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Nabighian (1984) and Nelson (1986) have both derived relations between horizontal and vertical gradients of magnetic fields (or any other potential field), whereby a knowledge of one enables one to calculate the other. As pointed out by Nelson, Nabighian's derivation is quite lengthy. In the following, I offer an alternative derivation in the wavenumber domain, which is even shorter than that given by Nelson.
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Laust B. Pedersen (1989) studied this question.
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