3-D Forward Modeling of Transient EM Field in Rough Media Using Implicit Time-Domain Finite-Element Method

Liu, Yunhe; Wang, Luyuan; Yin, Changchun; Ren, Xiuyan; Zhang, Bo; Su, Yang; Rong, Zhihao; Ma, Xinpeng

doi:10.1109/tgrs.2022.3231921

IEEE Trans. Geosci. Remote Sensing

2023

DOI: 10.1109/tgrs.2022.3231921

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3-D Forward Modeling of Transient EM Field in Rough Media Using Implicit Time-Domain Finite-Element Method

Yunhe Liu

Luyuan Wang

Changchun Yin

et al.

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2024

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Cited by 3 publications

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“…Zhang et al [22] introduced the so-called Caputo method to approximate fractional derivatives, and they showed that their method has high accuracies expect for the sign reversal region. Liu et al [31] used an unequal step length for the Caputo operator to consider the Maxwell's equations with heterogeneous medium. However, all electric and magnetic fields calculated in previous time steps need to be stored in memory to calculate the field values for the next time step.…”

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confidence: 99%

A Fast and Efficient Method for 3-D Transient Electromagnetic Modeling Considering IP Effect

Zhao,

Sun,

Liu

et al. 2024

IEEE Trans. Geosci. Remote Sensing

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Late-time negative responses in central-loop transient electromagnetic (TEM) data are often linked to the induced polarization (IP) effect. Early methods for modeling the IP effect in TEM data try to avoid calculating the fractional derivative arising from considering the Cole-Cole model by either using the Fourier transform to convert frequency-domain responses to the time domain or approximating the fractional derivative in the time domain directly. The frequency-to-time conversion method suffer from accuracy issues if the number of frequencies calculated is small. The time-domain approximation method also has accuracy issues because of simplified Cole-Cole models. The Caputo series can approximate fractional derivatives accurately if historic electromagnetic (EM) fields are saved.However, the storage of historic EM fields leads to a significant memory consumption. We introduce the sum-of-exponentials (SOE) method to discretize fractional derivatives, which does not need to store field values from previous times except for the first two time-steps. We discretize the resulting partial differential equations from the SOE discretization using a finite-difference time-domain (FDTD) approach. Additionally, we improve computational efficiency by employing the direct-splitting strategy to transform large sparse matrices into smaller diagonally dominant tridiagonal matrices. We validate the accuracy and efficiency of our algorithm by comparing it with the Caputo approximation method using a chargeable half-space model. Furthermore, we compare our results with existing literature data for a chargeable anomaly in a nonchargeable half space. Finally, we analyze the response characteristics of the IP effect using a block-in-half space model.

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confidence: 99%

A Fast and Efficient Method for 3-D Transient Electromagnetic Modeling Considering IP Effect

Zhao,

Sun,

Liu

et al. 2024

IEEE Trans. Geosci. Remote Sensing

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3-D Forward Modeling of Semi-Airborne TEM Method With IP Effect Based on Goal-Oriented Adaptive Finite Element Algorithm

Shu,

Qi,

Yang

et al. 2024

IEEE Trans. Geosci. Remote Sensing

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Three-dimensional simulation and characterization of airborne transient electromagnetic response in rough media

Gao,

Yin,

Liang

et al. 2024

GEOPHYSICS

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In fractal, porous, and cranny rough media, the diffusion of the electromagnetic (EM) field differs from that in piecewise smooth media. This phenomenon is known as an anomalous diffusion. To study the influence of anomalous diffusion on EM signals, we use the fractional time derivative and derive a governing equation describing the subdiffusion process of electric fields in rough media. Three-dimensional (3D) forward modeling of the time-domain airborne EM (AEM) is performed using the finite-difference method and frequencytime transformation. We verify the accuracy of our forward modeling method by comparing it with semi-analytical solutions for a layered earth model. The numerical results show that as the conductivity of rough media decreases with time, the amplitude of the EM field decreases during the early periods but increases during later periods compared to non-rough media. The EM field does not diffuse in the classical mode of the "smoke ring, but instead demonstrates a "trailing pattern, meaning that it maintains its maximum value at positions close to the source and diffuses outward and attenuates until it vanishes.

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3-D Forward Modeling of Transient EM Field in Rough Media Using Implicit Time-Domain Finite-Element Method

Cited by 3 publications

References 33 publications

A Fast and Efficient Method for 3-D Transient Electromagnetic Modeling Considering IP Effect

A Fast and Efficient Method for 3-D Transient Electromagnetic Modeling Considering IP Effect

3-D Forward Modeling of Semi-Airborne TEM Method With IP Effect Based on Goal-Oriented Adaptive Finite Element Algorithm

Three-dimensional simulation and characterization of airborne transient electromagnetic response in rough media

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