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Comparison of gradient analysis techniques for linear two‐dimensional magnetic sources

1988; Society of Exploration Geophysicists; Volume: 53; Issue: 8 Linguagem: Inglês

10.1190/1.1442545

1942-2156

J. Bradley Nelson,

Seismic Waves and Analysis

Six techniques are presented for analyzing magnetic gradient [Formula: see text] and most require the computation of the total gradient [Formula: see text] Four of the methods are mathematically rigorous: one is based on the crossing points of the [Formula: see text] and [Formula: see text] profiles; a second, reported by Atchuta Rao et al., uses G and [Formula: see text]; and two more are based on the total gradient line‐shape. Two other methods, based on the half‐slope points of [Formula: see text] and G, are rule‐of‐thumb techniques similar to the familiar half‐slope method for total field anomalies. These methods have been used to obtain depth estimates from simulated profiles over thick and narrow dikes contaminated by dc offsets, linear trends, and random noise. 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 geometry.