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.

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.

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.

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.

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.

A Bayesian framework for simultaneous determination of susceptibility and magnetic thickness from magnetic data

2021 ◽  
Author(s):  
Jörg Ebbing ◽  
Wolfgang Szwillus ◽  
Yixiati Dilixiati
Keyword(s):  
Heat Flow ◽  
Covariance Function ◽  
Thermal State ◽  
Synthetic Data ◽  
Magnetic Data ◽  
Spatial Behaviour ◽  
Flow Measurements ◽  
Space Domain ◽  
Curie Depth ◽  
Magnetic Inversion

<p>The thickness of the magnetized layer in the crust (or lithosphere) holds valuable information about the thermal state and composition of the lithosphere. Commonly, maps of magnetic thickness are estimated by spectral methods that are applied to individual data windows of the measured magnetic field strength. In each window, the measured power spectrum is fit by a theoretical function which depends on the average magnetic thickness in the window and a ‘fractal’ parameter describing the spatial roughness of the magnetic sources. The limitations of the spectral approach have long been recognized and magnetic thickness inversions are routinely calibrated using heat flow measurements, based on the assumption that magnetic thickness corresponds to Curie depth. However, magnetic spectral thickness determinations remain highly uncertain, underestimate uncertainties, do not properly integrate heat flow measurements into the inversion and fail to address the inherent trade-off between lateral thickness and susceptibility variations.</p><p>We present a linearized Bayesian inversion that works in space domain and addresses many issues of previous depth determination approaches. The ‘fractal’ description used in the spectral approaches translates into a Matérn covariance function in space domain. We use a Matérn covariance function to describe both the spatial behaviour of susceptibility and magnetic thickness. In a first step, the parameters governing the spatial behaviour are estimated from magnetic data and heat flow data using a Bayesian formulation and the Monte-Carlo-Markov-Chain (MCMC) technique. The second step uses the ensemble of parameter solution from MCMC to generate an ensemble of susceptibility and thickness distributions, which are the main output of our approach.</p><p>The newly developed framework is applied to synthetic data at satellite height (300 km) covering an area of 6000 x 6000 km. These tests provide insight into the sensitivity of satellite magnetic data to susceptibility and thickness. Furthermore, they highlight that magnetic inversion benefits greatly from a tight integration of heat flow measurements into the inversion process.</p>

Apparent magnetization mapping in the presence of strong remanent magnetization: The space-domain inversion approach

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. J11-J24 ◽  
Author(s):  
Lianghui Guo ◽  
Lei Shi ◽  
Xiaohong Meng ◽  
Rui Gao ◽  
Zhaoxi Chen ◽  
...  
Keyword(s):  
Remanent Magnetization ◽  
North China ◽  
Magnetic Layer ◽  
Real Data ◽  
Magnetic Data ◽  
Magnetization Distribution ◽  
Cross Sectional ◽  
Space Domain ◽  
Uniform Magnetization ◽  
Domain Inversion

Apparent magnetization mapping is a technique to estimate magnetization distribution in the subsurface magnetic layer from the observed magnetic data, of benefit in identifying lithologic units and delineating magnetic geologic boundaries. The conventional approaches for apparent magnetization mapping usually neglect effects of remanence, resulting in large geologic deviation and the occurrence of negative magnetization when the magnetic layer contains strong remanent magnetization. We have developed a space-domain inversion approach for apparent magnetization mapping based on the amplitude of magnetic anomaly (AMA), the analytic signal (AS), and the normalized source strength (NSS) to reduce effects of remanent magnetization. The AMA, AS, and NSS are three common quantities insensitive or weakly sensitive to the remanence transformed from the magnetic total field anomaly or components. The magnetic layer underground is first divided into a regular grid of vertical rectangular prisms, each having a cross-sectional area of one grid square and a uniform magnetization. Then, an iterative algorithm is adopted to invert each quantity of the AMA, AS, and NSS to obtain an optimum value of magnetization of each prism in the magnetic layer. The inversion approach permits the top and bottom surfaces of the magnetic layer to be constant or variable in depth, and requires no prior information of magnetization directions. Our tests on the synthetic and real data from the metallic ores area in the southern margin of North China have proved the feasibility and robustness of the presented inversion approach. All of the AMA, AS, and NSS inversions produced nonnegative magnetization distribution in the magnetic layer. Also, the AS and NSS inversions produced a better resolution of magnetization distribution than that of the AMA.

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.

