A 3D total magnetization inversion applicable when significant, complicated remanence is present

Geophysics ◽  
2009 ◽  
Vol 74 (3) ◽  
pp. L21-L30 ◽  
Author(s):  
Peter G. Lelièvre ◽  
Douglas W. Oldenburg
Keyword(s):  
Magnetization Vector ◽  
Real Data ◽  
Magnetic Data ◽  
Bound Constraints ◽  
Magnetization Direction ◽  
Total Magnetization ◽  
Additional Information ◽  
Available Information ◽  
Nonlinear Objective Function ◽  
Component Parallel

Inversion of magnetic data is complicated by the presence of remanent magnetization. To deal with this problem, we invert magnetic data for a three-component subsurface magnetization vector, as opposed to magnetic susceptibility (a scalar). The magnetization vector can be cast in a Cartesian or spherical framework. In the Cartesian formulation, the total magnetization is split into one component parallel and two components perpendicular to the earth’s field. In the spherical formulation, we invert for magnetization amplitude and the dip and azimuth of the magnetization direction. Our inversion schemes contain flexibility to obtain different types of magnetization models and allow for inclusion of geologic information regarding remanence. Allowing a vector magnetization increases the nonuniqueness of the magnetic inverse problem greatly, but additional information (e.g., knowledge of physical properties or geology) incorporated as constraints can improve the results dramatically. Commonly available information results in complicated nonlinear constraints in the Cartesian formulation. However, moving to a spherical formulation results in simple bound constraints at the expense of a now nonlinear objective function. We test our methods using synthetic and real data from scenarios involving complicated remanence (i.e., many magnetized bodies with many magnetization directions). All tests provide favorable results and our methods compare well against those of other authors.

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 magnetic anomaly on rugged observation surface in the presence of strong remanent magnetization

Geophysics ◽  
2014 ◽  
Vol 79 (2) ◽  
pp. J11-J19 ◽  
Author(s):  
Shu-Ling Li ◽  
Yaoguo Li
Keyword(s):  
Remanent Magnetization ◽  
Country Rock ◽  
Magnetization Vector ◽  
Magnetic Data ◽  
Magnetization Direction ◽  
Equivalent Source ◽  
Total Magnetization ◽  
Amplitude Inversion ◽  
Amplitude Data ◽  
And Inversion

We study the inversion of magnetic data acquired over a rugged observation surface and where the buried source bodies have strong remanent magnetization that leads to unknown total magnetization directions. These factors pose significant challenges for processing and inversion of such data. To tackle the challenges from both a rugged observation surface and an unknown magnetization direction, we propose a strategy through the joint use of the equivalent source technique and 3D amplitude inversion to obtain 3D magnetization strength. We use equivalent source processing to calculate the amplitude data in the space domain because the use of the wavenumber-domain method is invalid due to large variations in the data elevation. We then carried out an amplitude inversion to generate a 3D subsurface distribution of the magnitude of the total magnetization vector. The results from a synthetic example and aeromagnetic data in Daye Mine in China showed that this approach is effective and images the magnetic units whose contact zones with the limestone country rock host the mineralization. The method is general and can be applied to a variety of cases with similar challenges.

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.

Comprehensive approaches to 3D inversion of magnetic data affected by remanent magnetization

Geophysics ◽  
2010 ◽  
Vol 75 (1) ◽  
pp. L1-L11 ◽  
Author(s):  
Yaoguo Li ◽  
Sarah E. Shearer ◽  
Matthew M. Haney ◽  
Neal Dannemiller
Keyword(s):  
Mineral Exploration ◽  
Three Dimensional ◽  
Canadian Arctic ◽  
Magnetization Vector ◽  
Magnetic Data ◽  
Inversion Algorithm ◽  
3D Inversion ◽  
Magnetization Direction ◽  
Direct Inversion ◽  
Amplitude Data

Three-dimensional (3D) inversion of magnetic data to recover a distribution of magnetic susceptibility has been successfully used for mineral exploration during the last decade. However, the unknown direction of magnetization has limited the use of this technique when significant remanence is present. We have developed a comprehensive methodology for solving this problem by examining two classes of approaches and have formulated a suite of methods of practical utility. The first class focuses on estimating total magnetization direction and then incorporating the resultant direction into an inversion algorithm that assumes a known direction. The second class focuses on direct inversion of the amplitude of the magnetic anomaly vector. Amplitude data depend weakly upon magnetization direction and are amenable to direct inversion for the magnitude of magnetization vector in 3D subsurface. Two sets of high-resolution aeromagnetic data acquired for diamond exploration in the Canadian Arctic are used to illustrate the methods’ usefulness.

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.

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.

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

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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