An acoustic wave equation for anisotropic media

1998 ◽  
Author(s):  
Tariq Alkhalifah
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Anisotropic Media ◽  
Acoustic Wave Equation

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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