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.

Interactive 2D magnetic inversion: A tool for aiding forward modeling and testing geologic hypotheses

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. L43-L50 ◽  
Author(s):  
Valeria C. Barbosa ◽  
João B. Silva
Keyword(s):  
Complex Geometry ◽  
Synthetic Data ◽  
Magnetization Vector ◽  
Real Data ◽  
Forward Modeling ◽  
Data Fitting ◽  
Magnetic Data ◽  
Magnetization Distribution ◽  
Magnetic Inversion ◽  
Geometric Elements

We present a method for inverting magnetic data with interfering anomalies produced by multiple complex 2D magnetic sources having arbitrary shapes and known magnetization vectors. Our method is stable and can recover a complex 2D magnetization distribution, leading to a reliable delineation of sectionally homogeneous sources with complex shapes. Our method, although similar to interactive forward modeling, is unique in that it automatically fits the observations and only requires that the interpreter know the outlines of the sources expressed by simple geometric elements such as points and line segments. Each geometric element operates as a skeletal outline of a particular homogeneous section of the magnetic source to be reconstructed. Also, the interpreter can define the geometric elements interactively without worrying about data fitting because data are fit automatically. The examples with synthetic data illustrate the good performance of the method in mapping the complex geometry of magnetic sources. The solution sensitivity to uncertainties in the a priori information shows that to produce good results, the uncertainty on the magnetization intensity of each homogeneous extent of the source should be smaller than 40%. A wrong magnetization vector direction can be detected easily because it often leads to poor data fitting and to estimated sources with abrupt borders. The method is also applied to two sets of real data from the Northwest Ore Body at Iron Mountain Mine, Missouri, and the Hatton-Rockall Basin in the northeast Atlantic Ocean. The estimated magnetization distribution in all tests demonstrates a good correlation of estimated magnetic sources with corresponding known geologic features.

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.

Assessing and ameliorating edge effects in magnetic data transformations

2020 ◽  
Author(s):  
Peter Lelièvre ◽  
Dominique Fournier ◽  
Sean Walker ◽  
Nicholas Williams ◽  
Colin Farquharson
Keyword(s):  
Edge Effects ◽  
Mineral Exploration ◽  
Magnetization Vector ◽  
Magnetic Data ◽  
Separation Procedure ◽  
Magnetic Intensity ◽  
Source Inversion ◽  
Total Field ◽  
Equivalent Source ◽  
Amplitude Data

<p>Reduction to pole and other transformations of total field magnetic intensity data are often challenging to perform at low magnetic latitudes, when remanence exists, and when large topographic relief exists. Several studies have suggested use of inversion-based equivalent source methods for performing such transformations under those complicating factors. However, there has been little assessment of the importance of erroneous edge effects that occur when fundamental assumptions underlying the transformation procedures are broken. In this work we propose a transformation procedure that utilizes magnetization vector inversion, inversion-based regional field separation, and equivalent source inversion on unstructured meshes. We investigated whether edge effects in transformations could be reduced by performing a regional separation procedure prior to equivalent source inversion. We applied our proposed procedure to the transformation of total field magnetic intensity to magnetic amplitude data, using a complicated synthetic example based on a real geological scenario from mineral exploration. While the procedure performed acceptably on this test example, the results could be improved. We pose many questions regarding the various choices and control parameters used throughout the procedure, but we leave the investigation of those questions to future work.</p>

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.

Separation of regional and residual magnetic field data

Geophysics ◽  
1998 ◽  
Vol 63 (2) ◽  
pp. 431-439 ◽  
Author(s):  
Yaoguo Li ◽  
Douglas W. Oldenburg
Keyword(s):  
Magnetic Field ◽  
Field Data ◽  
Power Spectra ◽  
Magnetic Data ◽  
Inversion Algorithm ◽  
Large Area ◽  
Data Set ◽  
Regional Sources ◽  
Magnetic Inversion ◽  
Susceptibility Model

We present a method for separating regional and residual magnetic fields using a 3-D magnetic inversion algorithm. The separation is achieved by inverting the observed magnetic data from a large area to construct a regional susceptibility distribution. The magnetic field produced by the regional susceptibility model is then used as the regional field, and the residual data are obtained by simple subtraction. The advantages of this method of separation are that it introduces little distortion to the shape of the extracted anomaly and that it is not affected significantly by factors such as topography and the overlap of power spectra of regional and residual fields. The proposed method is tested using a synthetic example having varying relative positions between the local and regional sources and then using a field data set from Australia. Results show that the residual field extracted using this method enables good recovery of target susceptibility distribution from inversions.

Magnetic vector inversion using  XYZ measured by fluxgate magnetometer in UAV 

2021 ◽  
Author(s):  
Arto Karinen
Keyword(s):  
Magnetic Field ◽  
Remanent Magnetization ◽  
Magnetization Vector ◽  
Field Direction ◽  
Magnetic Data ◽  
Total Field ◽  
Main Field ◽  
Vector Inversion ◽  
The Magnetic Field ◽  
Measured Magnetic Field

