Fast numerical simulation of 2D gravity anomaly based on nonuniform fast Fourier transform in mixed space-wavenumber domain

Wang, Xulong; Liu, Jianxin; Dai, Shaotao; Guo, Ren; Li, Jian; Fan, Pingyang

doi:10.1016/j.jappgeo.2021.104465

Cited by 5 publications

(2 citation statements)

References 48 publications

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“…The efficiency is not dominant for the algorithm that needs iteration [29]. Wang et al applied the NUFFT algorithm based on Gaussian interpolation to 2D gravity numerical simulation and achieved good results [30]. Ouyang et al applied non-uniform Fourier transform to seismic wave field forward modeling and it performed well [31].…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

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

Dai

Zhang

et al. 2022

Applied Sciences

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“…Another method to evaluate the convolution integrals is transformed into the Fourier domain. Many researchers have considered fast computation of integral kernel, including the calculation of the integral in the Fourier domain [17][18][19][20] and by discretization of the operator and calculation in the space domain [21][22][23][24][25] . Then, Li et al 17 and Dai et al 18 developed the space-wavenumber domain method based on 2D Gauss-FFT 26 to calculate gravity and magnetic anomalies.…”

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confidence: 99%

Fast 3D gravity and magnetic modelling using midpoint quadrature and 2D FFT

Wang¹,

Liu²,

Li³

et al. 2023

Sci Rep

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To avoid the problem of the traditional methods consuming large computational resources to calculate the kernel matrix and 2D discrete convolution, we present a novel approach for 3D gravity and magnetic modelling. This method combines the midpoint quadrature method with a 2D fast Fourier transform (FFT) to calculate the gravity and magnetic anomalies with arbitrary density or magnetic susceptibility distribution. In this scheme, we apply the midpoint quadrature method to calculate the volume element of the integral. Then, the convolution of the weight coefficient matrix with density or magnetization is efficiently computed via the 2D FFT. Finally, the accuracy and efficiency of the proposed algorithm are validated by using an artificial model and a real topography model. The numerical results demonstrate that the proposed algorithm’s computation time and the memory requirement are decreased by approximately two orders of magnitude compared with the space-wavenumber domain method.

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Dynamic damage identification of tunnel portal and verification via shaking table test

Wang

Geng

et al. 2023

Tunnelling and Underground Space Technology

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Fast numerical simulation of 2D gravity anomaly based on nonuniform fast Fourier transform in mixed space-wavenumber domain

Cited by 5 publications

References 48 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

Fast 3D gravity and magnetic modelling using midpoint quadrature and 2D FFT

Dynamic damage identification of tunnel portal and verification via shaking table test

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