TWO‐DIMENSIONAL HARMONIC ANALYSIS AS A TOOL FOR MAGNETIC INTERPRETATION

Geophysics ◽  
1965 ◽  
Vol 30 (5) ◽  
pp. 829-857 ◽  
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.

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

Geophysics ◽  
2021 ◽  
pp. 1-47
Author(s):  
Rukuan Xie ◽  
Shengqing Xiong ◽  
Shuling Duan ◽  
Jinlong Wang ◽  
Ping Wang ◽  
...  
Keyword(s):  
Magnetic Anomaly ◽  
Geomagnetic Field ◽  
Approximation Error ◽  
Magnetic Data ◽  
Total Field ◽  
Projection Formula ◽  
Total Magnetization ◽  
Vector Formula ◽  
Relationship Of ◽  
Anomaly Formula

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.

THE DIRECT APPROACH TO MAGNETIC INTERPRETATION AND ITS PRACTICAL APPLICATION

Geophysics ◽  
1949 ◽  
Vol 14 (3) ◽  
pp. 290-320 ◽  
Author(s):  
Leo J. Peters
Keyword(s):  
Field Data ◽  
Potential Problem ◽  
Scalar Potential ◽  
Direct Calculation ◽  
Magnetic Data ◽  
Practical Application ◽  
Magnetic Field Data ◽  
Magnetic Interpretation ◽  
Basement Rocks ◽  
Derivatives Of

This paper discusses the solution of the inverse potential problem and its practical application in the interpretation of field data which have a scalar potential distribution. The discussion will be in terms of the interpretation of magnetic data. Among the topics discussed are: the direct calculation of basement relief, the derivation of the potential and the horizontal components of the field from the vertical intensity, the continuation of the field upward, the continuation of the field downward towards its source, the calculation of derivatives of the vertical intensity with special attention to the second and fourth, and the estimation of depths to igneous basement rocks. The uses of these tools and the information of practical value which can be obtained by their use are discussed and illustrated. Methods of rapidly making calculations using magnetic field data are given.

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

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. J43-J55 ◽  
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].

Automatic 3-D interpretation of potential field data using analytic signal derivatives

Geophysics ◽  
1997 ◽  
Vol 62 (1) ◽  
pp. 87-96 ◽  
Author(s):  
Nicole Debeglia ◽  
Jacques Corpel
Keyword(s):  
Signal Amplitude ◽  
Vertical Gradient ◽  
Analytic Signal ◽  
Magnetic Data ◽  
Practical Implementation ◽  
Potential Field Data ◽  
Gravity And Magnetic ◽  
Second Derivatives ◽  
Gravity And Magnetic Data ◽  
Derivatives Of

A new method has been developed for the automatic and general interpretation of gravity and magnetic data. This technique, based on the analysis of 3-D analytic signal derivatives, involves as few assumptions as possible on the magnetization or density properties and on the geometry of the structures. It is therefore particularly well suited to preliminary interpretation and model initialization. Processing the derivatives of the analytic signal amplitude, instead of the original analytic signal amplitude, gives a more efficient separation of anomalies caused by close structures. Moreover, gravity and magnetic data can be taken into account by the same procedure merely through using the gravity vertical gradient. The main advantage of derivatives, however, is that any source geometry can be considered as the sum of only two types of model: contact and thin‐dike models. In a first step, depths are estimated using a double interpretation of the analytic signal amplitude function for these two basic models. Second, the most suitable solution is defined at each estimation location through analysis of the vertical and horizontal gradients. Practical implementation of the method involves accurate frequency‐domain algorithms for computing derivatives with an automatic control of noise effects by appropriate filtering and upward continuation operations. Tests on theoretical magnetic fields give good depth evaluations for derivative orders ranging from 0 to 3. For actual magnetic data with borehole controls, the first and second derivatives seem to provide the most satisfactory depth estimations.

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.

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.

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

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. B121-B133 ◽  
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.

scholarly journals PEMETAAN SEBARAN BATUAN PENYUSUN PAGAR CANDI DI SITUS CANDI LOSARI DUSUN LOSARI, DESA SALAM, KECAMATAN SALAM, KABUPATEN MAGELANG BERDASARKAN METODE MAGNETIK

2013 ◽  
Vol 33 (1) ◽  
pp. 121-131
Author(s):  
Novi Dwi Ariani ◽  
Thaqibul Fikri Niyartama ◽  
Nugroho Budi Wibowo
Keyword(s):  
Magnetic Field ◽  
Field Data ◽  
Daily Variation ◽  
Local Magnetic Field ◽  
Magnetic Data ◽  
Reference Field ◽  
Magnetic Pole ◽  
Local Anomaly ◽  
Anomaly Pattern ◽  
Anomaly Map

Mapping geophysics research was conducted by geomagnetic method to know anomaly pattern of magnetic pole and to know distribution location and depth of temple gate composing stone in Losari Temple Site by using magnetic data. Data collection used Proton Precessions Magnetometer (PPM) G-856AX by area width of 88 km x 40 km and measurement space of 3 meter used looping method. Field data was corrected by daily variation and IGRF (International Geomagnetics Reference Field) correction and then reduction to pole. The slice modeling was conducted on local anomaly map on height of 6 meter. The result of the local magnetic field anomalies incision then interpolated to get an idea of the spread and depth of rocks making up the fence Losari temple. Local anomaly map shows that anomaly position lies in southwest, southeast, and northeast from main temple. Based from interpolated distribution of magnetic pole anomaly is dominated in depth of 2 meter to 4 meter. 

