scholarly journals 3D magnetic inversion in highly magnetic environments using an octree mesh discretization

2012 ◽  
Vol 2012 (1) ◽  
pp. 1-4 ◽  
Author(s):  
Kristofer Davis ◽  
Douglas W. Oldenburg
Keyword(s):  
Magnetic Inversion ◽  
Octree Mesh

scholarly journals Chaos on the hypercube

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Yiyang Jia ◽  
Jacobus J. M. Verbaarschot
Keyword(s):  
Magnetic Flux ◽  
Spectral Density ◽  
Hermite Polynomials ◽  
Weighted Sums ◽  
Majorana Fermions ◽  
Chord Diagrams ◽  
Magnetic Inversion ◽  
Constant Magnitude ◽  
Kitaev Model ◽  
Spectral Statistics

Abstract We analyze the spectral properties of a d-dimensional HyperCubic (HC) lattice model originally introduced by Parisi. The U(1) gauge links of this model give rise to a magnetic flux of constant magnitude ϕ but random orientation through the faces of the hypercube. The HC model, which also can be written as a model of 2d interacting Majorana fermions, has a spectral flow that is reminiscent of Maldacena-Qi (MQ) model, and its spectrum at ϕ = 0, actually coincides with the coupling term of the MQ model. As was already shown by Parisi, at leading order in 1/d, the spectral density of this model is given by the density function of the Q-Hermite polynomials, which is also the spectral density of the double-scaled Sachdev-Ye-Kitaev model. Parisi demonstrated this by mapping the moments of the HC model to Q-weighted sums on chord diagrams. We point out that the subleading moments of the HC model can also be mapped to weighted sums on chord diagrams, in a manner that descends from the leading moments. The HC model has a magnetic inversion symmetry that depends on both the magnitude and the orientation of the magnetic flux through the faces of the hypercube. The spectrum for fixed quantum number of this symmetry exhibits a transition from regular spectra at ϕ = 0 to chaotic spectra with spectral statistics given by the Gaussian Unitary Ensembles (GUE) for larger values of ϕ. For small magnetic flux, the ground state is gapped and is close to a Thermofield Double (TFD) state.

Magnetic inversion to recover the subsurface block structures based on L1 norm and total variation regularization

2021 ◽  
Author(s):  
Mitsuru Utsugi
Keyword(s):  
Total Variation ◽  
Magnetic Data ◽  
Preconditioned Conjugate Gradient ◽  
Inversion Method ◽  
Total Variation Regularization ◽  
Subsurface Structure ◽  
L1 Norm ◽  
Magnetic Inversion ◽  
Original Definition ◽  
Primal Dual

Summary This paper presents a new sparse inversion method based on L1 norm regularization for 3D magnetic data. In isolation, L1 norm regularization yields model elements which are unconstrained by the input data to be exactly zero, leading to a sparse model with compact and focused structure. Here, we complement the L1 norm with a penalty minimizing total variation, the L1 norm of the model gradients; it is expected that the sharp boundaries of the subsurface structure are not compromised by incorporating this penalty. Although this penalty is widely used in the geophysical inversion studies, it is often replaced by an alternative quadratic penalty to ease solution of the penalized inversion problem; in this study, the original definition of the total variation, i.e., form of the L1 norm of the model gradients, is used. To solve the problem with this combined penalty of L1 norm and total variation, this study introduces alternative direction method of multipliers (ADMM), which is a primal-dual optimization algorithm that solves convex penalized problems based on the optimization of an augmented Lagrange function. To improve the computational efficiency of the algorithm to make this method applicable to large-scale magnetic inverse problems, this study applies matrix compression using the wavelet transform and the preconditioned conjugate gradient method. The inversion method is applied to both synthetic tests and real data, the synthetic tests demonstrate that, when subsurface structure is blocky, it can be reproduced almost perfectly.

Inversion of airborne geophysics over the DO-27/DO-18 kimberlites — Part 1: Potential fields

2017 ◽  
Vol 5 (3) ◽  
pp. T299-T311 ◽  
Author(s):  
Sarah G. R. Devriese ◽  
Kristofer Davis ◽  
Douglas W. Oldenburg
Keyword(s):  
Magnetic Data ◽  
Gravity Gradiometry ◽  
3D Inversion ◽  
Potential Field Data ◽  
Electromagnetic Data ◽  
Magnetic Inversion ◽  
Geophysical Surveys ◽  
Airborne Geophysics ◽  
Joint Interpretation ◽  
Geologic Model

