Simulations of GPR in dispersive media using a frequency-dependent PSTD algorithm

Liu, Qing; Fan, Guo‐Xin

doi:10.1109/36.789628

Cited by 60 publications

(9 citation statements)

References 36 publications

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“…[15] In this study, after adopting the staggered grid method and the MFFTD operator, we applied an overlap domain decomposition method to the PSTD parallel computation of GPR waves. The details of staggered grid PSTD method of GPR wave simulation can be found elsewhere [Liu and Fan, 1999;Li et al, 2009]. For readers' convenience, we gave a brief introduction about the governing equations of GPR waves in lossy media with perfectly matched layer (PML) absorbing boundary conditions.…”

Section: Parallel Pstd Algorithmmentioning

confidence: 99%

“…The details of staggered grid PSTD method of GPR wave simulation can be found elsewhere [Liu and Fan, 1999;Li et al, 2009]. For readers' convenience, we gave a brief introduction about the governing equations of GPR waves in lossy media with perfectly matched layer (PML) absorbing boundary conditions.…”

Section: Parallel Pstd Algorithmmentioning

confidence: 99%

“…For readers' convenience, we gave a brief introduction about the governing equations of GPR waves in lossy media with perfectly matched layer (PML) absorbing boundary conditions. In the complex stretched coordinates [Chew and Weedon, 1994;Liu, 1997;Liu and Fan, 1999;Li et al, 2009],…”

Section: Parallel Pstd Algorithmmentioning

confidence: 99%

“…Comparing with FDTD method, the pseudospectral time domain (PSTD) method [Fornberg, 1996] has some potential merits in numerical computation, e.g., PSTD requires only two grids for a wavelength [Fornberg, 1996;Liu, 1997], while FDTD needs at least eight grids to achieve the same precision; the spatial derivatives are calculated by fast Fourier transform (FFT) in PSTD, leading to neglecting numerical dispersion due to its high precision, while strong numerical dispersion is expected for FDTD as long as the grid is not fine enough. Thus, PSTD showed potential applications in various disciplinary because it takes much less computer memory and computation time to achieve the same precision as FDTD [Fornberg, 1996;Liu and Fan, 1999;Wang et al, 2001;Liu et al, 2006;Li et al, 2009].…”

Section: Introductionmentioning

confidence: 99%

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A parallel 3‐D staggered grid pseudospectral time domain method for ground‐penetrating radar wave simulation

Huang

Wang

2010

J. Geophys. Res.

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[1] We presented a parallel 3-D staggered grid pseudospectral time domain (PSTD) method for simulating ground-penetrating radar (GPR) wave propagation. We took the staggered grid method to weaken the global effect in PSTD and developed a modified fast Fourier transform (FFT) spatial derivative operator to eliminate the wraparound effect due to the implicit periodical boundary condition in FFT operator. After the above improvements, we achieved the parallel PSTD computation based on an overlap domain decomposition method without any absorbing condition for each subdomain, which can significantly reduce the required grids in each overlap subdomain comparing with other proposed algorithms. We test our parallel technique for some numerical models and obtained consistent results with the analytical ones and/or those of the nonparallel PSTD method. The above numerical tests showed that our parallel PSTD algorithm is effective in simulating 3-D GPR wave propagation, with merits of saving computation time, as well as more flexibility in dealing with complicated models without losing the accuracy. The application of our parallel PSTD method in applied geophysics and paleoseismology based on GPR data confirmed the efficiency of our algorithm and its potential applications in various subdisciplines of solid earth geophysics. This study would also provide a useful parallel PSTD approach to the simulation of other geophysical problems on distributed memory PC cluster.

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Section: Parallel Pstd Algorithmmentioning

confidence: 99%

Section: Parallel Pstd Algorithmmentioning

confidence: 99%

Section: Parallel Pstd Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A parallel 3‐D staggered grid pseudospectral time domain method for ground‐penetrating radar wave simulation

Huang

Wang

2010

J. Geophys. Res.

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“…However, it is difficult for FDTD to solve the problems such as undulating surface, free boundary and serious numerical dispersion. Compared with FDTD, pseudo spectral time-domain (PSTD) method is a global calculation method characterized by its high calculation accuracy and weak numerical dispersion [6] [7] [8]. However, PSTD would result in numerical instabilities when dealing with the boundary problems of strongly inhomogeneous medium, and it is also difficult to solve the problems of undulating surface and free boundary condition [9].…”

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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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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Fast Fourier Transforms and Nufft

Liu

2005

Encyclopedia of RF and Microwave Engineering

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The fast Fourier transform (FFT) algorithm is one of most fundamental and powerful computational tools in computational science and engineering. In this article, the development of the fast Fourier transform algorithm is reviewed, some representative applications in electromagnetics are illustrated, and some recent developments in extending the FFT algorithms to nonuniformly sampled data and to discontinuous functions are summarized.

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Simulations of GPR in dispersive media using a frequency-dependent PSTD algorithm

Cited by 60 publications

References 36 publications

A parallel 3‐D staggered grid pseudospectral time domain method for ground‐penetrating radar wave simulation

A parallel 3‐D staggered grid pseudospectral time domain method for ground‐penetrating radar wave simulation

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

Fast Fourier Transforms and Nufft

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