 , Mar 1, 2003
• 0 Attachment
Soeren

That works if your matrix is made up of covariance terms rather than
variogram terms. However you should use the variance of the error term

So in your notation A_ij = C_ij = D - Gamma_ij

where Gamma_ij are the variogram values, D is the sill of the variogram
(or larger than the largest variogram value if your variogram does not have
a sill) and at the diagonal you use C_ii+K_ii where K_ii are the variance
error terms.

This will not interpolate your data! It will filter the noise terms (which
you say that you know the variance of at each point)

Regards

Colin Daly

----- Original Message -----
From: "Soeren Nymand Lophaven" <snl@...>
To: <ai-geostats@...>
Sent: Thursday, January 30, 2003 3:22 PM
Subject: AI-GEOSTATS: Observations with a known standard deviation

Dear list

I am currently working with spatial interpolation of geophysical
data. Each observation is associated with an individual and known standard
deviation. How should this infomation be incorporated if I want to use
ordinary kriging for interpolation ?? My idea was the following:

When finding the vector of weights (w) by solving the system of linear
equations A*w=b, I would exchange the zeros in the diagonal of the
A-matrix with the individual observation variances. Does this sound
reasonable ??

Best regards / Venlig hilsen

Søren Lophaven
****************************************************************************
**
Master of Science in Engineering | Ph.D. student
Informatics and Mathematical Modelling | Building 321, Room 011
Technical University of Denmark | 2800 kgs. Lyngby, Denmark
E-mail: snl@... | http://www.imm.dtu.dk/~snl
Telephone: +45 45253419 |
****************************************************************************
**

--
* To post a message to the list, send it to ai-geostats@...
* As a general service to the users, please remember to post a summary of
any useful responses to your questions.
* To unsubscribe, send an email to majordomo@... with no subject and
"unsubscribe ai-geostats" followed by "end" on the next line in the message
body. DO NOT SEND Subscribe/Unsubscribe requests to the list
* Support to the list is provided at http://www.ai-geostats.org

DISCLAIMER
This message contains information that may be privileged or confidential and is the property of the Roxar Group. It is intended only for the person to whom it is addressed. If you are not the intended recipient, you are not authorised to read, print, retain, copy, disseminate, distribute, or use this message or any part thereof. If you receive this message in error, please notify the sender immediately and delete all copies of this message.

--
* To post a message to the list, send it to ai-geostats@...
* As a general service to the users, please remember to post a summary of any useful responses to your questions.
* To unsubscribe, send an email to majordomo@... with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list
* Support to the list is provided at http://www.ai-geostats.org
Your message has been successfully submitted and would be delivered to recipients shortly.