A simplified calculation for adaptive coefficients of finite-difference frequency-domain method

Xu, Wen-Hao; Ba, Jing; Carcione, José Maria; Yang, Zhi-Fang; Yan, Xin-Fei

doi:10.1007/s11770-023-1045-8

Cited by 3 publications

(2 citation statements)

References 26 publications

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“…Solving the small system of linear equations in Equation ( 18) leads to the required adaptive FDFD coefficients for TFC equation without a source term and CFS PML. Furthermore, the applications of the AC FDFD method to acoustic the Equation (see [15]) and diffusive-viscous Equation (see [35]) reveal that the adaptive FDFD coefficients acquired by ignoring the influence of source term and CFS PML can also lead to a satisfying numerical solution for the computational area with the source term and CFS PML. Therefore, we directly determine the adaptive FDFD coefficients for the TFC equation with the source term and CFS PML by ignoring the influence of source term and CFS PML.…”

Section: Adaptive Fdfd Coefficientsmentioning

confidence: 99%

“…The existing numerical solutions to the TFC equation generally deal with Dirichlet boundary conditions. However, the applications of the TFC equation can involve an unbounded simulation using a bounded computational region, which requires absorbing boundary condition (see [13][14][15]). In addition, the classical perfectly matched layer (PML) absorbing boundary condition suffers from large artificial reflections for grazing incidences (see [16]), especially for the simulation of ultrasonic wave propagation for digital cores under laboratory studies (see [17,18]).…”

Section: Introductionmentioning

confidence: 99%

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Adaptive-Coefficient Finite Difference Frequency Domain Method for Solving Time-Fractional Cattaneo Equation with Absorbing Boundary Condition

Xu,

Ba,

Cao

et al. 2024

Fractal Fract

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The time-fractional Cattaneo (TFC) equation is a practical tool for simulating anomalous dynamics in physical diffusive processes. The existing numerical solutions to the TFC equation generally deal with the Dirichlet boundary conditions. In this paper, we incorporate the absorbing boundary condition as a complex-frequency-shifted (CFS) perfectly matched layer (PML) into the TFC equation. Then, we develop an adaptive-coefficient (AC) finite-difference frequency-domain (FDFD) method for solving the TFC with CFS PML. The corresponding analytical solution for homogeneous TFC equation with a point source is proposed for validation. The effectiveness of the developed AC FDFD method is verified by the numerical examples of four typical TFC models, including the different orders of time-fractional derivatives for both the homogeneous model and the layered model. The numerical examples show that the developed AC FDFD method is more accurate than the traditional second-order FDFD method for solving the TFC equation with the CFS PML absorbing boundary condition, while requiring similar computational costs.

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Section: Adaptive Fdfd Coefficientsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Adaptive-Coefficient Finite Difference Frequency Domain Method for Solving Time-Fractional Cattaneo Equation with Absorbing Boundary Condition

Xu,

Ba,

Cao

et al. 2024

Fractal Fract

View full text Add to dashboard Cite

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Finite-difference frequency-domain method with QR-decomposition-based complex-valued adaptive coefficients for 3D diffusive viscous wave modelling

Xu,

Ba,

Wang

et al. 2024

Journal of Geophysics and Engineering

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The diffusive viscous (DV) model is a useful tool for interpreting low-frequency seismic attenuation and the influence of fluid saturation on frequency-dependent reflections. Among present methods for the numerical solution of corresponding DV wave equation, the finite-difference frequency-domain (FDFD) method with complex-valued adaptive coefficients (CVAC) has the advantage of efficiently suppressing both numerical dispersion and numerical attenuation. In this research, the FDFD method with CVAC is first generalized to 3D DV equation. In addition, the current calculation of CVAC involves the numerical integration of propagation angles, conjugate gradient (CG) iterative optimization and the sequential selection of initial values, which is difficult and inefficient for implementation. An improved method is developed for calculating CVAC, where a complex-valued least-squares problem is constructed by substituting the 3D complex-valued plane-wave solutions into the FDFD scheme. The QR decomposition method is utilized to efficiently solve the least-squares problem. Numerical dispersion and attenuation analyses reveal that the FDFD method with CVAC requires about 2.5 spatial points in a wavelength within a dispersion deviation of 1% and an attenuation deviation of 10% for 3D DV equation. An analytic solution for 3D DV wave equation in homogeneous media is proposed to verify the effectiveness of the proposed method. And numerical examples demonstrate that the FDFD method with CVAC can obtain accurate wavefield modelling results for 3D DV models with a limited number of spatial points in a wavelength, and the FDFD method with QR-based CVAC requires less computational time than the FDFD method with CG-based CVAC.

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Wavefield simulation of the acoustic VTI wave equation based on the adaptive-coefficient finite-difference frequency-domain method

Zhao,

Wang,

2024

Journal of Geophysics and Engineering

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Many simulation methods have been developed for P-waves in vertically transversely isotropic (VTI) media. These methods are based on the acoustic approximation. The finite-difference frequency-domain (FDFD) method stands out for its ability to simulate multi-shot or narrowband seismic data. It has no temporal dispersion, facilitates attenuation modelling, and enables parallelization. The optimal FDFD method is commonly used to simulate the acoustic VTI wave equation, but it applies the same FDFD coefficients for different frequencies and model velocities, which cannot fully minimize the numerical dispersion error. To enhance its accuracy and effectiveness, we develop an adaptive-coefficient FDFD method specifically for the acoustic VTI wave equation. The FDFD coefficients depend on two factors: the number of wavelengths in each grid and the Thomsen parameters. The dispersion analysis reveals that the proposed FDFD method can achieve a reduction in the necessary number of grid points from 4 to 2.5 compared to the optimal 9-point average derivative method (ADM), while maintaining a maximum dispersion error of 1%. From three numerical examples, the developed FDFD method can obtain more accurate wavefield results than the ADM optimal FDFD method, while taking comparable computational time and memory.

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A simplified calculation for adaptive coefficients of finite-difference frequency-domain method

Cited by 3 publications

References 26 publications

Adaptive-Coefficient Finite Difference Frequency Domain Method for Solving Time-Fractional Cattaneo Equation with Absorbing Boundary Condition

Adaptive-Coefficient Finite Difference Frequency Domain Method for Solving Time-Fractional Cattaneo Equation with Absorbing Boundary Condition

Finite-difference frequency-domain method with QR-decomposition-based complex-valued adaptive coefficients for 3D diffusive viscous wave modelling

Wavefield simulation of the acoustic VTI wave equation based on the adaptive-coefficient finite-difference frequency-domain method

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