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 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.

3D time-domain airborne electromagnetic inversion based on secondary field finite-volume method

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. E219-E228 ◽  
Author(s):  
Xiuyan Ren ◽  
Changchun Yin ◽  
James Macnae ◽  
Yunhe Liu ◽  
Bo Zhang
Keyword(s):  
Finite Volume ◽  
Time Domain ◽  
High Efficiency ◽  
Background Field ◽  
Field Method ◽  
Secondary Field ◽  
Model Inversion ◽  
Airborne Electromagnetic ◽  
The Time Domain ◽  
Volume Method

We investigate an algorithm for 3D time-domain airborne electromagnetic (AEM) inversion based on the finite-volume (FV) method and direct Gauss-Newton optimization, where we obtain high efficiency by constraining the modeling volume to the AEM volume of influence (VOI) of a 3D source within the earth, rather than using the larger VOI of the AEM system. A half-space or layered earth is used to model the background field in the time domain, taking into account the transmitter waveform through convolution. Assuming that the 3D source of any secondary field detected at a survey point lies within the moving VOI of the airborne system, we conduct time-domain forward modeling and Jacobian calculation using an FV method within the 3D source VOI that requires a small number of cells for discretization. A local mesh and direct solver are shown to further speed up the computation. A synthetic isolated synclinal conductor inversion shows good agreement with the model geometry and provides a good fit to the data contaminated with noise. A synthetic multiple-body model inversion was also quite successful, showing that our algorithm is effective and about four times faster than inversion using the total-field method. Finally, we inverted GEOTEM data over the Lisheen deposit, where our inversion result was consistent with the published geology.

scholarly journals Modeling induced polarization effects in helicopter time domain electromagnetic data: Synthetic case studies

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. E31-E50 ◽  
Author(s):  
Andrea Viezzoli ◽  
Vladislav Kaminski ◽  
Gianluca Fiandaca
Keyword(s):  
Time Domain ◽  
A Priori ◽  
Induced Polarization ◽  
Earth Model ◽  
Model Parameters ◽  
Model Approximation ◽  
Generic Models ◽  
Time Domain Electromagnetic ◽  
Airborne Electromagnetic ◽  
Priori Information

We have developed a synthetic multiparametric modeling and inversion exercise undertaken to study the robustness of inverting airborne time-domain electromagnetic (TDEM) data to extract Cole-Cole parameters. The following issues were addressed: nonuniqueness, ill posedness, dependency on manual processing and the effect of constraints, and a priori information. We have used a 1D layered earth model approximation and lateral constraints. Synthetic simulations were performed for several models and the corresponding Cole-Cole parameters. The possibility to recover these models by means of laterally constrained multiparametric inversion was evaluated, including recovery of chargeability distributions from shallow and deep targets based on analysis of induced polarization (IP) effects, simulated in airborne TDEM data. Different scenarios were studied, including chargeable targets associated with the conductive and resistive environments. In particular, four generic models were considered for the exercise: a sulfide model, a kimberlite model, and two generic models focusing on the depth of investigation. Our study indicated that, in cases when relaxation time ([Formula: see text]) values are in the range to which the airborne electromagnetic is most sensitive (e.g., approximately 1 ms), it is possible to recover deep chargeable targets (to depths more than 130 m) in association with high electrical conductivity and in resistive environments. Furthermore, it was found that the recovery of a deep conductor, masked by a shallower chargeable target, became possible only when full Cole-Cole modeling was used in the inversion. Lateral constraints improved the recoverability of model parameters. Finally, modeling IP effects increased the accuracy of recovered electrical resistivity models.

