2D spectral element modeling of GPR wave propagation in inhomogeneous media

Zarei, S.; Oskooi, Behrooz; Amini, Navid; Dalkhani, A. Rahimi

doi:10.1016/j.jappgeo.2016.07.027

Cited by 15 publications

(8 citation statements)

References 17 publications

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“…Equation (18) is the second-order GPR wave equation based on the non-split PML boundary condition. Comparison among Equations (9), (12) and (18) shows that the non-split PML boundary condition neither needs split the electromagnetic field, nor needs the calculation of third derivative with respect to time, which means less calculation amount and higher calculation speed.…”

Section: Non-split Pml Boundary Conditionmentioning

confidence: 99%

“…Feng et al [17] applied the wavelet interpolation basis function to the FETD algorithm and carried out the GPR FETD forward modeling, demonstrating the advantages of the algorithm with numerical examples. Zarei et al [18] applied the orthogonal interpolation basis function to the FETD algorithm, showing that FETD is easier to eliminate the influence of numerical dispersion than FDTD with numerical examples.…”

Section: Introductionmentioning

confidence: 99%

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Non-Split PML Boundary Condition for Finite Element Time-Domain Modeling of Ground Penetrating Radar

Zhi¹,

Wang²,

Wang³

et al. 2019

JAMP

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As a highly efficient absorbing boundary condition, Perfectly Matched Layer (PML) has been widely used in Finite Difference Time Domain (FDTD) simulation of Ground Penetrating Radar (GPR) based on the first order electromagnetic wave equation. However, the PML boundary condition is difficult to apply in GPR Finite Element Time Domain (FETD) simulation based on the second order electromagnetic wave equation. This paper developed a non-split perfectly matched layer (NPML) boundary condition for GPR FETD simulation based on the second order electromagnetic wave equation. Taking two-dimensional TM wave equation as an example, the second order frequency domain equation of GPR was derived according to the definition of complex extending coordinate transformation. Then it transformed into time domain by means of auxiliary differential equation method, and its FETD equation is derived based on Galerkin method. On this basis, a GPR FETD forward program based on NPML boundary condition is developed. The merits of NPML boundary condition are certified by compared with wave field snapshots, signal and reflection errors of homogeneous medium model with split and non-split PML boundary conditions. The comparison demonstrated that the NPML algorithm can reduce memory occupation and improve calculation efficiency. Furthermore, numerical simulation of a complex model verifies the good absorption effects of the NPML boundary condition in complex structures.

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Section: Non-split Pml Boundary Conditionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Non-Split PML Boundary Condition for Finite Element Time-Domain Modeling of Ground Penetrating Radar

Zhi¹,

Wang²,

Wang³

et al. 2019

JAMP

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“…However, a complete knowledge of the fourth column of T −1 is unnecessary in the derivation of a contradiction. From (28) Then for i ∈ µ 0 ,…”

Section: 2mentioning

confidence: 99%

“…Such a method would lend itself well to structural mechanics [19], direct numerical simulations of computational fluid dynamics [19,16,24,6], atmospheric modeling [14,11], etc. [25,28,21,22]. This has driven research into high-order continuous Galerkin TFEM possessing diagonal mass matrices that maintain a high level of accuracy [15,4,27,8,17].…”

mentioning

confidence: 99%

A High-Order Lower-Triangular Pseudo-Mass Matrix for Explicit Time Advancement of hp Triangular Finite Element Methods

Appleton¹,

Helenbrook²

2019

Preprint

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Explicit time advancement for continuous finite elements requires the inversion of a global mass matrix. For spectral element simulations on quadrilaterals and hexahedra, there is an accurate approximate mass matrix which is diagonal, making it computationally efficient for explicit simulations. In this article it is shown that for the standard space of polynomials used with triangular elements, denoted T (p) where p is the degree of the space, there is no diagonal approximate mass matrix that permits accurate solutions. Accuracy is defined as giving an exact projection of functions in T (p − 1). In light of this, a lower-triangular pseudo-mass matrix method is introduced and demonstrated for the space T (3). The pseudo-mass matrix and accompanying high-order basis allow for computationally efficient time-stepping techniques without sacrificing the accuracy of the spatial approximation for unstructured triangular meshes.

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“…In the field of geophysics, mixed media are characterized by electromagnetic signal divergence and random particle distributions caused by dielectric dispersion (Aorigele, 2020). Therefore, the distribution state of mixed media affects the imaging effect and the dielectric properties of GPR (Teixeira, 2008;Zarei et al, 2016). The electromagnetic attenuation and energy dissipation in a fine grid model can be effectively reduced by selecting an algorithm with the same probability extraction and random distribution for arranging the grid model.…”

mentioning

confidence: 99%

Fine grid model for the dielectric characteristics of ground‐penetrating radar in mixed media

Ling

Liu

et al. 2022

Geophysical Prospecting

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The Fisher–Yates random shuffling algorithm combined with the finite‐difference time‐domain method is proposed to construct a fine grid model for the forward simulation of ground‐penetrating radar in mixed media. First, the finite‐difference time‐domain method was used to divide the coarse grid model into several fine grid models by conforming to the boundary conditions of different media, and the corresponding dielectric parameters were assigned to Yee cells in each fine grid model. Then, the Fisher–Yates random shuffling algorithm was used to randomly scramble all Yee cells with equal probability, and the array of scrambled Yee cells was recombined into a coarse grid model. Finally, the geoelectric model of mixed media was generated with the finite‐difference time‐domain method, and a ground‐penetrating radar image excited by electromagnetic wave pulses was obtained. To explore the characteristic signals and dielectric properties of the ground‐penetrating radar electromagnetic response in mixed media, image entropy theory was used to describe the ground‐penetrating radar image, and waveform analysis and wavelet transform mode maximum methods were used to analyse the single‐channel ground‐penetrating radar signal of the mixed media. The results showed that the Fisher–Yates random shuffling–finite‐difference time‐domain method can be used to construct a valid and stable fine grid model for simulating ground‐penetrating radar in mixed media. The model effectively inhibits electromagnetic attenuation and energy dissipation, and the wavelet transform mode maximum method explains the relative dielectric permittivity distribution of the mixed media. The findings of this study can be used as a theoretical basis for correcting radar parameters and interpreting images when ground‐penetrating radar is applied to mixed media.

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2D spectral element modeling of GPR wave propagation in inhomogeneous media

Cited by 15 publications

References 17 publications

Non-Split PML Boundary Condition for Finite Element Time-Domain Modeling of Ground Penetrating Radar

Non-Split PML Boundary Condition for Finite Element Time-Domain Modeling of Ground Penetrating Radar

A High-Order Lower-Triangular Pseudo-Mass Matrix for Explicit Time Advancement of hp Triangular Finite Element Methods

Fine grid model for the dielectric characteristics of ground‐penetrating radar in mixed media

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