Sinusoidal magnetic field stimulates magnetosome formation and affects mamA, mms13, mms6, and magA expression in Magnetospirillum magneticum AMB-1

2008 ◽  
Vol 54 (12) ◽  
pp. 1016-1022 ◽  
Author(s):  
Xiaoke Wang ◽  
Likun Liang ◽  
Tao Song ◽  
Longfei Wu
Keyword(s):  
Magnetic Field ◽  
Geomagnetic Field ◽  
Biomedical Applications ◽  
Magnetic Particles ◽  
Industrial Sector ◽  
Magnetic Pole ◽  
Variable Intensity ◽  
New Approach ◽  
Sinusoidal Magnetic Field ◽  
Magnetospirillum Magneticum

Magnetic particles are currently one of the most important materials in the industrial sector, where they have been widely used for biotechnological and biomedical applications. To investigate the effects of the imposed magnetic field on biomineralization in Magnetospirillum magneticum AMB-1 and to suggest a new approach that enhances formation of magnetosomes, cultures inoculated with either magnetic or nonmagnetic precultures were incubated under a sinusoidal magnetic field or geomagnetic field. The results showed that the sinusoidal magnetic field up-regulated mms6 expression in the cultures inoculated with magnetic cells, and magA, mms6, and mamA expression in the cultures inoculated with nonmagnetic cells. The applied sinusoidal magnetic field could block cell division, which could contribute to a decrease in the OD600 values and an increase in the coefficient of magnetism values of the cultures, which could mean that the percentage of mature magnetosome-containing bacteria was increased. The linearity of magnetosome chains was affected, but the number of magnetic particles in cells was increased when a sinusoidal magnetic field was applied to the cultures. The results imply that the variable intensity and orientation of the sinusoidal magnetic field resulted in magnetic pole conversion in the newly forming magnetic particles, which could affect the formation of magnetic crystals and the arrangement of the adjacent magnetosome.

Fast 3D magnetic inversion of a surface relief in the space domain

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. J57-J67 ◽  
Author(s):  
Marlon C. Hidalgo-Gato ◽  
Valéria C. F. Barbosa
Keyword(s):  
Hessian Matrix ◽  
Computational Cost ◽  
Magnetization Vector ◽  
Forward Modeling ◽  
Magnetic Data ◽  
Total Field ◽  
Inversion Algorithm ◽  
Sensitivity Matrix ◽  
Magnetic Inversion ◽  
Magnetic Basement

We have developed a fast 3D regularized magnetic inversion algorithm for depth-to-basement estimation based on an efficient way to compute the total-field anomaly produced by an arbitrary interface separating nonmagnetic sediments from a magnetic basement. We approximate the basement layer by a grid of 3D vertical prisms juxtaposed in the horizontal directions, in which the prisms’ tops represent the depths to the magnetic basement. To compute the total-field anomaly produced by the basement relief, the 3D integral of the total-field anomaly of a prism is simplified by a 1D integral along the prism thickness, which in turn is multiplied by the horizontal area of the prism. The 1D integral is calculated numerically using the Gauss-Legendre quadrature produced by dipoles located along the vertical axis passing through the prism center. This new magnetic forward modeling overcomes one of the main drawbacks of the nonlinear inverse problem for estimating the basement depths from magnetic data: the intense computational cost to calculate the total-field anomaly of prisms. The new sensitivity matrix is simpler and computationally faster than the one using classic magnetic forward modeling based on the 3D integrals of a set of prisms that parameterize the earth’s subsurface. To speed up the inversion at each iteration, we used the Gauss-Newton approximation for the Hessian matrix keeping the main diagonal only and adding the first-order Tikhonov regularization function. The large sparseness of the Hessian matrix allows us to construct and solve a linear system iteratively that is faster and demands less memory than the classic nonlinear inversion with prism-based modeling using 3D integrals. We successfully inverted the total-field anomaly of a simulated smoothing basement relief with a constant magnetization vector. Tests on field data from a portion of the Pará-Maranhão Basin, Brazil, retrieved a first depth-to-basement estimate that was geologically plausible.

scholarly journals A High-Precision Magnetic-Assisted Heading Angle Calculation Method Based on a 1D Convolutional Neural Network (CNN) in a Complicated Magnetic Environment

Micromachines ◽  
2020 ◽  
Vol 11 (7) ◽  
pp. 642
Author(s):  
Guanghui Hu ◽  
Hong Wan ◽  
Xinxin Li
Keyword(s):  
Neural Network ◽  
Convolutional Neural Network ◽  
High Precision ◽  
Geomagnetic Field ◽  
Field Data ◽  
Time Window ◽  
Magnetic Data ◽  
Navigation Systems ◽  
Pedestrian Navigation ◽  
Heading Angle

Due to its widespread presence and independence from artificial signals, the application of geomagnetic field information in indoor pedestrian navigation systems has attracted extensive attention from researchers. However, for indoors environments, geomagnetic field signals can be severely disturbed by the complicated magnetic, leading to reduced positioning accuracy of magnetic-assisted navigation systems. Therefore, there is an urgent need for methods which screen out undisturbed geomagnetic field data for realizing the high accuracy pedestrian inertial navigation indoors. In this paper, we propose an algorithm based on a one-dimensional convolutional neural network (1D CNN) to screen magnetic field data. By encoding the magnetic data within a certain time window to a time series, a 1D CNN with two convolutional layers is designed to extract data features. In order to avoid errors arising from artificial labels, the feature vectors will be clustered in the feature space to classify the magnetic data using unsupervised methods. Our experimental results show that this method can distinguish the geomagnetic field data from indoors disturbed magnetic data well and further significantly improve the calculation accuracy of the heading angle. Our work provides a possible technical path for the realization of high-precision indoor pedestrian navigation systems.

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