scholarly journals 3D Airborne EM Forward Modeling Based on Time-Domain Spectral Element Method

2021 ◽  
Vol 13 (4) ◽  
pp. 601
Author(s):  
Changchun Yin ◽  
Zonghui Gao ◽  
Yang Su ◽  
Yunhe Liu ◽  
Xin Huang ◽  
...  
Keyword(s):  
Time Domain ◽  
Spectral Element Method ◽  
Forward Modeling ◽  
Spectral Element ◽  
High Accuracy ◽  
Earth Model ◽  
Backward Euler ◽  
3D Forward Modeling ◽  
Interpolation Functions ◽  
Element Method

Airborne electromagnetic (AEM) method uses aircraft as a carrier to tow EM instruments for geophysical survey. Because of its huge amount of data, the traditional AEM data inversions take one-dimensional (1D) models. However, the underground earth is very complicated, the inversions based on 1D models can frequently deliver wrong results, so that the modeling and inversion for three-dimensional (3D) models are more practical. In order to obtain precise underground electrical structures, it is important to have a highly effective and efficient 3D forward modeling algorithm as it is the basis for EM inversions. In this paper, we use time-domain spectral element (SETD) method based on Gauss-Lobatto-Chebyshev (GLC) polynomials to develop a 3D forward algorithm for modeling the time-domain AEM responses. The spectral element method combines the flexibility of finite-element method in model discretization and the high accuracy of spectral method. Starting from the Maxwell's equations in time-domain, we derive the vector Helmholtz equation for the secondary electric field. We use the high-order GLC vector interpolation functions to perform spectral expansion of the EM field and use the Galerkin weighted residual method and the backward Euler scheme to do the space- and time-discretization to the controlling equations. After integrating the equations for all elements into a large linear equations system, we solve it by the multifrontal massively parallel solver (MUMPS) direct solver and calculate the magnetic field responses by the Faraday's law. By comparing with 1D semi-analytical solutions for a layered earth model, we validate our SETD method and analyze the influence of the mesh size and the order of interpolation functions on the accuracy of our 3D forward modeling. The numerical experiments for typical models show that applying SETD method to 3D time-domain AEM forward modeling we can achieve high accuracy by either refining the mesh or increasing the order of interpolation functions.

A new study for airborne EM forward modeling based on the Galerkin spectral-element method

2018 ◽  
Author(s):  
Xin Huang ◽  
Colin G. Farquharson ◽  
Changchun Yin ◽  
Xiaoyue Cao ◽  
Bo Zhang ◽  
...  
Keyword(s):  
Spectral Element Method ◽  
Forward Modeling ◽  
Spectral Element ◽  
Airborne Em ◽  
Element Method

scholarly journals Time domain room acoustic simulations using the spectral element method

2019 ◽  
Vol 145 (6) ◽  
pp. 3299-3310 ◽  
Author(s):  
Finnur Pind ◽  
Allan P. Engsig-Karup ◽  
Cheol-Ho Jeong ◽  
Jan S. Hesthaven ◽  
Mikael S. Mejling ◽  
...  
Keyword(s):  
Time Domain ◽  
Spectral Element Method ◽  
Spectral Element ◽  
Element Method

Spectral-element method with arbitrary hexahedron meshes for time-domain 3D airborne electromagnetic forward modeling

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. E37-E46 ◽  
Author(s):  
Xin Huang ◽  
Changchun Yin ◽  
Colin G. Farquharson ◽  
Xiaoyue Cao ◽  
Bo Zhang ◽  
...  
Keyword(s):  
Time Domain ◽  
Forward Modeling ◽  
Spectral Element ◽  
Earth Model ◽  
System Of Equations ◽  
Primary Field ◽  
Secondary Field ◽  
Efficient Treatment ◽  
Mixed Order ◽  
Airborne Electromagnetic

Mainstream numerical methods for 3D time-domain airborne electromagnetic (AEM) modeling, such as the finite-difference (FDTD) or finite-element (FETD) methods, are quite mature. However, these methods have limitations in terms of their ability to handle complex geologic structures and their dependence on quality meshing of the earth model. We have developed a time-domain spectral-element (SETD) method based on the mixed-order spectral-element (SE) approach for space discretization and the backward Euler (BE) approach for time discretization. The mixed-order SE approach can contribute an accurate result by increasing the order of polynomials and suppress spurious solutions. The BE method is an unconditionally stable technique without limitations on time steps. To deal with the rapid variation of the fields close to the AEM transmitting loop, we separate a secondary field from the primary field and simulate the secondary field only, for which the primary field is calculated in advance. To obtain a block diagonal mass matrix and hence minimize the number of nonzero elements in the system of equations to be solved, we apply Gauss-Lobatto-Legendre integral techniques of reduced order. A direct solver is then adopted for the system of equations, which allows for efficient treatment of the multiple AEM sources. To check the accuracy of our SETD algorithm, we compare our results with the semianalytical solution for a layered earth model. Then, we analyze the modeling accuracy and efficiency for different 3D models using deformed physical meshes and compare them against results from 3D FETD codes, to further show the flexibility of SETD for AEM forward modeling.

scholarly journals Removing the CFL stability criterion of the explicit time-domain very high degree spectral-element method with eigenvalue perturbation

Geophysics ◽  
2021 ◽  
pp. 1-29
Author(s):  
Chao Lyu ◽  
Yann Capdeville ◽  
Gang Lv ◽  
Liang Zhao
Keyword(s):  
Time Domain ◽  
Stability Criterion ◽  
Spectral Element Method ◽  
Waveform Inversion ◽  
Spectral Element ◽  
Time Step ◽  
Transform Method ◽  
Time Dispersion ◽  
The Stability ◽  
Element Method

The explicit time-domain spectral-element method (SEM) for synthesizing seismograms hasgained tremendous credibility within the seismological community at all scales. Althoughthe recent introduction of non-periodic homogenization has addressed the spatial meshing difficulty of the mechanical discontinuities, the Courant-Friedrichs-Lewy (CFL) stability criterionstrictly constrains the maximum time step, which still puts a great burden on the numericalsimulation. In the explicit time-domain SEM, the source of instability of using a time stepbeyond the stability criterion is that some unstable eigenvalues of the updated matrix are largerthan what can be accurately simulated. We succeed in removing the CFL stability condition inthe explicit time-domain SEM by combining the forward time dispersion-transform method,the eigenvalue perturbation, and the inverse time dispersion-transform method. Our theoretical analyses and numerical experiments both in the homogeneous, moderate and strong heterogeneous models, show that this combination can precisely simulate waveforms with timesteps dozens of the CFL limit even towards the Nyquist limit especially for the efficient veryhigh degree SEM, which abundantly saves the iteration times without suffering from the time-dispersion error. It demonstrates a potential application prospect in some situations such as thefull waveform inversion which requires multiple numerical simulations for the same model.

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