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.

Finite-Element Modeling of Time-Domain Controlled-Source Electromagnetic Survey with Weighted Laguerre Polynomials

Geophysics ◽  
2021 ◽  
pp. 1-43
Author(s):  
Qingtao Sun ◽  
Runren Zhang ◽  
Yunyun Hu
Keyword(s):  
Finite Element ◽  
Time Domain ◽  
Laguerre Polynomials ◽  
Time Integration ◽  
Sampling Interval ◽  
Controlled Source ◽  
Time Integration Method ◽  
Transient Electromagnetic ◽  
Backward Euler ◽  
Land Survey

To facilitate the modeling of time-domain controlled-source electromagnetic survey, we propose an efficient finite-element method with weighted Laguerre polynomials, which shows a much lower computational complexity than conventional time integration methods. The proposed method allows sampling the field at arbitrary time steps and also its accuracy is determined by the number of polynomials, instead of the time sampling interval. Analysis is given regarding the optimization of the polynomial number to be used and the criterion of selecting the time scale factor. Two numerical examples in marine and land survey environments are included to demonstrate the superiority of the proposed method over the existing backward Euler time integration method. The proposed method is expected to facilitate the modeling of transient electromagnetic surveys in the geophysical regime.

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.

A finite-element time-domain forward solver for electromagnetic methods with complex-shaped loop sources

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. E117-E132 ◽  
Author(s):  
Jianhui Li ◽  
Xushan Lu ◽  
Colin G. Farquharson ◽  
Xiangyun Hu
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Time Domain ◽  
Real Life ◽  
Euler Method ◽  
Stratified Medium ◽  
Tetrahedral Mesh ◽  
Fe Method ◽  
Circular Loop ◽  
Backward Euler

A finite-element time-domain (FETD) electromagnetic forward solver for a complex-shaped transmitting loop is presented. Any complex-shaped source can be viewed as a combination of electric dipoles (EDs), each of which can be further decomposed into two horizontal EDs along the [Formula: see text]- and [Formula: see text]-directions and one vertical ED along the [Formula: see text]-direction. Using this method, a complex-shaped loop can be easily handled when implementing an FE method based on the total-field algorithm and an unstructured tetrahedral mesh. The FETD solver that we developed used a vector FE method and the first-order backward Euler method to discretize in space and time, respectively. Unstructured tetrahedral girds combined with a local refinement technique was used to exactly delineate topography and a deformed loop. This FETD solver was tested by the five following scenarios: a rectangular loop on a flat-surface half-space, a circular loop on a stratified medium, a rectangular loop laid on a slope-surface half-space, a rectangular loop laid on a slope with a conductive cubic body, and a complex-shaped loop on a real-life topography. The results of this FETD solver agreed well with the ones evaluated by the analytic methods for the first three examples, and with a frequency-domain FE solver combined with a cosine transform for the last two examples.

3D time-domain airborne EM forward modeling based on adaptive finite-element method

2018 ◽  
Author(s):  
Bo Zhang ◽  
Changchun Yin ◽  
Yunhe Liu ◽  
Xiuyan Ren ◽  
Xin Huang ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Time Domain ◽  
Forward Modeling ◽  
Adaptive Finite Element Method ◽  
Adaptive Finite Element ◽  
Airborne Em ◽  
Element Method

3D time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach

Geophysics ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. F115-F126 ◽  
Author(s):  
Evan Schankee Um ◽  
Jerry M. Harris ◽  
David L. Alumbaugh
Keyword(s):  
Finite Element ◽  
Differential Equations ◽  
Electric Field ◽  
Time Domain ◽  
Dirichlet Boundary Conditions ◽  
Earth Model ◽  
Time Step ◽  
Transient Electromagnetic ◽  
Backward Euler ◽  
Diffusion Phenomena

We present a finite-element time-domain (FETD) approach for the simulation of 3D electromagnetic (EM) diffusion phenomena. The finite-element algorithm efficiently simulates transient electric fields and the time derivatives of magnetic fields in general anisotropic earth media excited by multiple arbitrarily configured electric dipoles with various signal waveforms. To compute transient electromagnetic fields, the electric field diffusion equation is transformed into a system of differential equations via Galerkin’s method with homogeneous Dirichlet boundary conditions. To ensure numerical stability and an efficient time step, the system of the differential equations is discretized in time using an implicit backward Euler scheme. The resultant FETD matrix-vector equation is solved using a sparse direct solver along with a fill-in reduced ordering technique. When advancing the solution in time, the FETD algorithm adjusts the time step by examining whether or not the current step size can be doubled without unacceptably affecting the accuracy of the solution. To simulate a step-off source waveform, the 3D FETD algorithm also incorporates a 3D finite-element direct current (FEDC) algorithm that solves Poisson’s equation using a secondary potential method for a general anisotropic earth model. Examples of controlled-source FETD simulations are compared with analytic and/or 3D finite-difference time-domain solutions and are used to confirm the accuracy and efficiency of the 3D FETD algorithm.

Hybrid technique combining finite element, finite difference and integral equation methods in time domain

2000 ◽  
Vol 36 (6) ◽  
pp. 506 ◽  
Author(s):  
A. Rubio Bretones ◽  
A. Monorchio ◽  
G. Manara ◽  
R. Gómez Martín ◽  
R. Mittra
Keyword(s):  
Integral Equation ◽  
Finite Element ◽  
Finite Difference ◽  
Time Domain ◽  
Hybrid Technique ◽  
Integral Equation Methods

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 goal-oriented adaptive finite-element method for 3D scattered airborne electromagnetic method modeling

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. E337-E346 ◽  
Author(s):  
Changchun Yin ◽  
Bo Zhang ◽  
Yunhe Liu ◽  
Jing Cai
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Normal Component ◽  
Adaptive Finite Element Method ◽  
Convergence Criteria ◽  
Adaptive Procedure ◽  
Material Interfaces ◽  
Hill Model ◽  
Airborne Electromagnetic ◽  
Element Method

We have developed a goal-oriented adaptive unstructured finite-element method based on the scattered field for 3D frequency-domain airborne electromagnetic (AEM) modeling. To guarantee the EM field divergence free within each element and the continuity conditions at electrical material interfaces, we have used the edge-based shape functions to approximate the electrical field. The posterior error for finite-element adaptive meshing procedure is estimated from the continuity of the normal component of the current density, whereas the influence functions are estimated by solving a dual forward problem. Because the imaginary part of the scattered current is discontinuous and the real part is continuous, we use the latter to estimate the posterior error. For the multisources and multifrequencies problem in AEM, we calculate the weighted posterior error for each element by considering only those transmitter-receiver pairs that do not adhere to our convergence criteria. Finally, we add a minimum volume constraint to improve the stability of the adaptive procedure. To check the accuracy, we compared our adaptive results with the semianalytical solutions for AEM systems over a half-space model. To test the effectiveness of our algorithm for multiple sources and multiple frequencies of AEM, we analyzed meshes for separate frequencies and for combined frequencies. Finally, we calculated the AEM responses over a hill model with and without embedded abnormal bodies to prove the feasibility of our algorithm for AEM variable topography modeling.

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