Date: Tue, 20 Jan 2004 09:34:49 -0500
Reply-To: "DePuy, Venita" <depuy001@DCRI.DUKE.EDU>
Sender: "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From: "DePuy, Venita" <depuy001@DCRI.DUKE.EDU>
Subject: Re: Prediction of Subsurface Elevations Across Faults
Content-Type: text/plain; charset="iso-8859-1"
Hi Kevin et al -
it's been a year since I took the course, so my recollection is rather fuzzy
-
but why aren't you using spatial statistics, ie Procs Variogram and Krig2ed?
There's a little $10 booklet SAS puts out on spatial statistics that is very
helpful - tan/brown cover and the name is something like SAS for Spatial
Statistics.
HTH, email me if you need more info.
Venita
> ----------
> From: Kevin Myers[SMTP:kevinmyers@austin.rr.com]
> Reply To: kevinmyers@austin.rr.com
> Sent: Sunday, January 18, 2004 4:28 PM
> To: SAS-L@LISTSERV.UGA.EDU
> Subject: Prediction of Subsurface Elevations Across Faults
>
> Howdy folks,
>
> Have a tricky problem and think I could use some help from the statistics
> gurus out there. I'd like to predict the subsurface elevations of a
> deeper geologic horizon based on the measured elevations of a shallower
> geologic horizon. As a training data set, I have the measured elevations
> of both horizons, along with the x and y map coordinates for certain
> measurement locations. I also have a data set with map coordinates and
> elevations for the shallower horizon where I wish to predict the
> elevations of the deeper horizon.
>
> Previously, I've been using the following approach:
>
> 1. Use multiple regression via PROC REG to obtain best fit coefficients
> for the following equation:
>
> z2 = C1*z1 + C2*x + C3*y + C4
>
> where z2 is the elevation of the deeper horizon, z1 is the elevation of
> the shallower horizon, x and y are the map coordinate values, and C1, C2,
> C3, and C4 are the best fit regression coefficients.
>
> 2. Obtain the error between the values predicted using the above equation
> and the actual values. Grid and contour these error values across the map
> area.
>
> 3. For each point where a predicted elevation of the deeper horizon is
> needed, compute a preliminary value for the deeper horizon using the map
> coordinates and the elevation of the shallower horizon using the equation
> previously determined in step 1. Then obtain the error value for these
> map coordinates based on the values contoured in step 2, and add the
> resulting anticipated error value to the preminary predicted value to
> obtain a final predicted elevation for the deeper horizon.
>
>
> For areas involving relatively simple "layer cake" sedimentary deposits,
> the above approach works reasonable well. However, it runs into problems
> in situations such as where the deeper horizon is cut by a fault that is
> truncated by subsequent erosion and does not intersect the shallower
> horizon. In this scenario, any such faults segregate the area to be
> mapped into multiple distinct regions where different relationships
> (different regression coefficients) between the two horizons apply.
>
> It is an extremely error prone, labor intensive, and time consuming
> process to attempt to manually detect such separate regions, and to split
> the data into multiple data sets accordingly so that the final results
> will be reasonably accurate. Therefore, I need some new approach to help
> automate this process. In some manner, the process needs to automatically
> detect the regions for which different correlations are applicable, and
> then automatically apply the proper relationship for determining the
> predicted values in each region.
>
> I briefly considered trying to use a neural net, but am not familiar
> enough with their design and use to be confident that I could come up with
> something that would work well in a reasonable amount of time. Besides
> that, I don't have access to Enterprise Miner so I'd have to use something
> else to implement the neural net.
>
> I'm wondering if there isn't something else in SAS that would be
> especially applicable to this problem. Perhaps something that
> automatically evaluates correlation coefficients to come up with some kind
> of piecewise regression? Unfortunately, I'm not a statistician, and don't
> know enough about all of the various stat procs to have any idea where to
> begin. But it seems like this kind of problem would be fairly common in
> many other fields, so I'm hoping there is already something out there that
> can do this. I'd hate to have to try inventing a solution for this on my
> own. All of the ideas that I have come up with so far would be extremely
> cumbersome, and I feel sure that someone else has probably already
> developed something much more robust.
>
> Any help would be greatly appreciated.
>
> Thanks,
> s/KAM
>
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