Using airborne vector magnetic data to calculate the projection of magnetic anomaly vector onto normal geomagnetic field

The total-field magnetic anomaly [Formula: see text] is an approximation of the projection [Formula: see text] of the magnetic anomaly vector [Formula: see text] onto the normal geomagnetic field [Formula: see text]. However, for highly magnetic sources, the approximation error of [Formula: see text] cannot be ignored. To reduce the error, we have developed a method for calculating [Formula: see text] by using airborne vector magnetic data based on the vector relationship of geomagnetic field [Formula: see text]. The calculation uses the magnitude of the vectors [Formula: see text], [Formula: see text], and [Formula: see text] through a simple approach. To ensure that each magnitude has the same level, we normalize the magnitude of [Formula: see text] using the total-field magnetic data measured by the scalar magnetic sensor. The method is applied to the measured airborne vector magnetic data at the Qixin area of the East Tianshan Mountains in China. The results indicate that the calculated [Formula: see text] has high precision and can distinguish the approximation error less than 3.5 nT. We also analyze the characteristics of the approximation error that are caused by the effects of different total magnetization inclinations. These error characteristics are used to predict the total magnetization inclination of a 2D magnetic source based on the measured airborne vector magnetic data.

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Transformation from total-field magnetic anomaly to the projection of the anomalous vector onto the normal geomagnetic field based on an optimization method

Geophysics ◽

10.1190/geo2018-0671.1 ◽

2019 ◽

Vol 84 (5) ◽

pp. J43-J55 ◽

Cited By ~ 2

Author(s):

Huixiang Zhen ◽

Yuanyuan Li ◽

Yushan Yang

Keyword(s):

Data Processing ◽

Magnetic Anomaly ◽

Geomagnetic Field ◽

Southern China ◽

Quadratic Function ◽

Maximum Error ◽

Magnetic Data ◽

Optimization Strategy ◽

Total Field ◽

The Difference

The total-field magnetic anomaly [Formula: see text] is approximated as the component [Formula: see text] of the anomalous vector [Formula: see text] along the direction of the normal geomagnetic field. It is widely used in magnetic data processing and interpretation practices as a routine if [Formula: see text] is relatively small. But in highly magnetic environments, the distinction between [Formula: see text] and [Formula: see text] is often too large to be ignored. We carefully investigate the difference between [Formula: see text] and [Formula: see text] and find that it will increase rapidly in the trend of the quadratic function as [Formula: see text] strengthens. We also test the effects of approximation on the component transformation and reduction to the pole on a synthetic single-sphere model. As expected, the error caused by inaccurate information will propagate into subsequent data processing procedures and adversely affect the results. Therefore, we have developed an optimization strategy based on the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm to transform the total-field anomaly into [Formula: see text]. First, we have constructed an objective function after transforming [Formula: see text] into [Formula: see text] through the component transformation in the frequency domain. Then, using [Formula: see text] as the initial value of [Formula: see text], [Formula: see text] is calculated iteratively by the L-BFGS algorithm. To test the validity of the optimization algorithm, [Formula: see text] is transformed for noise-free and noise-corrupted models and models with a background field. The synthetics indicate that the transformed [Formula: see text] is almost the same as the model [Formula: see text], whose maximum error is approximately one-hundredth (30 nT) of the difference (8000 nT) between the modeled [Formula: see text] and [Formula: see text]. The synthetics and field data example from the Yangshan Iron Mine, Fujian Province, southern China, also indicate that the data transformation and forward-modeling results can benefit from the direct use of transformed [Formula: see text] instead of [Formula: see text].

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Stepped inversion of magnetic data

Geophysics ◽

10.1190/1.2711661 ◽

2007 ◽

Vol 72 (3) ◽

pp. L21-L30 ◽

Cited By ~ 3

Author(s):

Soraya Lozada Tuma ◽

Carlos Alberto Mendonça

Keyword(s):

