One-step extrapolation method for reverse time migration

Geophysics ◽  
2009 ◽  
Vol 74 (4) ◽  
pp. A29-A33 ◽  
Author(s):  
Yu Zhang ◽  
Guanquan Zhang
Keyword(s):  
Wave Equation ◽  
Extrapolation Method ◽  
New Method ◽  
Numerical Dispersion ◽  
Finite Difference Schemes ◽  
Order Partial Differential Equation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
One Step

We have proposed a new method, a one-step extrapolation algorithm, to solve the acoustic wave equation. By introducing a square-root operator, the two-way wave equation can be formulated as a first-order partial differential equation in time, which is similar to the one-way wave equation. To solve the new wave equation, we used a stable explicit extrapolation method in the time direction and handled lateral velocity variations in the space and wavenumber domains. Unlike the conventional explicit finite-difference schemes, the new method does not suffer from numerical instability or numerical dispersion problems. It can be used to design cost-effective and high-quality reverse time migration or modeling code.

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.

Reverse-time migration in acoustic VTI media using a high-order stereo operator

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. WA3-WA11 ◽  
Author(s):  
Wei Xie ◽  
Dinghui Yang ◽  
Faqi Liu ◽  
Jingshuang Li
Keyword(s):  
Computational Cost ◽  
High Order ◽  
New Method ◽  
Numerical Dispersion ◽  
Staggered Grid ◽  
Imaging Method ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Velocity Models ◽  
Time Migration

With the capability of handling complicated velocity models, reverse-time migration (RTM) has become a powerful imaging method. Improving imaging accuracy and computational efficiency are two significant but challenging tasks in the applications of RTM. Despite being the most popular numerical technique applied in RTM, finite-difference (FD) methods often suffer from undesirable numerical dispersion, leading to a noticeable loss of imaging resolution. A new and effective FD operator, called the high-order stereo operator, has been developed to approximate the partial differential operators in the wave equation, from which a numerical scheme called the three-step stereo method (TSM) has been developed and has shown effectiveness in suppressing numerical dispersion. Numerical results show that compared with the conventional numerical methods such as the Lax-Wendroff correction (LWC) scheme and the staggered-grid (SG) FD method, this new method significantly reduces numerical dispersion and computational cost. Tests on the impulse response and the 2D prestack Hess acoustic VTI model demonstrated that the TSM achieves higher image quality than the LWC and SG methods do, especially when coarse computation grids were used, which indicated that the new method can be a promising algorithm for large-scale anisotropic RTM.

One-step wave extrapolation matrix method for reverse time migration

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. S359-S366 ◽  
Author(s):  
Daniel E. Revelo ◽  
Reynam C. Pestana
Keyword(s):  
Wave Equation ◽  
Chebyshev Polynomial ◽  
Matrix Method ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
First Order ◽  
Full Wave ◽  
Time Migration ◽  
The Matrix ◽  
One Step

We have developed a new method for solving the acoustic full-wave equation, which we call the one-step wave extrapolation (OSE) matrix method. In our method, the wave equation is redefined by introducing a complex (analytic) wavefield and reformulating the traditional acoustic full-wave equation as a first-order partial differential equation in time. Afterward, the analytical wavefield is separated to its real and imaginary parts, and the resulting first-order coupled set of equations is solved by the Tal-Ezer’s technique, which consists of using the Chebyshev polynomial expansion to approximate the matrix exponential operator. The matrix is antisymmetrical with a square-root pseudodifferential operator, which is computed using the Fourier method. In this way, the implementation of the proposed method is straightforward and if the appropriate number of Chebyshev polynomial expansion terms is chosen, the proposed numerical algorithm is unconditionally stable and propagates seismic waves free of numerical dispersion for any seismic velocity variation in a recursive manner. Moreover, in our method, the number of Fourier transforms is explicitly determined and it is a function of the maximum eigenvalue of the matrix operator and time-step size. A numerical modeling example is shown to demonstrate that the proposed method has the capability to extrapolate waves using a time stepping up to Nyquist limit. We have also developed a reverse time migration example with illumination compensation. The migration results based on the OSE method demonstrate the capability of this new method to image complex structures in the presence of strong velocity contrasts.

