In the magnetic exploration theory, total-field anomaly ΔT is regarded as the component Tap of the magnetic anomaly vector Ta on the main field (T0) direction and thus constitutes the theoretical basis. However, there is an error in this approximation. Theoretical calculations and experiments have proved that this approximation error will increase rapidly as the Ta increases. When the magnetic anomaly Ta is much smaller than T0, the influence of the error is small and negligible. In the case of a strong magnetic anomaly, the error is large, and the processing interpretation accuracy of the ΔT anomaly is greatly affected. For high-precision magnetic exploration, ΔT must be converted to a magnetic anomaly component Tap for processing and interpretation. In this paper, the method of accurately calculating the magnetic anomaly component using Tap based on the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm is proposed. Firstly, the authors derived the forward formula for ΔT from Tap, and then constructed the objective function of Tap inversion by the difference function between ΔT and Tap. L-BFGS algorithm was used to solve the Tap from ΔT. Model experiments show that the Tap calculated by this method is very close to the real value, which can reduce the error by two orders of magnitude. This method also yields good results in the presence of noise and background fields. The method was applied to the processing of ΔT magnetic survey data of the Yangshan iron mine in Fujian Province, and the results of processing and interpretation which are more consistent with the actual results were obtained.
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