```Date: Tue, 20 Jan 2004 09:34:49 -0500 Reply-To: "DePuy, Venita" Sender: "SAS(r) Discussion" From: "DePuy, Venita" Subject: Re: Prediction of Subsurface Elevations Across Faults Comments: To: "kevinmyers@austin.rr.com" 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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