基于L-BFGS反演算法的ΔT精确计算磁异常分量Tap方法

doi:10.11720/wtyht.2019.1383

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Abstract

In the magnetic exploration theory, total-field anomaly ΔT is regarded as the component T_ap of the magnetic anomaly vector T_a 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 T_a increases. When the magnetic anomaly T_a 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 T_ap 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 T_ap. 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.

Key words： magnetic anomaly total-field anomaly ΔT magnetic anomaly component T_ap high-precision processing and interpretation L-BFGS

Received: 24 October 2018 Published: 31 May 2019

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Corresponding Authors: Yu-Shan YANG E-mail: samyys@126.com

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	Hui-Xiang ZHEN
	Yu-Shan YANG
	Yuan-Yuan LI
	Tian-You LIU

Cite this article:

Hui-Xiang ZHEN,Yu-Shan YANG,Yuan-Yuan LI, et al. Method for accurately calculating magnetic anomaly component using ΔT based on L-BFGS inversion algorithm[J]. Geophysical and Geochemical Exploration, 2019, 43(3): 598-607.

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https://www.wutanyuhuatan.com/EN/10.11720/wtyht.2019.1383 OR https://www.wutanyuhuatan.com/EN/Y2019/V43/I3/598

Schematic diagram of total field anomaly ΔT and other related physical quantities

Reduction to the pole (RTP) results comparison of ΔT and T_ap under strong magnetic anomalies
a—ΔT of the sphere model; b—T_ap of the sphere model; c—RTP of the sphere model ΔT; d—RTP of the sphere model T_ap;the red circle in the figure represents the projection of the sphere model and the black dot represents the midpoint of the sphere model

Model geometric parameters of and magnetization

Model horizontal and profile projection
a—single sphere model; b—combined sphere model

Comparison of T_ap, ΔT and calculated T_ap
a—the projection component T_ap of the magnetic anomaly in the direction of the normal geomagnetic field; b—the total field anomaly ΔT; c—the magnetic anomaly component T_ap obtained by the inversion

Single sphere model inversion error
a—difference between ΔT and T_ap (ie, initial deviation); b—error between the inverted T_ap and the theoretical T_ap

The result of the inversion of the magnetic anomaly component T_ap
The red circle in the figure represents the projection of the sphere model, and the black dot represents the midpoint of the sphere model

Comparison of T_ap, ΔT and calculated T_ap
a—the projection component T_ap of the magnetic anomaly in the direction of the earth’s magnetic field; b—the total field anomaly ΔT; c—the magnetic anomaly component T_ap obtained by the inversion

Inversion error of combined sphere model
a—difference between ΔT and T_ap (ie, initial deviation); b—error between the inverted T_ap and the theoretical T_ap

The RTP result of the magnetic anomaly component T_ap obtained by inversion
The red circle in the figure represents the projection of the sphere model, and the black dot represents the midpoint of the sphere model

error of T_ap obtained by inversion of combined sphere model under weak magnetic anomaly
a—difference between ΔT and T_ap (ie, initial deviation); b—error between the inverted T_ap and the theoretical T_ap

Model experiment for superimposed noise
a—0~100 nT random noise; b—approximation error of ΔT superimposed with random noise; c—error of T_ap obtained by ΔT inversion of superimposed noise; d—T_ap error result obtained by inversion (after noise elimination)

The model experiment of the superimposed background field
a—the background field; b—approximation error of ΔT (overlay background field); c—error of T_ap obtained by ΔT inversion of superimposed background field; d—T_ap error result obtained by inversion (after eliminating the background field)

Comparison of ΔT reduction to the pole result of measured data and T_ap RTP result obtained by inversion
a—ΔT RTP result of measured data; b—T_ap RTP result obtained by inversion; c—difference between two polarization results

Profile inversion comparison of ΔT and calculated T_ap
a—ΔT reduction to the pole curve, T_apreduction to the pole curve and their inversion fitting results along the section AB; b—inversion result of the observed ΔT data; c—inversion result of the calculated T_ap data; See ore through dring bore ck40, ck42, no mine ore is found in borehole ck39, zk4298

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