Three-dimensional numerical modeling of gravity anomalies based on Poisson equation in space-wavenumber mixed domain

Dai, Shaotao; Zhao, Dongdong; Zhang, Qian-Jiang; Li, Kun; Chen, Qing-Rui; Wang, Xulong

doi:10.1007/s11770-018-0702-9

Cited by 12 publications

(6 citation statements)

References 25 publications

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“…In this section, the proposed 2D AS-FT algorithm is applied to the 3D space-wavenumber domain numerical simulation of weak and strong magnetic fields in exploration geophysics to test the adaptability and efficiency of the AS-FT algorithm [33,34,37].…”

Section: Resultsmentioning

confidence: 99%

“…Based on the 3D numerical simulation algorithm of a magnetic anomaly in the spacewavenumber domain [37], the model was designed and simulated by the standard-FFT, Gauss-FFT [24], and AS-FT method proposed in this paper.…”

Section: Efficiency Comparison Of Different Fourier Transform Methodsmentioning

confidence: 99%

“…The modeling theory of magnetic fields in the space-wavenumber domain reduces the 3D partial differential equation satisfied by the magnetic potential to a 1D ordinary differential equation independent of different wavenumbers by performing a 2D Fourier transform in the horizontal direction that reduces the amount of calculation and storage requirements. The vertical direction is reserved as the spatial domain, and the density of the elements can be adjusted according to the actual situation, which can consider the calculation accuracy and efficiency [37].…”

Section: Theory Of Magnetic Field Modeling In Space-wavenumber Domainmentioning

confidence: 99%

“…It should be pointed out that when the magnetic susceptibility of the abnormal body is less than 0.01 SI, it is a weak magnetic situation, and the abnormal field H a can be ignored. The literature [37] analyzes the numerical simulation algorithm of the weak magnetic field in the space-wavenumber domain based on Gauss-FFT and the standard expanded FFT method, which will not be repeated here. The weak magnetic field can be obtained by directly solving Equation (25).…”

Section: Theory Of Magnetic Field Modeling In Space-wavenumber Domainmentioning

confidence: 99%

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Arbitrary Sampling Fourier Transform and Its Applications in Magnetic Field Forward Modeling

Dai

Zhang

et al. 2022

Applied Sciences

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Numerical simulation and inversion imaging are essential in geophysics exploration. Fourier transform plays a vital role in geophysical numerical simulation and inversion imaging, especially in solving partial differential equations. This paper proposes an arbitrary sampling Fourier transform algorithm (AS-FT) based on quadratic interpolation of shape function. Its core idea is to discretize the Fourier transform integral into the sum of finite element integrals. The quadratic shape function represents the function change in each element, and then all element integrals are calculated and accumulated. In this way, the semi-analytical solution of the Fourier oscillation operator in each integral interval can be obtained, and the Fourier transform coefficient can be calculated in advance, so the algorithm has high calculation accuracy and efficiency. Based on the one-dimensional (1D) transform, the two-dimensional (2D) transform is realized by integrating the 1D Fourier transform twice, and the three-dimensional (3D) transform is realized by integrating the 1D Fourier transform three times. The algorithm can sample flexibly according to the distribution of integrated values. The correctness and efficiency of the algorithm are verified by Fourier transform pairs. The AS-FT algorithm is applied to the numerical simulation of magnetic anomalies. The accuracy and efficiency are compared with the standard Fast Fourier transform (standard-FFT) and Gauss Fast Fourier transform (Gauss-FFT). It shows that the AS-FT algorithm has no edge effects and has a higher computational speed. The AS-FT algorithm has good adaptability to continuous medium, weak magnetic catastrophe medium, and strong magnetic catastrophe medium. It can achieve the same as or even higher accuracy than Gauss-FFT through fewer sampling points. The AS-FT algorithm provides a new means for partial differential equation solution in geophysics. It successfully solves the boundary problems, which makes it an efficient and high-precision Fourier transform approach with promising applications. Therefore, the AS-FT algorithm has excellent advantages in solving partial differential equations, providing a new means for solving geophysical forward and inverse problems.

