2-D magnetotelluric modeling using finite element method incorporating unstructured quadrilateral elements

Sarakorn, Weerachai

doi:10.1016/j.jappgeo.2017.02.005

Cited by 11 publications

(9 citation statements)

References 13 publications

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“…Therefore, substituting Equations (13) and (14) into Equation (6), the difference equation for TE-mode can be written as…”

Section: Fd Representation For 2d Magnetotelluric Problemmentioning

confidence: 99%

“…The efficiency and accuracy of the FD method for modeling magnetotelluric responses were proven for the 2D geo-electric model [9,10]. The FE method is another numerical approach that is often used for 2D and 3D magnetotelluric modeling, which involves assumed functional forms for the model and fields in small regions of specified geometry [11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

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Finite Difference Algorithm on Non-Uniform Meshes for Modeling 2D Magnetotelluric Responses

2018

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A finite-difference approach with non-uniform meshes was presented for simulating magnetotelluric responses in 2D structures. We presented the calculation formula of this scheme from the boundary value problem of electric field and magnetic field, and compared finite-difference solutions with finite-element numerical results and analytical solutions of a 1D model. First, a homogeneous half-space model was tested and the finite-difference approach can provide very good accuracy for 2D magnetotelluric modeling. Then we compared them to the analytical solutions for the two-layered geo-electric model; the relative errors of the apparent resistivity and the impedance phase were both increased when the frequency was increased. To conclude, we compare our finite-difference simulation results with COMMEMI 2D-0 model with the finite-element solutions. Both results are in close agreement to each other. These comparisons can confirm the validity and reliability of our finite-difference algorithm. Moreover, a future project will extend the 2D structures to 3D, where non-uniform meshes should perform especially well.

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“…Therefore, substituting Equations (13) and (14) into Equation (6), the difference equation for TE-mode can be written as…”

Section: Fd Representation For 2d Magnetotelluric Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Finite Difference Algorithm on Non-Uniform Meshes for Modeling 2D Magnetotelluric Responses

2018

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“…Finite difference (FD) and finite element (FE) methods are mostly developed and applied as the main process of forward calculation for 2-D and 3-D inversions (Egbert and Kelbert 2012;Franke et al 2007;Key and Weiss 2006;Kordy et al 2016a, b;Lee et al 2009;Mackie et al 1993;Nam et al 2007;Ren et al 2013;Sarakorn 2017;Sharma and Kaikkonen 1998;Siripunvaraporn et al 2002;Usui 2015;Usui et al 2017Usui et al , 2018Wannamaker et al 1986Wannamaker et al , 1987. The FD method is accurate for simple modeling and, because of the limitation of the structured rectangular mesh, consumes less memory storage and computation time.…”

Section: Introductionmentioning

confidence: 99%

“…The FD method is accurate for simple modeling and, because of the limitation of the structured rectangular mesh, consumes less memory storage and computation time. The FE method is accurate for real-world complex modeling, especially topography and bathymetry, because of the greater flexibility of mesh schemes (Franke et al 2007;Grayver and Kolev 2015;Grayver 2015;Key and Weiss 2006;Kordy et al 2016a, b;Lee et al 2009;Nam et al 2007;Ren et al 2013;Sarakorn 2017;Sharma and Kaikkonen 1998;Usui 2015;Usui et al 2017Usui et al , 2018Wannamaker et al 1986Wannamaker et al , 1987. However, the disadvantages of FE are greater consumption of memory storage and longer computation time.…”

Section: Introductionmentioning

confidence: 99%

Hybrid finite difference–finite element method to incorporate topography and bathymetry for two-dimensional magnetotelluric modeling

Sarakorn

Vachiratienchai²

2018

Earth Planets Space

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In this research, a new numerical method, called the hybrid finite difference-finite element (hybrid FD-FE) method, is developed to solve 2-D magnetotelluric modeling by taking advantage of both the finite difference (FD) and finite element (FE) methods. With the hybrid FD-FE method, the model is first discretized as rectangular blocks and separated into two zones: the FD and FE zones. The FD zone is set for the subregions where topography or bathymetry does not appear. The FD approximation, which is fast, accurate and requires less memory resources, is then applied. For the FE zones where topography or bathymetry exists, the rectangular blocks are transformed into quadrilateral elements to handle the topography or bathymetry appropriately. Then, the FE approximation with quadrilateral elements, which is more accurate for topography or bathymetry zones, is applied. The system of equations for the hybrid FD-FE method is then formed according to the FD and FE schemes. The obtained system is a combination of the FD and FE equations. Three numerical methods are applied to test models with and without topography and bathymetry. The accuracy and efficiency in terms of errors, computational time and memory storage are presented, compared and discussed. The numerical experiments indicate that the FD scheme has a shorter computational time than the other schemes when modeling without topography and retains accuracy equivalent to that of the FE method, whereas FE is more practical when modeling with topography and bathymetry. However, our proposed hybrid FD-FE method is efficient in both situations. Without topography or bathymetry, its efficiency and accuracy approach those of the FD scheme. With topography and bathymetry, the hybrid FD-FE method is as accurate as FE, but its speed is slightly slower than that of FD. In terms of memory storage, the hybrid FD-FE method consumes slightly more storage than the FD method. This hybrid FD-FE method can be further extended and implemented for 3-D magnetotelluric modeling for more efficient computation.

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“…The efficiency and accuracy of the FD method for modeling magnetotelluric responses were proven for the 2D geo-electric model [9][10]. The FE method is another numerical technique that is often used for 2D and 3D magnetotelluric modeling, which involves assumed functional forms for the model and fields in small regions of specified geometry [11][12][13][14]. The FE method is accurate for real-world complex modeling, especially topography and bathymetry, because of the greater flexibility of mesh discretization.…”

Section: Introductionmentioning

confidence: 99%

Finite Difference Algorithm on Non-uniform Meshes for Modeling 2D Magnetotelluric Responses

Xiao-zhong¹,

Guo²,

Xie³

2018

Preprint

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A finite-difference approach with non-uniform meshes was presented for simulating magnetotelluric responses in 2D structures. We presented the formulation of this scheme and gave some sights into its successful implementation, and compared finite-difference solution with known numerical results and simple analytical solutions. First, a homogeneous half-space model was tested and the finite-difference approach can provide very good accuracy for 2D magnetotelluric modeling. Then we compared to the analytical solutions for the two-layered model, the relative errors of the apparent resistivity and the impedance phase were both increased when the frequency was increased. In the end, we compare our finite-difference simulation results with COMMEMI 2D-0 model with the finite-element solutions. Both results are in close agreement to each other. These comparisons confirm the validity and reliability of our finite-difference algorithm.

show abstract

2-D magnetotelluric modeling using finite element method incorporating unstructured quadrilateral elements

Cited by 11 publications

References 13 publications

Finite Difference Algorithm on Non-Uniform Meshes for Modeling 2D Magnetotelluric Responses

Finite Difference Algorithm on Non-Uniform Meshes for Modeling 2D Magnetotelluric Responses

Hybrid finite difference–finite element method to incorporate topography and bathymetry for two-dimensional magnetotelluric modeling

Finite Difference Algorithm on Non-uniform Meshes for Modeling 2D Magnetotelluric Responses

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