The Tli Kwi Cho (TKC) kimberlite complex contains two pipes, called DO-27 and DO-18, which were discovered during the Canadian diamond exploration rush in the 1990s. The complex has been used as a testbed for ground and airborne geophysics, and an abundance of data currently exist over the area. We have evaluated the historical and geologic background of the complex, the physical properties of interest for kimberlite exploration, and the geophysical surveys. We have carried out 3D inversion and joint interpretation of the potential field data. The magnetic data indicate high susceptibility at DO-18, and the magnetic inversion maps the horizontal extent of the pipe. DO-27 is more complicated. The northern part is highly magnetic and is contaminated with remanent magnetization; other parts of DO-27 have a low susceptibility. Low densities, obtained from the gravity and gravity gradiometry data, map the horizontal extents of DO-27 and DO-18. We combine the 3D density contrast and susceptibility models into a single geologic model that identifies three distinct kimberlite rock units that agree with drilling data. In further research, our density and magnetic susceptibility models are combined with information from electromagnetic data to provide a multigeophysical interpretation of the TKC kimberlite complex.

The Implementation of Visualization Software of the Rapid 3D Apparent Physical Properties Inversion Method

2013 ◽  
Vol 734-737 ◽  
pp. 3026-3029
Author(s):  
Hai Xia Li ◽  
Hai Long Yu ◽  
Ping Chuan Zhang
Keyword(s):  
Physical Properties ◽  
Potential Field ◽  
Implementation Process ◽  
Inversion Method ◽  
Main Function ◽  
Dynamic Link Library ◽  
Software Interface ◽  
Visualization Software ◽  
Magnetic Inversion ◽  
Key Techniques

The main function of the application software of the rapid inversion method of 3D apparent physical properties, and the key techniques used to achieve software are described in this paper. The core modules of the software is apparent physical properties inversion which can achieve the 3D apparent density and the 3D apparent magnetic inversion calculation, in addition, the software provides data preprocessing, reduction to the pole, the potential field continuation and potential field cut function. In software implementation process, first, compiling the calculation program modules by Fortran90 language, and then combining with dynamic link library, multi-threading and Surfer automated call technology, we compiled the visualization software interface to realize the function of the new method by C, C + + language, under the C + + Builder6.0 environment.

3-D magnetic inversion and satellite imagery for the Um Salatit gold occurrence, Central Eastern Desert, Egypt

2018 ◽  
Vol 11 (21) ◽  
Author(s):  
Hassan Mohamed ◽  
Hakim Saibi ◽  
Mohand Bersi ◽  
Sami Abdelnabi ◽  
Baher Geith ◽  
...  
Keyword(s):  
Satellite Imagery ◽  
Eastern Desert ◽  
Central Eastern Desert ◽  
Gold Occurrence ◽  
Magnetic Inversion ◽  
Central Eastern

Radial magnetic inversion to retrieve the geometry of 3D sources

2019 ◽  
Author(s):  
Leonardo B. Vital ◽  
Vanderlei C. Oliveira ◽  
Valéria C. F. Barbosa
Keyword(s):  
Magnetic Inversion

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.

Inversion of magnetic and frequency-domain electromagnetic data for investigating lithologies associated with gold mineralization in the Canadian Malartic area, Québec, Canada

2020 ◽  
pp. 1-20
Author(s):  
Mehrdad Darijani ◽  
Colin G. Farquharson
Keyword(s):  
Frequency Domain ◽  
Gold Mineralization ◽  
Volcanic Rocks ◽  
Tetrahedral Mesh ◽  
Iron Formation ◽  
Magnetic Data ◽  
Low Grade ◽  
Metasedimentary Rocks ◽  
Magnetic Inversion ◽  
Northern Edge

Canadian Malartic is an Archean low-grade bulk tonnage native gold deposit. The deposit is mostly located in altered clastic metasedimentary rocks, mafic–ultramafic dykes, and monzodioritic porphyry intrusions. Airborne magnetic and frequency-domain electromagnetic (EM) data were inverted to reconstruct the geological units associated with the mineralization, especially the intrusive masses. The 3-D inversion of magnetic data, which used a tetrahedral mesh to a depth of 2.4 km, shows that mafic volcanic rocks and iron formation rocks extend to depth in the area, more so than diabase dykes. The magnetic inversion also shows that the diorite and monzodiorite rocks of the Lac Fournière A pluton are dipping toward the south on its northern edge at the contact with the metasedimentary rocks. The 1-D inversion of the frequency-domain EM data, for both electrical conductivity and magnetic susceptibility, is able to reconstruct geological structures to a depth of approximately 100 m, providing more details and information about these features. The intrusive masses such as diabase dykes, diorite and monzodiorite rocks, and mafic volcanic rocks are reconstructed as electrically conductive structures in the inversion results. The metasedimentary rocks are resistive, and the overburden is conductive in most of the area. The geophysical data and inversion results suggest the presence of some features (such as diabase dykes and monzodiorite rocks) that are not yet present on some parts of the geology map. A comparison of the EM-derived susceptibility and the magnetic-derived susceptibility over the iron formations can reveal the effect of remanent magnetization.

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