Stepped inversion of magnetic data

Geophysics ◽  
2007 ◽  
Vol 72 (3) ◽  
pp. L21-L30 ◽  
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.

Magnetization vector imaging for borehole magnetic data based on magnitude magnetic anomaly

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. D429-D444 ◽  
Author(s):  
Shuang Liu ◽  
Xiangyun Hu ◽  
Tianyou Liu ◽  
Jie Feng ◽  
Wenli Gao ◽  
...  
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Magnetization Vector ◽  
Real Data ◽  
Magnetic Anomalies ◽  
Magnetic Data ◽  
Preconditioned Conjugate Gradient ◽  
Magnetization Direction ◽  
Magnetization Intensity

Remanent magnetization and self-demagnetization change the magnitude and direction of the magnetization vector, which complicates the interpretation of magnetic data. To deal with this problem, we evaluated a method for inverting the distributions of 2D magnetization vector or effective susceptibility using 3C borehole magnetic data. The basis for this method is the fact that 2D magnitude magnetic anomalies are not sensitive to the magnetization direction. We calculated magnitude anomalies from the measured borehole magnetic data in a spatial domain. The vector distributions of magnetization were inverted methodically in two steps. The distributions of magnetization magnitude were initially solved based on magnitude magnetic anomalies using the preconditioned conjugate gradient method. The preconditioner determined by the distances between the cells and the borehole observation points greatly improved the quality of the magnetization magnitude imaging. With the calculated magnetization magnitude, the distributions of magnetization direction were computed by fitting the component anomalies secondly using the conjugate gradient method. The two-step approach made full use of the amplitude and phase anomalies of the borehole magnetic data. We studied the influence of remanence and demagnetization based on the recovered magnetization intensity and direction distributions. Finally, we tested our method using synthetic and real data from scenarios that involved high susceptibility and complicated remanence, and all tests returned favorable results.

Inversion of the power spectrum from magnetic anomalies

Geophysics ◽  
1994 ◽  
Vol 59 (3) ◽  
pp. 391-401 ◽  
Author(s):  
Juan Garca‐Abdeslem ◽  
Gordon E. Ness
Keyword(s):  
Magnetic Anomaly ◽  
Source Parameters ◽  
Real Data ◽  
Power Density Spectrum ◽  
Magnetic Data ◽  
Synthetic Spectrum ◽  
Model Parameters ◽  
Density Spectrum ◽  
Uniform Distributions ◽  
And Inversion

We develop methods for the modeling and inversion of the power‐density spectrum from magnetic anomaly data assuming that the crustal magnetic field is caused by an ensemble of vertical‐sided and uniformly magnetized prisms. The solution of the forward problem is achieved in the wavenumber domain, where a synthetic spectrum is given by the product of the mathematical expectations of single‐valued functions that describe depth, thickness, and horizontal dimensions of prisms in the ensemble. We use Gaussian and uniform distributions to describe the ensemble and provide a variety of functions from which different statistical models can be obtained. The solution of the inverse problem is achieved iteratively, starting from an initial set of model parameters. It is based on the ridge‐regression algorithm, and its usefulness is assessed in a number of examples with numeric, synthetic and real data spectra. The methods are first tested on the spectrum obtained from a simple artificial magnetic anomaly and on the artificial spectrum caused by an ensemble of source bodies and are found to be capable of recovering the source parameters. Next, the methods are applied to marine magnetic data from a survey offshore of the Yucatán Peninsula, Mexico. The results of this last application are consistent with the crustal structure observed at Chicxulub hole.

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.

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.

Improving the crosscorrelation method to estimate the total magnetization direction vector of isolated sources: A space-domain approach for unstable inclination values

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. J59-J70 ◽  
Author(s):  
Nelson Ribeiro-Filho ◽  
Rodrigo Bijani ◽  
Cosme Ponte-Neto
Keyword(s):  
Magnetic Field ◽  
Real Data ◽  
Magnetic Anomalies ◽  
Direction Vector ◽  
Total Field ◽  
Magnetization Direction ◽  
Ambient Magnetic Field ◽  
Total Magnetization ◽  
Synthetic Test ◽  
Equivalent Sources

