An Approximate Acoustic Wave Equation for VTI Media

2011 ◽  
Vol 54 (4) ◽  
pp. 599-607
Author(s):  
Yi-Jian HUANG ◽  
Guang-Ming ZHU ◽  
Chi-Yang LIU
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Acoustic Wave Equation ◽  
Vti Media

Hybrid Fourier finite-difference 3D depth migration for anisotropic media

Geophysics ◽  
2008 ◽  
Vol 73 (2) ◽  
pp. S27-S34 ◽  
Author(s):  
Tong W. Fei ◽  
Christopher L. Liner
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Acoustic Wave ◽  
Seismic Data ◽  
Transversely Isotropic ◽  
Acoustic Wave Equation ◽  
Near Surface ◽  
Depth Migration ◽  
Surface Distortions ◽  
Vti Media

When a subsurface is anisotropic, migration based on the assumption of isotropy will not produce accurate migration images. We develop a hybrid wave-equation migration algorithm for vertical transversely isotropic (VTI) media based on a one-way acoustic wave equation, using a combination of Fourier finite-difference (FFD) and finite-difference (FD) approaches. The hybrid method can suppress an additional solution that exists in the VTI acoustic wave equation, and it offers speed and other advantages over conventional FFD or FD methods alone. The algorithm is tested on a synthetic model involving log data from onshore eastern Saudi Arabia, including estimates of both intrinsic and layer-induced VTI parameters. Results indicate that VTI imaging in this region offers some improvement over isotropic imaging, primarily with respect to subtle structure and stratigraphy and to image continuity. These benefits probably will be overshadowed by perennial land seismic data issues such as near-surface distortions and multiples.

An acoustic wave equation for anisotropic media

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1239-1250 ◽  
Author(s):  
Tariq Alkhalifah
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Acoustic Wave ◽  
Computation Time ◽  
Transversely Isotropic ◽  
Acoustic Medium ◽  
Acoustic Wave Equation ◽  
P Waves ◽  
Kinematic Approximation ◽  
Vti Media

A wave equation, derived using the acoustic medium assumption for P-waves in transversely isotropic (TI) media with a vertical symmetry axis (VTI media), yields a good kinematic approximation to the familiar elastic wave equation for VTI media. The wavefield solutions obtained using this VTI acoustic wave equation are free of shear waves, which significantly reduces the computation time compared to the elastic wavefield solutions for exploding‐reflector type applications. From this VTI acoustic wave equation, the eikonal and transport equations that describe the ray theoretical aspects of wave propagation in a TI medium are derived. These equations, based on the acoustic assumption (shear wave velocity = 0), are much simpler than their elastic counterparts, yet they yield an accurate description of traveltimes and geometrical amplitudes. Numerical examples prove the usefulness of this acoustic equation in simulating the kinematic aspects of wave propagation in complex TI models.

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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