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What happens to the negative or 0 data when I grid the data in Surfer with a log transform?

You cannot take the log of a negative number or 0. The number must be positive and non-zero. This is not Surfer's rule, but a mathematical one.  The log of (X) becomes asymptotic as X approaches 0. 

If you are gridding data that contains negative or 0 values, then these data points are ignored if you are gridding with the Z Transform set to either Log, save as log or Log, save as linear.

 

Updated September 11, 2017

 

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