Knowledge of the total magnetization direction of geologic sources is valuable for interpretation of magnetic anomalies. Although the magnetization direction of causative sources is assumed to be induced by the ambient magnetic field, the presence of remanence should not be neglected. An existing method of correlating total and vertical gradients of the reduced-to-the-pole (RTP) anomaly estimates the total magnetization direction well. However, due to the numerical instability of RTP transformation in the Fourier domain, an assumption should be considered for dealing with inclination values at approximately 0°. We have adopted an extension to the standard crosscorrelation method for estimating the total magnetization direction vector, computing the RTP anomaly by means of the classic equivalent layer technique for low inclination values. Additionally, an ideal number of equivalent sources within the layer is considered for reducing the computational demands. To investigate the relevant aspects of the adopted method, two simple synthetic scenarios are presented. First, a magnetic anomaly produced by a homogeneous and isolated vertical dike is considered. This test illustrates the good performance of the adopted approach, finding the true magnetization direction, even for low inclination values. In the second synthetic test, a long-wavelength component is added to the previous magnetic total-field anomaly. In this case, the method adopted here fails to estimate a reliable magnetization direction vector, showing weak performance for strong interfering magnetic anomalies. On the real data example, the application tests an isolated total-field anomaly of the Carajás Mineral Province, in northern Brazil, where the inclination of the ambient magnetic field is close to zero. The obtained results indicate weak remanence in the estimated total magnetization direction vector, which would never be reached in the standard formulation of the crosscorrelation technique.

scholarly journals Three-dimensional interpretation of magnetic and gravity anomalies using the finite-difference similarity transform

Geophysics ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. L79-L90 ◽  
Author(s):  
Daniela Gerovska ◽  
Marcos J. Araúzo-Bravo ◽  
Kathryn Whaler ◽  
Petar Stavrev ◽  
Alan Reid
Keyword(s):  
Finite Difference ◽  
Random Noise ◽  
Source Parameters ◽  
Magnetization Vector ◽  
Real Data ◽  
Index Formula ◽  
Magnetic Data ◽  
Horizontal Position ◽  
Structural Index ◽  
Similarity Transform

We present an automatic procedure for interpretation of magnetic or gravity gridded anomalies based on the finite-difference similarity transform (FDST). It is called MaGSoundFDST (magnetic and gravity sounding based on the finite-difference similarity transform) and uses a “focusing” principle in contrast to deriving multiple clusters of many solutions as in the widely used Euler deconvolution method. The source parameters are characterized by isolated solutions, and the interpreter obtains parallel images showing the horizontal position, depth, and structural index [Formula: see text] value. The underlying principle is that the FDST of a potential field anomaly becomes zero or linear at all observation points when the central point of similarity (CPS) of the transform coincides with a source field’s singular point and a correct [Formula: see text] value is used. The procedure involves calculating a 3D function that evaluates the linearity of the FDST for a series of [Formula: see text] values, using a moving window and sounding the subsurface along a verticalline under each window center. We then combine the 3D results for different [Formula: see text] values into a single map whose minima determine the horizontal position of the sources. The [Formula: see text] value and the CPS depth associated with each minimum determine the [Formula: see text] value and depth of the corresponding source. Only one estimate characterizes a simple source, which is a major advantage over other window-based procedures. MaGSoundFDST uses only the measured anomalous field and its upward continuation, thus avoiding the direct use of field derivatives. It is independent of the magnetization-vector direction in the magnetic data case. The procedure accounts for a linear background of local gravity or magnetic anomalies and has been applied effectively to several cases of synthetic and real data. MaGSoundFDST shares common features with the magnetic and gravity sounding based on the differential similarity transform (MaGSoundDST) but is more stable in estimating depth and structural index in the presence of random noise.

Tracking of moving magnetic target based on magnetic gradient system with total field magnetometers

Sensor Review ◽  
2018 ◽  
Vol 38 (4) ◽  
pp. 501-508 ◽  
Author(s):  
Liming Fan ◽  
Xiyuan Kang ◽  
Quan Zheng ◽  
Xiaojun Zhang ◽  
Xuejun Liu ◽  
...  
Keyword(s):  
Magnetic Anomaly ◽  
Optimization Problem ◽  
Real Data ◽  
Magnetic Sensor ◽  
Gradient System ◽  
Direction Vector ◽  
Total Field ◽  
Content Type ◽  
Tracking Method ◽  
Magnetic Target

