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Three-dimensional modeling of magnetic anomaly integral solution in a mixed space-wavenumber domain

TitleThree-dimensional modeling of magnetic anomaly integral solution in a mixed space-wavenumber domain
Publication TypeJournal Article
Year of Publication2019
AuthorsLi K., Dai S.K, Chen Q.R, Zhang Q.J, Zhao D.D, Wang S.G, Ling J.X
Date Published2019/11
Type of ArticleArticle
ISBN Number0001-5733
Accession NumberWOS:000495446500028
Keywords3-d; bodies; computation; density; Fourier; Geochemistry & Geophysics; gradient; gravity; Magnetic anomaly 3D modeling; Mixed space-wavenumber domain; optimum expression; potential-field; prism; Shape function method; spectrum; transform

The paper presents a three-dimensional (3D) modeling method, engaged with a mixed space-wavenumber domain, for the magnetic anomaly field. Based on the fact that the 3D space domain integral for magnetic potential is convolution, the 3D integral problem of magnetic potential in space domain can be transformed into one dimensional (1D) integral problems in vertical direction independently to each other using the two-dimensional (2D) Fourier transform along the horizontal directions. By the proposed method, the depth direction is kept in space domain, which can provide two advantages in the modeling. Firstly, the shallow grid can be as fine as necessary for topography, however, with the increase of depth, the grid becomes coarse in order to reduce calculation cost. Thus, the calculation accuracy and efficiency in modeling can be guaranteed simultaneously. Secondly, the one-dimensional integral can be discretized into the sum of multiple element integrals along the depth direction. Each unit uses the second-order shape function to calculate the magnetization with the analytical expression of element integral. This method makes full use of 1D shape function for high accuracy, high parallelization among different wavenumbers, and fast Fourier transform to achieve high efficiency and high accuracy modeling of magnetic anomaly field. A prismatic model is designed to verify the correctness and high accuracy of the method by the comparison between the analytical solution and the numerical solution obtained by the proposed method. A complex model is designed to compare the accuracy and efficiency of the standard FFT expansion method and of the Gauss-FFT method. The strategy of edge selection for standard FFT method was also summarized based on the complex model. The paper presents a fast magnetic anomaly field calculation method and verify its validity in order to solve the problem of magnetic anomaly simulation under any complex terrain conditions.

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