Arısoy and Dikmen (2015) discuss the application of fractional order derivatives to magnetic data. In particular, they fix the phase difference of the horizontal derivative with respect to the original data to be 90°, regardless of the order n of the derivative that is used. This is equivalent to the order n1 vertical derivative of the first horizontal derivative; i.e.,  
nfxn=n1zn1(fx)=x(n1fzn−...
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