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Section: Resultsmentioning

confidence: 99%

Section: Efficiency Comparison Of Different Fourier Transform Methodsmentioning

confidence: 99%

Section: Theory Of Magnetic Field Modeling In Space-wavenumber Domainmentioning

confidence: 99%

Section: Theory Of Magnetic Field Modeling In Space-wavenumber Domainmentioning

confidence: 99%

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Arbitrary Sampling Fourier Transform and Its Applications in Magnetic Field Forward Modeling

Dai

Zhang

et al. 2022

Applied Sciences

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“…Li et al (2018) presented a solution for the 2D FFT magnetic field 𝐵 𝑧 (𝑢, 𝑣, 𝑧) for a prism to calculate the field in three dimensions by a one-dimensional (1D) vertical integration over 𝑧. Dai et al (2019) developed a solution for the 2D FFT gravity and magnetic potentials by implementing a 1D vertical integration over 𝑧 of the differential Poisson equation. Here in particular, the solution of these differential equations for the gravity and magnetic cases is formulated with the finite element method based on a quadratic shape function and applied to solve the 1D ordinary differential equation.…”

Section: Introductionmentioning

confidence: 99%

2D fast Fourier transform analytical solutions in all space for all gravity and magnetic components

Boulanger

2023

Geophysical Prospecting

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Forward modeling of potential field data is an important part of optimization algorithms used to invert large datasets such as those involving rugged terrain or borehole data. 2D fast Fourier transform (FFT) modeling with a prism or a dipole is one of the most efficient methods compared to the forward modeling in the space domain. However the exact solution of a prismatic source is limited to the case of a half‐space with the computation of data on a horizontal datum above the topography. Starting from the 3D Fourier forward modeling analytical formulation for a prism, an integration according to the wavenumber w is accomplished which allowed to find a 2D Fourier exact analytical formulation outside, at the interfaces of, and inside a prism for all potential field components. This new formulation requires the calculation of only four integrals. The gravity and magnetic fields are computed with this 2D FFT formulation in the entire domain, and compared with the analytical space domain and the 3D FFT formulations. From the 3D calculated field, each component can be interpolated with the tri‐linear interpolation method along a borehole or on a drape surface simulating an airborne survey. Based on experiments demonstrated in this work, the 2D formulation in the Fourier domain gave accurate results with greater speed of execution in comparison to modeling in the space domain. The forward modelling method is tested on real gravity data from the north of Alberta (Canada).This article is protected by copyright. All rights reserved

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Development of an infinite element boundary to model gravity for subsurface civil engineering applications

Haji

Faramarzi

Metje

et al. 2019

Num Anal Meth Geomechanics

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The accurate modelling of gravity is of crucial importance for a variety of issues including, but not restricted to, the identification of buried objects. Gravity is an unbounded problem, which causes challenges when applying numerical models, i..e.., it results in computational difficulties when specifying the relevant boundary conditions. In order to address this, previous research has tended to generate artificial boundary conditions, e.g., truncating the simulated domain and adding many unrealistic zero-density layers, which introduces more unknown parameters and unnecessarily excessive computational time. In order to overcome such inaccuracies, this paper proposes an innovative development of the finite element modelling technique, which represents a step change in the field of gravity forward modelling. A comprehensive formulation of an infinite element to reproduce the far-field boundary effect using only one layer of infinite elements is presented. The developed model considerably reduces the computational time while obtaining high degrees of accuracy. The model is validated against the exact solution of the problem, and its results show an excellent performance. The proposed method can significantly improve the postprocessing and interpretation stages of data analysis relevant to micro-gravity sensors. The new method is applied to subsurface civil engineering although its applicability is manifold.

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Three-dimensional numerical modeling of gravity anomalies based on Poisson equation in space-wavenumber mixed domain

Cited by 12 publications

References 25 publications

Arbitrary Sampling Fourier Transform and Its Applications in Magnetic Field Forward Modeling

Arbitrary Sampling Fourier Transform and Its Applications in Magnetic Field Forward Modeling

2D fast Fourier transform analytical solutions in all space for all gravity and magnetic components

Development of an infinite element boundary to model gravity for subsurface civil engineering applications

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