Hi Sean, Your problem seems to bear some similarity with modeling of river networks where meaningful distances cannot be defined in the Euclidian space and downstream/upstream relationships need to be fulfilled. A few days ago, Pascal Monestiez from INRA Avignon gave a talk on Geostatistical modelling of spatial processes on trees: applications to drainage networks, which might be of interest to you... and there should be other related papers in the literature.
Cheers, Pierre <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><> Dr. Pierre Goovaerts President of PGeostat, LLC Chief Scientist with Biomedware Inc. 710 Ridgemont Lane Ann Arbor, Michigan, 48103-1535, U.S.A. E-mail: [EMAIL PROTECTED] Phone: (734) 668-9900 Fax: (734) 668-7788 http://alumni.engin.umich.edu/~goovaert/ <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><> On Fri, 12 Sep 2003, McKenna, Sean A wrote: > All, I have an interesting problem that is a bit off the usual geostat > track. The problem is the estimation of the amount of tracer deposited in a > cave system. The cave system is composed of multiple rooms and passages > connecting the rooms. Air flow and transport models can be used to model > the deposition of the tracer, but are difficult to set up and calibrate and > I'd like to pursue a more geostatistical approach to the problem (if > possible). > > However, a straight forward application of kriging the amount of deposition > based on a number of samples will not work for at least two reasons: > 1) Euclidean distance is not very meaningful as two rooms in the system may > only be separated by a 10 meter thick wall, yet the tortuous air flow path > from one room to the other may be over 500 meters. Therefore the > connections between sample points resemble something like a connected graph > ala graph theory. But perhaps it is possible to use this information to > remap the cave system into some sort of "connection space" and build > variograms and do kriging in that space before remapping to the actual > coordiante system (?) > 2) If it were possible to develop a covariance matrix using the sample data > in some transformed coordinate system, it would not be symmetric. Due to > the air flow patterns in the cave system, point B may be "downwind" of point > A and there is a B->A connection, but there is no A->B connectivity. In the > parlance of graph theory, this would be a "directed graph". > > I've found work across several different fields where the "best" places to > take a sample in such a system can be determined using graph theory coupled > with linear programming and/or heurisitc optimization techniques. I have > not come across any work where estimations are made in the system based on a > finite number of existing samples, except for those that resort to physics > based models (i.e., flow and transport). > > If anyone has pondered this problem before and can point me towards any > publications, I would be very appreciative. > > thanks > > Sean > > > > Sean A. McKenna Ph.D. > Geohydrology Department > Sandia National Laboratories > PO Box 5800 MS 0735 > Albuquerque, NM 87185-0735 > ph: 505 844-2450 > > > > -- > * 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 > -- * 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
