An efficient reverse time migration method using local nearly analytic discrete operator

Geophysics ◽  
2013 ◽  
Vol 78 (1) ◽  
pp. S15-S23 ◽  
Author(s):  
Jingshuang Li ◽  
Dinghui Yang ◽  
Faqi Liu
Keyword(s):  
Finite Difference ◽  
Numerical Dispersion ◽  
Imaging Method ◽  
Discrete Operator ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Velocity Models ◽  
Time Migration ◽  
Nearly Analytic Discrete Operator

In recent years, reverse time migration (RTM), the most powerful depth imaging method, has become the preferred imaging tool in many geologic settings because of its ability to handle complex velocity models including steeply dipping interfaces. Finite difference is one of the most popular numerical methods applied in RTM in the industry. However, it often encounters a serious issue of numerical dispersion, which is typically suppressed by reducing the propagation grid sizes, resulting in large computation and memory increment. Recently, a nearly analytic discrete operator has been developed to approximate the partial differential operators, from which many antidispersion schemes have been proposed, and are confirmed to be superior to conventional algorithms in suppressing numerical dispersion. We apply an optimal nearly analytic discrete (ONAD) method to RTM to improve its accuracy and performance. Numerical results show that ONAD can be used effectively in seismic modeling and migration based on the full wave equations. This method produces little numerical dispersion and requires much less computation and memory compared to the traditional finite-difference methods such as Lax-Wendroff correction method. The reverse time migration results of the 2D Marmousi model and the Sigsbee2B data set show that ONAD can improve the computational efficiency and maintain image quality by using large extrapolation grids.

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.

scholarly journals 3D weak-dispersion reverse time migration using a stereo-modeling operator

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. S19-S30 ◽  
Author(s):  
Jingshuang Li ◽  
Michael Fehler ◽  
Dinghui Yang ◽  
Xueyuan Huang
Keyword(s):  
Fourth Order ◽  
Propagation Model ◽  
Numerical Dispersion ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Complex Velocity ◽  
Data Set ◽  
Velocity Models ◽  
Time Migration ◽  
Project Model

Reliable 3D imaging is a required tool for developing models of complex geologic structures. Reverse time migration (RTM), as the most powerful depth imaging method, has become the preferred imaging tool because of its ability to handle complex velocity models including steeply dipping interfaces and large velocity contrasts. Finite-difference methods are among the most popular numerical approaches used for RTM. However, these methods often encounter a serious issue of numerical dispersion, which is typically suppressed by reducing the grid interval of the propagation model, resulting in large computation and memory requirements. In addition, even with small grid spacing, numerical anisotropy may degrade images or, worse, provide images that appear to be focused but position events incorrectly. Recently, stereo-operators have been developed to approximate the partial differential operator in space. These operators have been used to develop several weak-dispersion and efficient stereo-modeling methods that have been found to be superior to conventional algorithms in suppressing numerical dispersion and numerical anisotropy. We generalized one stereo-modeling method, fourth-order nearly analytic central difference (NACD), from 2D to 3D and applied it to 3D RTM. The RTM results for the 3D SEG/EAGE phase A classic data set 1 and the SEG Advanced Modeling project model demonstrated that, even when using a large grid size, the NACD method can handle very complex velocity models and produced better images than can be obtained using the fourth-order and eighth-order Lax-Wendroff correction (LWC) schemes. We also applied 3D NACD and fourth-order LWC to a field data set and illustrated significant improvements in terms of structure imaging, horizon/layer continuity and positioning. We also investigated numerical dispersion and found that not only does the NACD method have superior dispersion characteristics but also that the angular variation of dispersion is significantly less than for LWC.

scholarly journals Reverse time migration of transmitted wavefields for salt boundary imaging

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. S71-S82 ◽  
Author(s):  
Chris Willacy ◽  
Maksym Kryvohuz
Keyword(s):  
Imaging Techniques ◽  
Velocity Model ◽  
Seismic Profile ◽  
Imaging Method ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Velocity Models ◽  
Transmission Imaging ◽  
Time Migration

The imaging of steep salt boundaries has received much attention with the advent of improved wider azimuth acquisition designs and advanced imaging techniques such as reverse time migration (RTM), for example. However, despite these advancements in capability, there are cases in which the salt boundary is either poorly illuminated or completely absent in the migrated image. To provide a solution to this problem, we have developed two RTM methods for imaging salt boundaries, which use transmitted wavefields. In the first technique, downgoing waves, typically recorded in walkaway vertical seismic profile surveys, are used to image the salt flank via the generation of aplanatic isochrones. This image can be generated in the absence of an explicit interpretation of the salt flank using dual migration velocity models, as demonstrated on a 3D walkaway field data set from the Gulf of Mexico. In the second technique, we extend the basic theory to include imaging of upgoing source wavefields, which are transmitted at the base salt from below, as acquired by a surface acquisition geometry. This technique has similarities to the prism-imaging method, yet it uses transmitted instead of reflected waves at the salt boundary. Downgoing and upgoing methods are shown to satisfactorily generate an image of the salt flank; however, transmission imaging can create artifacts if reflection arrivals are included in the migration or the acquisition geometry is limited in extent. Increased wavelet stretch is also observed due to the higher transmission coefficient. An important benefit of these methods is that transmission imaging produces an opposite depth shift to errors in the velocity model compared with imaging of reflections. When combined with conventional seismic reflection surveys, this behavior can be used to provide a constraint on the accuracy of the salt and/or subsalt velocities.