Adaptive finite element for 3D time-domain airborne electromagnetic modeling based on hybrid posterior error estimation

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. WB71-WB79 ◽  
Author(s):  
Bo Zhang ◽  
Changchun Yin ◽  
Xiuyan Ren ◽  
Yunhe Liu ◽  
Yanfu Qi
Keyword(s):  
Finite Element ◽  
Time Domain ◽  
Forward Modeling ◽  
Adaptive Method ◽  
Hybrid Technique ◽  
Electromagnetic Modeling ◽  
Hill Model ◽  
Adaptive Process ◽  
Backward Euler ◽  
Airborne Electromagnetic

Airborne electromagnetic (AEM) forward modeling has been extensively developed in past years. However, not much attention has been paid to the adaptive numerical algorithms for time-domain electromagnetic modeling. We have created an adaptive method that can generate an effective mesh for time-domain 3D AEM full-wave modeling using an unstructured finite-element method and a backward Euler scheme. For the estimation of the posterior error in the adaptive process, we use a hybrid technique based on the continuity of the normal current density for modeling the off-time channels, and on the continuity of the tangential magnetic field for the on-time channels. To improve the stability of the forward modeling and control the number of grids in the adaptive process, a random grid-selection technique is applied. We check the modeling accuracy of the algorithm by comparing our adaptive results with the semianalytical solution for a time-domain AEM system over a homogeneous half-space. Furthermore, we test the effectiveness of our algorithm for multiple-source time-domain AEM systems by analyzing the meshes generated by the adaptive method and the model results. Finally, we study the topographic effect by calculating time-domain AEM responses over a hill model with an abnormal body embedded.

2.5-D forward modeling and inversion of time domain IP method

2017 ◽  
Vol 70 (0) ◽  
pp. 69-79
Author(s):  
Hideki Mizunaga ◽  
Kiyotaka Ishinaga
Keyword(s):  
Time Domain ◽  
Forward Modeling ◽  
And Inversion

3D parametric hybrid inversion of time-domain airborne electromagnetic data

Geophysics ◽  
2015 ◽  
Vol 80 (6) ◽  
pp. K25-K36 ◽  
Author(s):  
Michael S. McMillan ◽  
Christoph Schwarzbach ◽  
Eldad Haber ◽  
Douglas W. Oldenburg
Keyword(s):  
Time Domain ◽  
Electromagnetic Data ◽  
Airborne Electromagnetic ◽  
Airborne Electromagnetic Data

A special circumstance of airborne induced‐polarization measurements

Geophysics ◽  
1996 ◽  
Vol 61 (1) ◽  
pp. 66-73 ◽  
Author(s):  
Richard S. Smith ◽  
Jan Klein
Keyword(s):  
Time Domain ◽  
Eddy Currents ◽  
High Arctic ◽  
Induced Polarization ◽  
Laboratory Measurements ◽  
Dielectric Polarization ◽  
Special Circumstance ◽  
Polarization Measurements ◽  
Airborne Electromagnetic

Airborne induced‐polarization (IP) measurements can be obtained with standard time‐domain airborne electromagnetic (EM) equipment, but only in the limited circumstances when the ground is sufficiently resistive that the normal EM response is small and when the polarizability of the ground is sufficiently large that the IP response can dominate the EM response. Further, the dispersion in conductivity must be within the bandwidth of the EM system. One example of what is hypothesized to be IP effects are the negative transients observed on a GEOTEM® survey in the high arctic of Canada. The dispersion in conductivity required to explain the data is very large, but is not inconsistent with some laboratory measurements. Whether the dispersion is caused by an electrolytic or dielectric polarization is not clear from the limited ground follow‐up, but in either case the polarization can be considered to be induced by eddy currents associated with the EM response of the ground. If IP effects are the cause of the negative transients in the GEOTEM data, then the data can be used to estimate the polarizabilities in the area.

CS-based 3D Foward Modeling for Time-Domain Airborne Electromagnetic Method

2020 ◽  
Author(s):  
H. Wang ◽  
C. Yin ◽  
X. Ren ◽  
Y. Liu ◽  
J. Cao ◽  
...  
Keyword(s):  
Time Domain ◽  
Electromagnetic Method ◽  
Airborne Electromagnetic
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