Nonzero offset seismic forward modeling by one‐way acoustic wave‐equation

1998 ◽  
Author(s):  
He Zhenhua ◽  
Xiong Gaojun ◽  
Zhang Yixiang
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Forward Modeling ◽  
Acoustic Wave Equation

A two‐way nonreflecting wave equation

Geophysics ◽  
1984 ◽  
Vol 49 (2) ◽  
pp. 132-141 ◽  
Author(s):  
Edip Baysal ◽  
Dan D. Kosloff ◽  
J. W. C. Sherwood
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Forward Modeling ◽  
Conventional Approach ◽  
Reflection Coefficients ◽  
Constant Density ◽  
Acoustic Wave Equation ◽  
Seismic Modeling ◽  
Homogeneous Regions ◽  
Dominant Direction

In seismic modeling and in migration it is often desirable to use a wave equation (with varying velocity but constant density) which does not produce interlayer reverberations. The conventional approach has been to use a one‐way wave equation which allows energy to propagate in one dominant direction only, typically this direction being either upward or downward (Claerbout, 1972). We introduce a two‐way wave equation which gives highly reduced reflection coefficients for transmission across material boundaries. For homogeneous regions of space, however, this wave equation becomes identical to the full acoustic wave equation. Possible applications of this wave equation for forward modeling and for migration are illustrated with simple models.

Modified imaging principle: An alternative to preserved-amplitude least-squares wave-equation migration

Geophysics ◽  
2007 ◽  
Vol 72 (6) ◽  
pp. S221-S230 ◽  
Author(s):  
Denis Kiyashchenko ◽  
René-Edouard Plessix ◽  
Boris Kashtan
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Acoustic Wave ◽  
Least Squares ◽  
Forward Modeling ◽  
Acoustic Wave Equation ◽  
Impedance Contrast ◽  
Least Squares Migration

Impedance contrast images can result from a least-squares migration or from a modified imaging principle. Theoretically, the two approaches should give similar results, but in practice they lead to different estimates of the impedance contrasts because of limited acquisition geometry, difficulty in computing exact weights for least-squares migration, and small contrast approximation. To analyze those differences, we compare the two approaches based on 2D synthetics. Forward modeling is either a finite-difference solver of the full acoustic wave equation or a one-way wave-equation solver that correctly models the amplitudes. The modified imaging principle provides better amplitude estimates of the impedance contrasts and does not suffer from the artifacts at-tributable to diving waves, which can be seen in two-way, least-squares migrated sections. However, because of the shot-based formulation, artifacts appear in the modified imaging principle results in shadow zones where energy is defocused. Those artifacts do not exist with the least-squares migration algorithm because all shots are processed simultane-ously.

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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