Magnetic Anomaly ◽

Shape Function ◽

Source Parameters ◽

Real Data ◽

Magnetic Data ◽

Total Field ◽

Magnetization Direction ◽

Magnetization Intensity ◽

Magnetic Inversion ◽

Total Gradient

We present a three-step magnetic inversion procedure in which invariant quantities with respect to source parameters are inverted sequentially to give (1) shape cross section, (2) magnetization intensity, and (3) magnetization direction for a 2D (elongated) magnetic source. The quantity first inverted (called here the shape function) is obtained from the ratio of the gradient intensity of the total-field anomaly to the intensity of the anomalous vector field. For homogenous sources, the shape function is invariant with source magnetization and allows reconstruction of the source geometry by attributing an arbitrary magnetization to trial solutions. Once determined, the source shape is fixed and magnetization intensity is estimated by fitting the total gradient of the total-field anomaly (equivalent to the amplitude of the analytic signal of magnetic anomaly). Finally, the source shape and magnetization intensity are fixed and the magnetization direction is determined by fitting the magnetic anomaly. As suggested by numerical modeling and real data application, stepped inversion allows checking whether causative sources are homogeneous. This is possible because the shape function from inhomogeneous sources can be fitted by homogeneous models, but a model obtained in this way fits neither the total gradient of the magnetic anomaly nor the magnetic anomaly itself. Such a criterion seems effective in recognizing strongly inhomogeneous sources. Stepped inversion is tested with numerical experiments, and is used to model a magnetic anomaly from intrusive basic rocks from the Paraná Basin, Brazil.

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TWO‐DIMENSIONAL HARMONIC ANALYSIS AS A TOOL FOR MAGNETIC INTERPRETATION

Geophysics ◽

10.1190/1.1439658 ◽

1965 ◽

Vol 30 (5) ◽

pp. 829-857 ◽

Cited By ~ 119

Author(s):

B. K. Bhattacharyya

Keyword(s):

Geomagnetic Field ◽

Polarization Vector ◽

Double Fourier Series ◽

Fourier Series Expansion ◽

Magnetic Data ◽

Block Type ◽

Total Field ◽

Magnetic Pole ◽

Magnetic Interpretation ◽

Derivatives Of

The total magnetic field values over an area can be represented exactly by a double Fourier series expansion. In this analysis, such an expansion is used to evaluate very accurately the fields continued downward and upward from the plane of observation and the vertical derivatives of the total field. This harmonic expansion of the anomalous total field makes it possible to calculate, with exceptional accuracy, the field reduced to the magnetic pole and its second derivative. The results of the calculations are free from the effect of the inclination of the earth’s main geomagnetic field and that of the polarization vector, at all magnetic latitudes and for all possible directions of polarization. In order to determine the influence of remanence on the above field, a number of anomalies caused by rectangular block‐type bodies with known polarization are reduced to the magnetic pole, correcting only for the obliquity of the earth’s normal field. It is concluded from a study of these anomalies that the interpretation of magnetic data based on the assumption of rock magnetization due solely to induction in the earth’s field may yield erroneous results, particularly when remanence is important.

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A New Method of Cross-Correlation by Magnetic Dipole for Estimating Magnetization Direction under the Influence of Remanent Magnetization

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.644-650.3459 ◽

2014 ◽

Vol 644-650 ◽

pp. 3459-3462 ◽

Cited By ~ 1

Author(s):

Lei Shi ◽

Liang Hui Guo ◽

Feng Yi Guo

Keyword(s):

Correlation Coefficient ◽

Magnetic Dipole ◽

Remanent Magnetization ◽

Cross Correlation ◽

New Method ◽

Magnetic Data ◽

Dipole Source ◽

Total Field ◽

Magnetization Direction ◽

Total Magnetization

Processing and interpretation of magnetic data usually require information of total magnetization direction. However, under the effects of remanent magnetization, total magnetization direction is different from induced magnetization direction, which makes data processing and interpretation complexity. In this paper, we present a new method by cross-correlation of magnetic dipole source for determination of magnetization direction from relatively isolated and approximate equiaxial-shape magnetic total field anomaly. This method calculates cross-correlation coefficient between observed magnetic total field anomaly and theoretical magnetic total field anomaly caused by a magnetic dipole source, by using a set of varying parameters of positions and total magnetization direction of dipole source for trial and error. The corresponding magnetization direction of maximum correlation coefficient is regarded as estimated total magnetization direction. Test on synthetic data indicates that this method reliably and effectively estimates the magnetization direction from relatively isolated and approximate equiaxial-shape magnetic total field anomaly.

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Estimating the Magnetization Direction of Sources through Correlation between Reduced-to-Pole Anomaly and Normalized Source Strength

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.644-650.3793 ◽

2014 ◽

Vol 644-650 ◽

pp. 3793-3796

Author(s):

Liang Hui Guo ◽

Rui Gao ◽

Guo Li Zhang

Keyword(s):

Geomagnetic Field ◽

Remanent Magnetization ◽

Cross Correlation ◽

Synthetic Data ◽

Field Direction ◽

Magnetic Data ◽

Source Strength ◽

Magnetization Direction ◽

New Approach ◽

Total Magnetization

Under the effects of remanent magnetization, total magnetization direction is different from geomagnetic field direction, which makes magnetic data processing and interpretation complexity. In this paper, we present a new approach for estimating the total magnetization direction of sources via cross-correlation between the reduced-to-pole anomaly and the normalized source strength (who is less sensitive to remanent magnetization). The geomagnetic field direction is used to calculated the normalized source strength, while various assumed total magnetization directions are used to calculated the RTP anomalies. The maximum correlation between the RTP anomalies and the normalized corresponds to the estimated total magnetization direction. Test on synthetic data showed that the new approach is simple and effective.

