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Overlapping Z values do not match when using Split Raster Tool

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I have a large 11457 row by 9560 column raster 180m-resolution DEM that I would like to split into 95 parts, where each part has one row/column overlapping with its adjacent parts. It is absolutely vital that these overlapping rows/columns match up correctly in X, Y, and Z. I have been using the Split Raster tool to split the raster into 19 rows and 5 columns (19 x 5 = 95 parts). I chose these numbers specifically because 19 divides into 11457 cleanly, as does 5 into 9560. I chose to overlap by 1 pixel, assuming that 1 pixel = 180 meters.

After splitting the raster, I convert each part into an ASCII file using the Raster to ASCII tool, which I then convert into a text file that gives me the X Y and Z coordinates of the raster. When I compared two text files of XYZ coordinates of two adjacent files, I found that although each file shared a row with the same X and Y coordinates, the Z values that corresponded to these coordinates did not match up. They were similar in magnitude (as in, not a thousand meters off), but still not exactly the same like I need them to be.

This occurs regardless of which resampling technique I use (I first used BILINEAR, and then tried NEAREST). I wanted to try not using a resampling technique, but that isn't an option. I have relentlessly checked the script that converts the ASCII file to the XYZ coordinate text file, and I am positive that what it is doing is correct.

Does anyone have any insight on how I can split a raster with overlapping columns/rows that share the exact same XYZ values in each part?

Anyhow, please let me know if I need to make any clarifications. Any help or insight would be greatly appreciated! If I am not able to figure this out using ArcMap 10, I may have to resort to trying to write code that works with a humungous ASCII file from the original large DEM, and split that into 95 parts somehow---unfortunately, I don't think I am a skilled enough coder to be able to do that. :(

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