Suppress numerical dispersion in reverse-time migration of acoustic wave equation using optimal nearly analytic discrete method

2020 ◽  
Vol 17 (1) ◽  
pp. 133-142
Author(s):  
Ming-Zhu Liu ◽  
Bing-Shoug He
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Numerical Dispersion ◽  
Acoustic Wave Equation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Discrete Method ◽  
Time Migration

An optimized wave equation for seismic modeling and reverse time migration

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCA153-WCA158 ◽  
Author(s):  
Faqi Liu ◽  
Guanquan Zhang ◽  
Scott A. Morton ◽  
Jacques P. Leveille
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Acoustic Wave ◽  
Computational Cost ◽  
Numerical Dispersion ◽  
New Wave ◽  
Acoustic Wave Equation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration

The acoustic wave equation has been widely used for the modeling and reverse time migration of seismic data. Numerical implementation of this equation via finite-difference techniques has established itself as a valuable approach and has long been a favored choice in the industry. To ensure quality results, accurate approximations are required for spatial and time derivatives. Traditionally, they are achieved numerically by using either relatively very fine computation grids or very long finite-difference operators. Otherwise, the numerical error, known as numerical dispersion, is present in the data and contaminates the signals. However, either approach will result in a considerable increase in the computational cost. A simple and computationally low-cost modification to the standard acoustic wave equation is presented to suppress numerical dispersion. This dispersion attenuator is one analogy of the antialiasing operator widely applied in Kirchhoff migration. When the new wave equation is solved numerically using finite-difference schemes, numerical dispersion in the original wave equation is attenuated significantly, leading to a much more accurate finite-difference scheme with little additional computational cost. Numerical tests on both synthetic and field data sets in both two and three dimensions demonstrate that the optimized wave equation dramatically improves the image quality by successfully attenuating dispersive noise. The adaptive application of this new wave equation only increases the computational cost slightly.

Angle-Domain Gathers Computation Using Poynting Vector of Two-Way Acoustic Wave Equation

2014 ◽  
Vol 962-965 ◽  
pp. 2984-2987
Author(s):  
Jia Jia Yang ◽  
Bing Shou He ◽  
Ting Chen
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Real Data ◽  
Flow Density ◽  
Acoustic Wave Equation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Wave Fields ◽  
Time Migration ◽  
Source Wave

Based on two-way acoustic wave equation, we present a method for computing angle-domain common-image gathers for reverse time migration. The method calculates the propagation direction of source wave-fields and receiver wave-fields according to expression of energy flow density vectors (Poynting vectors) of acoustic wave equation in space-time domain to obtain the reflection angle, then apply the normalized cross-correlation imaging condition to achieve the angle-domain common-image gathers. The angle gathers obtained can be used for migration velocity analysis, AVA analysis and so on. Numerical examples and real data examples demonstrate the effectiveness of this method.

scholarly journals Reverse Time Migration Based on the Pseudo-Space-Domain First-Order Velocity-Stress Acoustic Wave Equation

2021 ◽  
Vol 9 ◽  
Author(s):  
Xiaobo Zhang ◽  
Xiutian Wang ◽  
Baohua Liu ◽  
Peng Song ◽  
Jun Tan ◽  
...  
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Imaging Method ◽  
Acoustic Wave Equation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Space Domain ◽  
First Order ◽  
Time Migration ◽  
Rectangular Mesh

Reverse time migration (RTM) is an ideal seismic imaging method for complex structures. However, in conventional RTM based on rectangular mesh discretization, the medium interfaces are usually distorted. Besides, reflected waves generated by the two-way wave equation can cause artifacts during imaging. To overcome these problems, a high-order finite-difference (FD) scheme and stability condition for the pseudo-space-domain first-order velocity-stress acoustic wave equation were derived, and based on the staggered-grid FD scheme, the RTM of the pseudo-space-domain acoustic wave equation was implemented. Model experiments showed that the proposed RTM of the pseudo-space-domain acoustic wave equation could systematically avoid the interface distortion problem when the velocity interfaces were considered to compute the pseudo-space-domain intervals. Moreover, this method could effectively suppress the false scattering of dipping interfaces and reflections during wavefield extrapolation, thereby reducing migration artifacts on the profile and significantly improving the quality of migration imaging.

A stable TTI reverse time migration and its implementation

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. WA3-WA11 ◽  
Author(s):  
Yu Zhang ◽  
Houzhu Zhang ◽  
Guanquan Zhang
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Stable Solution ◽  
Pseudospectral Method ◽  
Wave System ◽  
System Of Equations ◽  
Acoustic Wave Equation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration

Modeling and reverse time migration based on the tilted transverse isotropic (TTI) acoustic wave equation suffers from instability in media of general inhomogeniety, especially in areas where the tilt abruptly changes. We develop a stable TTI acoustic wave equation implementation based on the original elastic anisotropic wave equation. We, specifically, derive a vertical transversely isotropic wave system of equations that is equivalent to their elastic counterpart and introduce the self-adjoint differential operators in rotated coordinates to stabilize the TTI acoustic wave equations. Compared to the conventional formulations, the new system of equations does not add numerical complexity; a stable solution can be found by either a pseudospectral method or a high-order explicit finite difference scheme. We demonstrate by examples that our method provides stable and high-quality TTI reverse time migration images.

scholarly journals 3D reverse-time migration using the acoustic wave equation: An experience with the SEG/EAGE data set

2003 ◽  
Vol 22 (1) ◽  
pp. 38-41 ◽  
Author(s):  
Kwangjin Yoon ◽  
Changsoo Shin ◽  
Sangyong Suh ◽  
Larry R. Lines ◽  
Soonduk Hong
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Acoustic Wave Equation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Time Migration
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