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THE STUDY OF LONGITUDINAL AND LATITUDINAL VARIATION OF EQUATORIAL ELECTROJET SIGNATURE AT STATIONS WITHIN THE 96°MM AND 210°MM AFRICAN AND ASIAN SECTORS RESPECTIVELY UNDER QUIET CONDITIONS.

FUDMA Journal of Sciences ◽

10.33003/fjs-2021-0502-662 ◽

2021 ◽

Vol 5 (2) ◽

pp. 511-532

Author(s):

Aniefiok Akpaneno ◽

Matthew Joshua ◽

K. R. Ekundayo

Keyword(s):

Seasonal Variation ◽

Geomagnetic Field ◽

Satellite Communication ◽

Equatorial Electrojet ◽

Latitudinal Variation ◽

Magnetic Data ◽

Horizontal Magnetic Field ◽

Baseline Values ◽

The Difference ◽

Current Systems

Solar quiet current (S_q) and Equatorial Electrojet (EEJ) are two current systems which are produced by electric current in the ionosphere. The enhancement of the horizontal magnetic field is the EEJ. This research is needed for monitoring equatorial geomagnetic current which causes atmospheric instabilities and affects high frequency and satellite communication. This study presents the longitudinal and latitudinal variation of equatorial electrojet signature at stations within the 96°mm and 210°mm African and Asian sectors respectively during quiet condition. Data from eleven observatories were used for this study. The objectives was to determine the longitudinal and latitudinal geomagnetic field variations during solar quiet conditions, Investigate monthly variation and diurnal transient seasonal variation; Measure the strength of the EEJ at stations within the same longitudinal sectors and find out the factors responsible for the longitudinal and latitudinal variation of EEJ. Horizontal (H) component of geomagnetic field for the year 2008 from Magnetic Data Acquisition System (MAGDAS) network were used for the study. The International Quiet Days (IQDs) were used to identify quiet days. Daily baseline values for each of the geomagnetic element H were obtained. The monthly average of the diurnal variation was found. The seasonal variation of dH was found. Results showed that: The longitudinal and latitudinal variation in the dH differs in magnitude from one station to another within the same longitude due to the difference in the influence of the EEJ on them.

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Constrained 3D inversion of magnetic data with structural orientation and borehole lithology: A case study in the Macheng iron deposit, Hebei, China

Geophysics ◽

10.1190/geo2018-0257.1 ◽

2019 ◽

Vol 84 (2) ◽

pp. B121-B133 ◽

Cited By ~ 4

Author(s):

Shida Sun ◽

Chao Chen ◽

Yiming Liu

Keyword(s):

Remanent Magnetization ◽

Magnetic Data ◽

Iron Deposit ◽

Reference Field ◽

Total Field ◽

Equivalent Source ◽

Structural Orientation ◽

Amplitude Data ◽

Ore Bodies

We have developed a case study on the use of constrained inversion of magnetic data for recovering ore bodies quantitatively in the Macheng iron deposit, China. The inversion is constrained by the structural orientation and the borehole lithology in the presence of high magnetic susceptibility and strong remanent magnetization. Either the self-demagnetization effect caused by high susceptibility or strong remanent magnetization would lead to an unknown total magnetization direction. Here, we chose inversion of amplitude data that indicate low sensitivity to the direction of magnetization of the sources when constructing the underground model of effective susceptibility. To reduce the errors that arise when treating the total-field anomaly as the projection of an anomalous field vector in the direction of the geomagnetic reference field, we develop an equivalent source technique to calculate the amplitude data from the total-field anomaly. This equivalent source technique is based on the acquisition of the total-field anomaly, which uses the total-field intensity minus the magnitude of the reference field. We first design a synthetic model from a simplified real case to test the new approach, involving the amplitude data calculation and the constrained amplitude inversion. Then, we apply this approach to the real data. The results indicate that the structural orientation and borehole susceptibility bounds are compatible with each other and are able to improve the quality of the recovered model to obtain the distribution of ore bodies quantitatively and effectively.

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