Purpose This paper aims to focus on the tracking of a moving magnetic target by using total field magnetometers and to present a tracking method based on the gradient of a magnetic anomaly. In the tracking, it is assumed that the motion of the target is equivalent to a first-order Markov process. And the unit direction vector of the magnetic moment from the gradient of the magnetic anomaly can be obtained. According to the unit direction vector, the inverse problem is turned into an optimization problem to estimate the parameters of the target. The particle swarm optimization algorithm is used to solve this optimization problem. The proposed method is validated by the numerical simulation and real data. The parameters of the target can be calculated rapidly using the proposed method. And the results show that the estimated parameters of the mobile target using the proposed method are very close to the true values. Design/methodology/approach The authors focus on the tracking of a moving magnetic target by using total field magnetometers and present a tracking method based on the gradient of a magnetic anomaly. Findings The paper provides an effective method for tracking the magnetic target based on an array with total field sensors. Originality/value Comparing with a vector magnetic sensor, the measurement of the scalar magnetic sensor is almost not influenced by its orientation. In this paper, a moving magnetic target was tracked by using total field magnetometers and a tracking method presented based on the gradient of a magnetic anomaly.

Estimation of density, magnetization, and depth to source: A nonlinear and noniterative 3-D potential‐field method

Geophysics ◽  
1997 ◽  
Vol 62 (3) ◽  
pp. 814-830 ◽  
Author(s):  
Maurizio Fedi
Keyword(s):  
A Priori ◽  
Real Data ◽  
Field Method ◽  
Magnetic Data ◽  
System Of Equations ◽  
Source Depth ◽  
A Priori Information ◽  
Magnetization Direction ◽  
Priori Information ◽  
Magnetic Case

The depth to the top, or bottom, and the density of a 3-D homogeneous source can be estimated from its gravity or magnetic anomalies by using a priori information on the maximum and minimum source depths. For the magnetic case, the magnetization direction is assumed to be constant and known. The source is assumed to be within a layer of known depth to the top h and thickness t. A depth model, satisfying both the data and the a priori information is found, together with its associated density/magnetization contrast. The methodology first derives, from the measured data, a set of apparent densities [Formula: see text] (or magnetizations), which do not depend on the layer parameters h and t, but only on source thickness. A nonlinear system of equations based on [Formula: see text], with source thicknesses as unknowns, is constructed. To simplify the solution, a more practical system of equations is formed. Each equation depends on only one value of thickness. Solving for the thicknesses, taking into account the above a priori information, the source depth to the top (or to the bottom) is determined uniquely. Finally, the depth solutions allow a unit‐density gravity model to be computed, which is compared to the observed gravity to determine the density contrast. A similar procedure can be used for magnetic data. Tests on synthetic anomalies and on real data demonstrate the good performance of this method.

Reduction to the pole and transformations of scattered magnetic data using Newtonian equivalent sources

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. L67-L73 ◽  
Author(s):  
Fernando Guspí ◽  
Iván Novara
Keyword(s):  
Real Data ◽  
Computer Time ◽  
Magnetic Data ◽  
Newtonian Potential ◽  
Two Stage ◽  
Magnetization Direction ◽  
Magnetic Dipoles ◽  
Equivalent Source ◽  
Reduction To The Pole ◽  
Equivalent Sources

We have developed an equivalent-source method for performing reduction to the pole and related transforms from magnetic data measured on unevenly spaced stations at different elevations. The equivalent source is composed of points located vertically beneath the measurement stations, and their magnetic properties are chosen in such a way that the reduced-to-the-pole magnetic field generated by them is represented by an inverse-distance Newtonian potential. This function, which attenuates slowly with distance, provides better coverage for discrete data points. The magnetization intensity is determined iteratively until the observed field is fitted within a certain tolerance related to the level of noise; thus, advantages in computer time are gained over the resolution of large systems of equations. In the case of induced magnetization, the iteration converges well for verticalor horizontal inclinations, and results are stable if noise is taken into account properly. However, for a range of intermediate inclinations near 35°, a factor tending to zero makes it necessary to perform the reduction through a two-stage procedure, using an auxiliary magnetization direction, without significantly affecting the speed and stability of the method. The performance of the procedure was tested on a synthetic example based on a field generated on randomly scattered stations by a random set of magnetic dipoles, contaminated with noise, which is reduced to the pole for three different magnetization directions. Results provide a good approximation to the theoretical reduced-to-the-pole field using a one- or a two-stage reduction, showing minor noise artifacts when the direction is nearly horizontal. In a geophysical example with real data, the reduction to the pole was used to correct the estimated magnetization direction that originates an isolated anomaly over Sierra de San Luis, Argentina.

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

2014 ◽  
Vol 644-650 ◽  
pp. 3459-3462 ◽  
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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