Nelson, J.B., Comparison of gradient analysis techniques for linear two-dimensional magnetic sources, Geophysics, 53, 1088-1095, 1988.
Six techniques are presented for analyzing magnetic gradient profiles over two dimensional structures. All use the vertical gradient Gz and most require the computation of the total gradient G = Ö
(Gx2 + Gz2). Four of the methods are mathematically rigorous: one is based on the crossing points of the Gx and Gz profiles; a second, reported by Atchuta Rao et al., uses G and
Æ = arctan(Gx / Gz ); and two more are based on the total gradient line-shape.
The methods vary in their sensitivities to small dc offsets, local trends, and random noise. The crossing-point method is found to be very sensitive to all three types of noise, while the complex gradient is quite sensitive to offsets and trends, but only slightly affected by random noise. Depth estimates based on these methods, using real data, may contain errors of 5-10 percent.
The two line-shape analysis methods are only slightly sensitive to trends and offsets and, depending upon the relative values of the maxima and minima, may or may not be sensitive to random noise. However, they are only applicable to wide dikes. Depth estimates from these techniques (for wide dikes) are considered to be the most accurate of the four mathematically rigorous methods investigated (errors < 5 percent).
The half-slope methods are not sensitive to trends or offsets but are sensitive to random noise (»5 percent). However, uncertainty in the source geometry may produce small errors in the depth estimates for thick dikes (2-4 percent) and sizable errors in the depth estimates for narrow dikes (> 10 percent). While these uncertainties are much less than those found when the half-slope method is applied to the total field profile, they are significant compared to the errors caused by the various noise sources considered. Thus, the accuracy of these methods is quite dependent upon the source geomtery.
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