Seismic Wave Simulation Using a TTI Pseudo-acoustic Wave Equation

ICIPEG 2016 ◽  
2017 ◽  
pp. 499-507
Author(s):  
S. Y. Moussavi Alashloo ◽  
D. Ghosh ◽  
W. I. Wan Yusoff
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Seismic Wave ◽  
Acoustic Wave Equation ◽  
Wave Simulation ◽  
Seismic Wave Simulation

Adaptive 27-point finite difference frequency domain method for wave simulation of 3D acoustic wave equation

Geophysics ◽  
2021 ◽  
pp. 1-39
Author(s):  
Wenhao Xu ◽  
Bangyu Wu ◽  
Yang Zhong ◽  
Jinghuai Gao ◽  
Qing Huo Liu
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Acoustic Wave ◽  
Frequency Domain ◽  
Difference Frequency ◽  
Lookup Table ◽  
Acoustic Wave Equation ◽  
Wave Simulation ◽  
Finite Difference Frequency Domain ◽  
Point Stencil

The finite-difference frequency-domain (FDFD) method has important applications in the wave simulation of various wave equations. To promote the accuracy and efficiency for wave simulation with the FDFD method, we have developed a new 27-point FDFD stencil for 3D acoustic wave equation. In the developed stencil, the FDFD coefficients not only depend on the ratios of cell sizes in the x-, y-, and z-directions, but we also depend on the spatial sampling density (SD) in terms of the number of wavelengths per grid. The corresponding FDFD coefficients can be determined efficiently by making use of the plane-wave expression and the lookup table technique. We also develop a new way for designing an adaptive FDFD stencil by directly adding some correction terms to the conventional second-order FDFD stencil, which is simpler to use and easier to generalize. Corresponding dispersion analysis indicates that, compared to the optimal 27-point stencil derived from the average-derivative method (ADM), the developed adaptive 27-point stencil can reduce the required SD from approximately 4 to 2.2 points per wavelength (PPW) for a cubic mesh and to 2.7 PPW for a general cuboid mesh. Numerical examples of a 3D homogeneous model and SEG/EAGE salt-dome model indicate that the developed stencil is more accurate than the ADM 27-point stencil for cubic and general cuboid meshes, while requiring similar CPU time and computational memory as the ADM 27-point stencil for direct and iterative solvers.

A 1.8 trillion degrees-of-freedom, 1.24 petaflops global seismic wave simulation on the K computer

2016 ◽  
Vol 30 (4) ◽  
pp. 411-422 ◽  
Author(s):  
Seiji Tsuboi ◽  
Kazuto Ando ◽  
Takayuki Miyoshi ◽  
Daniel Peter ◽  
Dimitri Komatitsch ◽  
...  
Keyword(s):  
Seismic Wave ◽  
Degrees Of Freedom ◽  
Wave Simulation ◽  
Seismic Wave Simulation

Direct Solution of the Acoustic Wave Equation using the Wavelet-Galerkin Method

2013 ◽  
Author(s):  
Rodrigo Bird Burgos ◽  
Marco Antonio Cetale Santos ◽  
Raul Rosas e Silva
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Galerkin Method ◽  
Direct Solution ◽  
Acoustic Wave Equation ◽  
Wavelet Galerkin Method

An analytic signal based accurate time-domain visco-acoustic wave equation from the Constant-Q theory

Geophysics ◽  
2021 ◽  
pp. 1-58
Author(s):  
Hongwei Liu ◽  
Yi Luo
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Time Domain ◽  
Seismic Waves ◽  
Heterogeneous Media ◽  
Relaxation Property ◽  
Analytic Signal ◽  
Acoustic Wave Equation ◽  
Real Component ◽  
Frequency Components

We present a concise time-domain wave equation to accurately simulate wave propagation in visco-acoustic media. The central idea behind this work is to dismiss the negative frequency components from a time-domain signal by converting the signal to its analytic format. The negative frequency components of any analytic signal are always zero, meaning we can construct the visco-acoustic wave equation to honor the relaxation property of the media for positive frequencies only. The newly proposed complex-valued wave equation (CWE) represents the wavefield with its analytic signal, whose real part is the desired physical wavefield, while the imaginary part is the Hilbert transform of the real component. Specifically, this CWE is accurate for both weak and strong attenuating media in terms of both dissipation and dispersion and the attenuation is precisely linear with respect to the frequencies. Besides, the CWE is easy and flexible to model dispersion-only, dissipation-only or dispersion-plus-dissipation seismic waves. We have verified these CWEs by comparing the results with analytical solutions, and achieved nearly perfect matching. Except for the homogeneous Q media, we have also extended the CWEs to heterogeneous media. The results of the CWEs for heterogeneous Q media are consistent with those computed from the nonstationary operator based Fourier Integral method and from the Standard Linear Solid (SLS) equations.

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