Phi-notation

In geological literature dealing with particle size distribution [ 130,131 ] a very advantageous transformation of particle size is commonly used. This transformation replaces scale numbers based on linear millimeter values by the logarithms of these values. Because it is a logarithmic transformation it simplifies computation. 

The standard deviation cr used in this notation is defined as  

Other statistical measurements used in geology for particle size distribution characterization (moment, quartile and others) have been defined [135,136]. 

2 Growl, V.T. (1963), Paint Research Station Report, No 235, Teddington, London, 62, 75 

3 Anon. (1985), Image Analysis, Principles and Practice, Joyce Loebl, 63 

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