Acoustic and elastic numerical wave simulations by recursive spatial derivative operators

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. T167-T174 ◽  
Author(s):  
Dan Kosloff ◽  
Reynam C. Pestana ◽  
Hillel Tal-Ezer
Keyword(s):  
Synthetic Data ◽  
Analytic Solutions ◽  
Numerical Dispersion ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Lamb’S Problem ◽  
Dynamic Elasticity ◽  
Time Migration ◽  
Recursive Operators

A new scheme for the calculation of spatial derivatives has been developed. The technique is based on recursive derivative operators that are generated by an [Formula: see text] fit in the spectral domain. The use of recursive operators enables us to extend acoustic and elastic wave simulations to shorter wavelengths. The method is applied to the numerical solution of the 2D acoustic wave equation and to the solution of the equations of 2D dynamic elasticity in an isotropic medium. An example of reverse-time migration of a synthetic data set shows that the numerical dispersion can be significantly reduced with respect to schemes that are based on finite differences. The method is tested for the solutions of the equations of dynamic elasticity by comparing numerical and analytic solutions to Lamb’s problem.

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.

Visibility analysis for optimal imaging of target areas and its application to a Gulf of Mexico deep-water data set

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. WB119-WB126 ◽  
Author(s):  
Elive Menyoli ◽  
Shengwen Jin ◽  
Shiyong Xu ◽  
Stuart Graber
Keyword(s):  
Gulf Of Mexico ◽  
Synthetic Data ◽  
Target Area ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Visibility Analysis ◽  
Velocity Models ◽  
Time Migration ◽  
Subsalt Imaging

Marine wide-azimuth data in the Gulf of Mexico, reverse time migration (RTM) and anisotropic velocity models have led to significant improvement in subsalt imaging. However, imaging of some steeply dipping subsalt targets such as three-way closures against salt is still difficult. This can be attributed to poor illumination and noise contaminations from various shot records. We apply the visibility analysis method that quantitatively determines which shot records contribute most energy on a specific subsalt prospect area. As a result we selectively migrate only those shot records thereby reducing noise contamination from low energy contributing shot records, improving signal continuity and better trap definition in the target area. Like conventional illumination analysis, the computation takes into account the overburden velocity distribution, acquisition geometry, target reflectivity and dip angle. We used 2D and 3D synthetic data examples to test the concepts and applicability of the method. A Gulf of Mexico case study example using wide-azimuth data demonstrated its use in an industry scale project. It is shown that for the particular 60°–65° subsalt target of interest only 30% of the wide-azimuth shot records are sufficient for the imaging. By reducing noise, the image results show significant improvement in the subsalt area compared to the full shot record RTM volume.

Efficient iterative prestack least-squares reverse time migration through surface-offset gather compression

Geophysics ◽  
2021 ◽  
pp. 1-65
Author(s):  
Carlos Alberto da Costa Filho ◽  
Gregório Goudel Azevedo ◽  
Roberto Pereira ◽  
Adel Khalil
Keyword(s):  
Least Squares ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Compression Scheme ◽  
Data Set ◽  
Velocity Models ◽  
Model Compression ◽  
Time Migration ◽  
Amplitude Versus Offset ◽  
2D Data

Extended least-squares inversion is superior to stack-based least-squares inversion for imaging the subsurface because it can better account for amplitude-versus-offset (AVO) effects as well as residual moveout (RMO) effects induced by erroneous velocity models. Surface-offset extensions have proved to be a robust alternative to angle gathers as well as subsurface extensions when applied to narrow-azimuth (NAZ) data acquisitions, especially when using erroneous velocity models. As such, least-squares reverse time migration (LSRTM) applied to surface-offset gathers (SOGs) obtains accurate surface-offset-dependent estimates of the reflectivity with better AVO behavior, while respecting curvatures of the events in the gathers. Nevertheless, the computational expense incurred by SOG demigration generally renders this process unfeasible in many practical situations. We exploit a compression scheme for SOGs that captures AVO and some RMO effects to improve efficiency of extended LSRTM. The decompression operator commutes with the demigration operator, so gathers compressed in the model domain may be decompressed in the data domain. This obviates the need to demigrate all SOGs, requiring only the demigration of a few compressed gathers. We demonstrate the accuracy of this compression, both in the model and data domains with a synthetic 2D data set. We then use our model-compression/data-decompression scheme to SOG-extended iterative LSRTM for two field data examples from offshore Brazil. These examples demonstrate that our compression can capture most AVO and some RMO information accurately, while greatly improving efficiency in many practical scenarios.

Application of RTM 3D angle gathers to wide-azimuth data subsalt imaging

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. WB175-WB182 ◽  
Author(s):  
Yan Huang ◽  
Bing Bai ◽  
Haiyong Quan ◽  
Tony Huang ◽  
Sheng Xu ◽  
...  
Keyword(s):  
Model Updating ◽  
Velocity Model ◽  
Azimuth Angle ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Additional Information ◽  
Time Migration ◽  
Reflection Angle ◽  
Subsalt Imaging

The availability of wide-azimuth data and the use of reverse time migration (RTM) have dramatically increased the capabilities of imaging complex subsalt geology. With these improvements, the current obstacle for creating accurate subsalt images now lies in the velocity model. One of the challenges is to generate common image gathers that take full advantage of the additional information provided by wide-azimuth data and the additional accuracy provided by RTM for velocity model updating. A solution is to generate 3D angle domain common image gathers from RTM, which are indexed by subsurface reflection angle and subsurface azimuth angle. We apply these 3D angle gathers to subsalt tomography with the result that there were improvements in velocity updating with a wide-azimuth data set in the Gulf of Mexico.

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