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: [EMAIL PROTECTED] | http://www.imm.dtu.dk/~snl Telephone: +45 45253419 | ** -- * To post a message to the list, send it to [EMAIL PROTECTED] * 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 [EMAIL PROTECTED] 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
Re: AI-GEOSTATS: Observations with a known standard deviation
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 the standard deviation. 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" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> 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: [EMAIL PROTECTED] | http://www.imm.dtu.dk/~snl Telephone: +45 45253419 | ** -- * To post a message to the list, send it to [EMAIL PROTECTED] * 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 [EMAIL PROTECTED] 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 [EMAIL PROTECTED] * 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 [EMAIL PROTECTED] 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
Re: AI-GEOSTATS: Observations with a known standard deviation
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 weights under the uncertainty admitted for your data 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 [EMAIL PROTECTED] * 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 [EMAIL PROTECTED] 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