<p>Traditionally, the inversion of magnetic data assumes the magnetization of the local geology to run parallel to the Earth’s internal magnetic field that is usually modelled using International Geomagnetic Reference Field (IGRF). Assuming the magnetization parallel to the main field, only the total (scalar) magnetic data are the sufficient input for the inversion of source susceptibility.</p><p>Local magnetization may alter from the main field direction in areas of remanent magnetization. Recently, magnetization vector inversion (MVI) using the total field has become an important tool trying to distinguish magnetic data affected by remanenence. Total field as a scalar field exclude all information of the direction of the internal magnetization and more information is required to reveal any remanent magnetization from the main field direction.  Compared to total field using the 3-component XYZ vector magnetic measurements provide more information of the source.  More measurements increase the unambiguous nature of data and may reveal the areas of possible remanence. </p><p>To measure XYZ vector magnetic field we use fluxgate 3-component magnetometer with rigid installation on a fixed-wing UAV. With the help of accurate inertial measurement units the measured magnetic field can be determined in the direction of fixed coordinate system. The components of the measured magnetic field rotated into the geographical coordinate represent the magnetic field at survey area.</p><p>UAV survey provided the data as the input for the inversions. We made the inversion separately for both susceptibility and magnetization vector. Susceptibility inversion means inversion of induced magnetization, i.e., a single component of magnetization parallel to the main field direction. Magnetization vector inversion, however, resolves all three components of magnetization, which may or may not include remanent magnetization in addition to induced one.</p><p>The benefits from utilizing XYZ components of the magnetic field with magnetization inversion seem promising in finding remanenence magnetization.</p><p> </p><p> </p>

Adaptive sampling of potential-field data: A direct approach to compressive inversion

Geophysics ◽  
2014 ◽  
Vol 79 (1) ◽  
pp. IM1-IM9 ◽  
Author(s):  
Nathan Leon Foks ◽  
Richard Krahenbuhl ◽  
Yaoguo Li
Keyword(s):  
Potential Field ◽  
Adaptive Sampling ◽  
Field Data ◽  
Computational Cost ◽  
Large Field ◽  
Magnetic Data ◽  
Data Sampling ◽  
Data Types ◽  
Data Set ◽  
Potential Field Data

Compressive inversion uses computational algorithms that decrease the time and storage needs of a traditional inverse problem. Most compression approaches focus on the model domain, and very few, other than traditional downsampling focus on the data domain for potential-field applications. To further the compression in the data domain, a direct and practical approach to the adaptive downsampling of potential-field data for large inversion problems has been developed. The approach is formulated to significantly reduce the quantity of data in relatively smooth or quiet regions of the data set, while preserving the signal anomalies that contain the relevant target information. Two major benefits arise from this form of compressive inversion. First, because the approach compresses the problem in the data domain, it can be applied immediately without the addition of, or modification to, existing inversion software. Second, as most industry software use some form of model or sensitivity compression, the addition of this adaptive data sampling creates a complete compressive inversion methodology whereby the reduction of computational cost is achieved simultaneously in the model and data domains. We applied the method to a synthetic magnetic data set and two large field magnetic data sets; however, the method is also applicable to other data types. Our results showed that the relevant model information is maintained after inversion despite using 1%–5% of the data.

Computer Application in Geosciences: Imaging of the Subsurface by Structural Coupled Inversion of Potential Field Data

2014 ◽  
Vol 644-650 ◽  
pp. 2670-2673
Author(s):  
Jun Wang ◽  
Xiao Hong Meng ◽  
Fang Li ◽  
Jun Jie Zhou
Keyword(s):  
Potential Field ◽  
Field Data ◽  
Gravity Data ◽  
Computer Application ◽  
Magnetic Data ◽  
Imaging Method ◽  
Inversion Algorithm ◽  
Constant Property ◽  
Near Surface ◽  
Potential Field Data

With the continuing growth in influence of near surface geophysics, the research of the subsurface structure is of great significance. Geophysical imaging is one of the efficient computer tools that can be applied. This paper utilize the inversion of potential field data to do the subsurface imaging. Here, gravity data and magnetic data are inverted together with structural coupled inversion algorithm. The subspace (model space) is divided into a set of rectangular cells by an orthogonal 2D mesh and assume a constant property (density and magnetic susceptibility) value within each cell. The inversion matrix equation is solved as an unconstrained optimization problem with conjugate gradient method (CG). This imaging method is applied to synthetic data for typical models of gravity and magnetic anomalies and is tested on field data.

ESTIMATION OF SOURCE PARAMETERS IN IBADAN, SOUTH – WESTERN NIGERIA USING DIGITIZED AEROMAGNETIC DATA

2018 ◽  
Vol 14 (2) ◽  
pp. 15-28
Author(s):  
A A ALABI ◽  
O OLOWOFELA
Keyword(s):  
Magnetic Susceptibility ◽  
Source Parameters ◽  
Granite Gneiss ◽  
Geological Structure ◽  
Magnetic Data ◽  
Susceptibility Map ◽  
Rock Types ◽  
Upward Continuation ◽  
Magnetic Basement ◽  
Local Wavenumber

Airborne magnetic data covering geographical latitudes of 7000‟N to 7030‟N and longitudes of 3 30′E to 4 00′E within Ibadan area were obtained from Nigeria Geology Survey Agency. The data were ana-lyzed to map the sub surface structure and the source parameters were deduced from the quantitative and qualitative interpretation of magnetic data. The upward continuation technique was used to de-emphasize short – wavelength anomaly while the depth to magnetic sources in the area was deter-mined using local wavenumber technique, the analytic signal was also employed to obtain the depths of the magnetic basement. Analysis involving the local wavenumber, upward continuation and appar-ent magnetic susceptibility techniques significantly improves the interpretation of magnetic data in terms of delineating the geological structure, source parameter and magnetic susceptibility within Iba-dan area.. These depth ranges from 0.607km to 2.48km. The apparent susceptibility map at the cut-off wavelength of 50 m ranges from -0.00012 to 0.00079 which agree with the susceptibility value of some rock types; granite gneiss, migmatite biotite gneiss, biotite muscovite granite, hornblende granite, quartz and schists. The result of the local wavenumber suggests variation along the profiles in the surface of magnetic basement across the study area.

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