scholarly journals Depth-Extrapolation-Based True-Amplitude Full-Wave-Equation Migration from Topography

2021 ◽  
Vol 11 (7) ◽  
pp. 3010
Author(s):  
Hao Liu ◽  
Xuewei Liu
Keyword(s):  
Wave Equation ◽  
Partial Derivative ◽  
Model Experiment ◽  
Surface Velocity ◽  
Seismic Exploration ◽  
Initial Condition ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Full Wave ◽  
Time Migration

The lack of an initial condition is one of the major challenges in full-wave-equation depth extrapolation. This initial condition is the vertical partial derivative of the surface wavefield and cannot be provided by the conventional seismic acquisition system. The traditional solution is to use the wavefield value of the surface to calculate the vertical partial derivative by assuming that the surface velocity is constant. However, for seismic exploration on land, the surface velocity is often not uniform. To solve this problem, we propose a new method for calculating the vertical partial derivative from the surface wavefield without making any assumptions about the surface conditions. Based on the calculated derivative, we implemented a depth-extrapolation-based full-wave-equation migration from topography using the direct downward continuation. We tested the imaging performance of our proposed method with several experiments. The results of the Marmousi model experiment show that our proposed method is superior to the conventional reverse time migration (RTM) algorithm in terms of imaging accuracy and amplitude-preserving performance at medium and deep depths. In the Canadian Foothills model experiment, we proved that our method can still accurately image complex structures and maintain amplitude under topographic scenario.

Q least-squares reverse time migration based on the first-order viscoacoustic quasidifferential equations

Geophysics ◽  
2021 ◽  
pp. 1-65
Author(s):  
Yingming Qu ◽  
Yixin Wang ◽  
Zhenchun Li ◽  
Chang Liu
Keyword(s):  
Wave Equation ◽  
Least Squares ◽  
Surface Topography ◽  
Density Perturbation ◽  
Second Order ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
First Order ◽  
Time Migration ◽  
Grid Scheme

Seismic wave attenuation caused by subsurface viscoelasticity reduces the quality of migration and the reliability of interpretation. A variety of Q-compensated migration methods have been developed based on the second-order viscoacoustic quasidifferential equations. However, these second-order wave-equation-based methods are difficult to handle with density perturbation and surface topography. In addition, the staggered grid scheme, which has an advantage over the collocated grid scheme because of its reduced numerical dispersion and enhanced stability, works in first-order wave-equation-based methods. We have developed a Q least-squares reverse time migration method based on the first-order viscoacoustic quasidifferential equations by deriving Q-compensated forward-propagated operators, Q-compensated adjoint operators, and Q-attenuated Born modeling operators. Besides, our method using curvilinear grids is available even when the attenuating medium has surface topography and can conduct Q-compensated migration with density perturbation. The results of numerical tests on two synthetic and a field data sets indicate that our method improves the imaging quality with iterations and produces better imaging results with clearer structures, higher signal-to-noise ratio, higher resolution, and more balanced amplitude by correcting the energy loss and phase distortion caused by Q attenuation. It also suppresses the scattering and diffracted noise caused by the surface topography.

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.

Implicit interpolation in reverse‐time migration

Geophysics ◽  
1997 ◽  
Vol 62 (3) ◽  
pp. 906-917 ◽  
Author(s):  
Jinming Zhu ◽  
Larry R. Lines
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Real Data ◽  
Seismic Sources ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Difference Wave ◽  
Time Migration ◽  
Seismic Acquisition ◽  
Recorded Data

Reverse‐time migration applies finite‐difference wave equation solutions by using unaliased time‐reversed recorded traces as seismic sources. Recorded data can be sparsely or irregularly sampled relative to a finely spaced finite‐difference mesh because of the nature of seismic acquisition. Fortunately, reliable interpolation of missing traces is implicitly included in the reverse‐time wave equation computations. This implicit interpolation is essentially based on the ability of the wavefield to “heal itself” during propagation. Both synthetic and real data examples demonstrate that reverse‐time migration can often be performed effectively without the need for explicit interpolation of missing traces.

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