Perfectly matched layer on curvilinear grid for the second-order seismic acoustic wave equation

Yuan, Sanyi; Wang, Shangxu; Sun, Wenju; Miao, Lina; Li, Zhenhua

doi:10.1071/eg13066

Cited by 29 publications

(7 citation statements)

References 33 publications

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“…e total PCB concentration ranged from 112.79 to 542.95 ng/g, with mean of 203.73 ng/g) (Table 4). e PCB concentrations detected were lower than the results obtained by Yuan and co-workers who found total PCB concentrations in topsoils of Beijing in China ranging from 47.04 to 3 883.77 ng/g, with a mean of 679.62 ng/g (Yuan et al, 2014). Levels of PCBs in eastern Romania were determined by Dragan and co-workers who found this to range between 34 and 1 132 ng/g, with a mean of 278 ng/g (Dragan et al, 2006).…”

Section: Comparison Of Levels Of Pcbs and Ocps In Soil From Various Lcontrasting

confidence: 68%

Evaluation of persistent organochlorine pesticides and polychlorinated biphenyls in Umgeni River bank soil, KwaZulu-Natal, South Africa

Gakuba

Moodley

Ndungu

et al. 2019

WSA

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This study investigated the presence and distribution of organochlorine pesticides (OCPs) and polychlorinated biphenyls (PCBs) in soil collected along the banks of the Umgeni River, one of the largest rivers in the province of KwaZulu-Natal, South Africa. The analysis was performed using gas chromatography-mass spectrometry (GC-MS). The results showed that the levels of OCPs ranged from 3.58±0.09 ng/g for hexachlorobenzene (HCB) to 82.65±2.82 ng/g for HCH, with an individual mean concentration of 24.33±2.00 ng/g dry weight (dw). The levels of PCBs ranged from 10.46 ng/g for PCB105 to 89.46 ng/g for PCB180, with an average PCB value of 25.47±1.26 ng/g, dw. The highest levels of OCPs and PCBs were found at Northern Wastewater Treatment Plant (mean OCP: 32.39±3.97 ng/g and PCB: 67.87±1.67 ng/g). The two most abundant contaminants in the river were endrin and PCB180.

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Section: Comparison Of Levels Of Pcbs and Ocps In Soil From Various Lcontrasting

confidence: 68%

Evaluation of persistent organochlorine pesticides and polychlorinated biphenyls in Umgeni River bank soil, KwaZulu-Natal, South Africa

Gakuba

Moodley

Ndungu

et al. 2019

WSA

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“…By using the complex coordinate stretching method, the integration of the CFS‐PML boundary condition into the frequency‐domain anisotropic elastic wave equations can be expressed as (Yuan et al . ):

\begin{matrix} true \\ right ρ ω^{2} u & + & left \frac{1}{e_{x}} \frac{\partial}{\partial x} [0true C_{11} \frac{1}{e_{x}} \frac{\partial u}{\partial x} + C_{13} \frac{1}{e_{z}} \frac{\partial v}{\partial z}] \\ + & left \frac{1}{e_{z}} \frac{\partial}{\partial z} [0true C_{44} \frac{1}{e_{x}} \frac{\partial v}{\partial x} + C_{44} \frac{1}{e_{z}} \frac{\partial u}{\partial z}] + f false(ω false) = 0 \end{matrix}

\begin{matrix} true \\ right ρ ω^{2} v & + & left \frac{1}{e_{x}} \frac{\partial}{\partial x} ([], C_{44} \frac{1}{e_{x}} \frac{\partial v}{\partial x} + C_{44} \frac{1}{e_{z}} \frac{\partial u}{\partial z}) \\ + & left \frac{1}{e_{z}} \frac{\partial}{\partial z} ([], C_{33} \frac{1}{e_{z}} \frac{\partial v}{\partial z} + C_{13} \frac{1}{e_{x}} \frac{\partial u}{\partial x}) + g (ω) = 0 . \end{matrix}

…”

Section: Boundary Conditionsmentioning

confidence: 99%

Complex frequency‐shifted multi‐axial perfectly matched layer for frequency‐domain seismic wavefield simulation in anisotropic media

Zhao

Chen

2019

Geophysical Prospecting

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A B S T R A C TSeismic anisotropy has an important influence on seismic data processing and interpretation. Although the frequency-domain seismic wavefield simulation has a problem of solving the large scale linear sparse matrix due to the computational limitations, it has some advantages over the time-domain seismic wavefield simulation including efficient inversion using only a limited number of frequency components and easy implementation of multiple sources. To accurately simulate seismic wave propagation in the frequency domain, we also need to choose the absorbing boundary conditions to absorb artificial reflections from edges of the model as we do in the time domain. Compared with the classical boundary conditions including the perfectly matched layer and complex frequency-shifted perfectly matched layer, the complex frequencyshifted multi-axial perfectly matched layer has been proven to effectively suppress the unwanted reflections at grazing incidence and solve the instability problem in the time-domain seismic numerical modelling in anisotropic elastic media. In this paper, we propose to extend the complex frequency-shifted multi-axial perfectly matched layer absorbing boundary condition to the frequency-domain seismic wavefield simulation in anisotropic elastic media. To test the validity of our proposed algorithm, we compare the results (snapshots and seismograms) of the frequency-domain seismic wavefield simulation with those of the time-domain modelling. The model studies indicate that the complex frequency-shifted multi-axial perfectly matched layer absorbing boundary condition is stable in the frequency-domain seismic wavefield simulation in anisotropic media, and provides better absorbing performance than the complex frequency-shifted perfectly matched layer boundary condition.

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“…The relations among different PML formulations are summarized by Kristek et al (2009). Additionally, several PMLs have also been applied to the second-order wave equation (e.g., Komatitsch and Tromp, 2003;Basu and Chopra, 2004;Yuan et al, 2014).…”

Section: Introductionmentioning

confidence: 99%

Application of unsplit convolutional perfectly matched layer for scalar arbitrarily wide-angle wave equation

Chen

Zhou

2014

GEOPHYSICS

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A classical split perfectly matched layer (PML) method has recently been applied to the scalar arbitrarily wide-angle wave equation (AWWE) in terms of displacement. However, the classical split PML obviously increases computational cost and cannot efficiently absorb waves propagating into the absorbing layer at grazing incidence. Our goal was to improve the computational efficiency of AWWE and to enhance the suppression of edge reflections by applying a convolutional PML (CPML). We reformulated the original AWWE as a first-order formulation and incorporated the CPML with a general complex frequency shifted stretching operator into the renewed formulation. A staggered-grid finite-difference (FD) method was adopted to discretize the first-order equation system. For wavefield depth continuation, the first-order AWWE with the CPML saved memory compared with the original second-order AWWE with the conventional split PML. With the help of numerical examples, we verified the correctness of the staggered-grid FD method and concluded that the CPML can efficiently absorb evanescent and propagating waves.

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Perfectly matched layer on curvilinear grid for the second-order seismic acoustic wave equation

Cited by 29 publications

References 33 publications

Evaluation of persistent organochlorine pesticides and polychlorinated biphenyls in Umgeni River bank soil, KwaZulu-Natal, South Africa

Evaluation of persistent organochlorine pesticides and polychlorinated biphenyls in Umgeni River bank soil, KwaZulu-Natal, South Africa

Complex frequency‐shifted multi‐axial perfectly matched layer for frequency‐domain seismic wavefield simulation in anisotropic media

Application of unsplit convolutional perfectly matched layer for scalar arbitrarily wide-angle wave equation

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