Method of determination of the text direction on the image with the use of convolutional neural network

2020 ◽  
pp. 96-99
Author(s):  
P.L. Nikolaev
Keyword(s):  
Neural Network ◽  
Convolutional Neural Network ◽  
Deep Neural Network ◽  
Binary Classification ◽  
Synthetic Data ◽  
Real Data ◽  
Method Of Determination ◽  
Classification Of Images

This article deals with method of binary classification of images with small text on them Classification is based on the fact that the text can have 2 directions – it can be positioned horizontally and read from left to right or it can be turned 180 degrees so the image must be rotated to read the sign. This type of text can be found on the covers of a variety of books, so in case of recognizing the covers, it is necessary first to determine the direction of the text before we will directly recognize it. The article suggests the development of a deep neural network for determination of the text position in the context of book covers recognizing. The results of training and testing of a convolutional neural network on synthetic data as well as the examples of the network functioning on the real data are presented.

scholarly journals G-Tric: generating three-way synthetic datasets with triclustering solutions

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
João Lobo ◽  
Rui Henriques ◽  
Sara C. Madeira
Keyword(s):  
State Of The Art ◽  
Synthetic Data ◽  
Ground Truth ◽  
Real Data ◽  
Three Dimensions ◽  
Additional Advantage ◽  
Urban Dynamics ◽  
Data Generator ◽  
Real World Datasets ◽  
Synthetic Datasets

Abstract Background Three-way data started to gain popularity due to their increasing capacity to describe inherently multivariate and temporal events, such as biological responses, social interactions along time, urban dynamics, or complex geophysical phenomena. Triclustering, subspace clustering of three-way data, enables the discovery of patterns corresponding to data subspaces (triclusters) with values correlated across the three dimensions (observations $$\times$$ × features $$\times$$ × contexts). With increasing number of algorithms being proposed, effectively comparing them with state-of-the-art algorithms is paramount. These comparisons are usually performed using real data, without a known ground-truth, thus limiting the assessments. In this context, we propose a synthetic data generator, G-Tric, allowing the creation of synthetic datasets with configurable properties and the possibility to plant triclusters. The generator is prepared to create datasets resembling real 3-way data from biomedical and social data domains, with the additional advantage of further providing the ground truth (triclustering solution) as output. Results G-Tric can replicate real-world datasets and create new ones that match researchers needs across several properties, including data type (numeric or symbolic), dimensions, and background distribution. Users can tune the patterns and structure that characterize the planted triclusters (subspaces) and how they interact (overlapping). Data quality can also be controlled, by defining the amount of missing, noise or errors. Furthermore, a benchmark of datasets resembling real data is made available, together with the corresponding triclustering solutions (planted triclusters) and generating parameters. Conclusions Triclustering evaluation using G-Tric provides the possibility to combine both intrinsic and extrinsic metrics to compare solutions that produce more reliable analyses. A set of predefined datasets, mimicking widely used three-way data and exploring crucial properties was generated and made available, highlighting G-Tric’s potential to advance triclustering state-of-the-art by easing the process of evaluating the quality of new triclustering approaches.

Single Depth View Based Real-Time Reconstruction of Hand-Object Interactions

2021 ◽  
Vol 40 (3) ◽  
pp. 1-12
Author(s):  
Hao Zhang ◽  
Yuxiao Zhou ◽  
Yifei Tian ◽  
Jun-Hai Yong ◽  
Feng Xu
Keyword(s):  
Real Time ◽  
Synthetic Data ◽  
Real Data ◽  
Depth Image ◽  
Real Time System ◽  
The Real ◽  
Time Performance ◽  
Contact Constraint ◽  
Object Shapes ◽  
Object Interactions

Reconstructing hand-object interactions is a challenging task due to strong occlusions and complex motions. This article proposes a real-time system that uses a single depth stream to simultaneously reconstruct hand poses, object shape, and rigid/non-rigid motions. To achieve this, we first train a joint learning network to segment the hand and object in a depth image, and to predict the 3D keypoints of the hand. With most layers shared by the two tasks, computation cost is saved for the real-time performance. A hybrid dataset is constructed here to train the network with real data (to learn real-world distributions) and synthetic data (to cover variations of objects, motions, and viewpoints). Next, the depth of the two targets and the keypoints are used in a uniform optimization to reconstruct the interacting motions. Benefitting from a novel tangential contact constraint, the system not only solves the remaining ambiguities but also keeps the real-time performance. Experiments show that our system handles different hand and object shapes, various interactive motions, and moving cameras.

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