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.

Reverse time migration of multiples: Reducing migration artifacts using the wavefield decomposition imaging condition

Geophysics ◽  
2017 ◽  
Vol 82 (4) ◽  
pp. S307-S314 ◽  
Author(s):  
Yibo Wang ◽  
Yikang Zheng ◽  
Qingfeng Xue ◽  
Xu Chang ◽  
Tong W. Fei ◽  
...  
Keyword(s):  
Complex Function ◽  
Synthetic Data ◽  
Velocity Model ◽  
High Amplitude ◽  
Frequency Noise ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Time Migration ◽  
Wavefield Decomposition

In the implementation of migration of multiples, reverse time migration (RTM) is superior to other migration algorithms because it can handle steeply dipping structures and offer high-resolution images of the complex subsurface. However, the RTM results using two-way wave equation contain high-amplitude, low-frequency noise and false images generated by improper wave paths in migration velocity model with sharp velocity interfaces or strong velocity gradients. To improve the imaging quality in RTM of multiples, we separate the upgoing and downgoing waves in the propagation of source and receiver wavefields. A complex function involved with the Hilbert transform is used in wavefield decomposition. Our approach is cost effective and avoids the large storage of wavefield snapshots required by the conventional wavefield separation technique. We applied migration of multiples with wavefield decomposition on a simple two-layer model and the Sigsbee 2B synthetic data set. Our results demonstrate that the proposed approach can improve the image generated by migration of multiples significantly.

Fast 3D target-oriented reverse-time datuming

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCA141-WCA151 ◽  
Author(s):  
Shuqian Dong ◽  
Yi Luo ◽  
Xiang Xiao ◽  
Sergio Chávez-Pérez ◽  
Gerard T. Schuster
Keyword(s):  
Synthetic Data ◽  
Data Sets ◽  
Target Area ◽  
Complex Structures ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Salt Domes ◽  
Time Migration ◽  
Subsalt Imaging

Imaging of subsalt sediments is a challenge for traditional migration methods such as Kirchhoff and one-way wave-equation migration. Consequently, the more accurate two-way method of reverse-time migration (RTM) is preferred for subsalt imaging, but its use can be limited by high computation cost. To overcome this problem, a 3D target-oriented reverse-time datuming (RTD) method is presented, which can generate redatumed data economically in target areas beneath complex structures such as salt domes. The redatumed data in the target area then can be migrated inexpensively using a traditional migration method. If the target area is much smaller than the acquisition area, computation costs are reduced significantly by the use of a novel bottom-up strategy to calculate the extrapolated Green’s functions. Target-oriented RTD is tested on 2D and 3D SEG/EAGE synthetic data sets and a 3D field data set from the Gulf of Mexico. Results show that target-oriented RTD combined with standard migration can image sediments beneath complex structures accurately with much less calculation effort than full volume RTM. The requirement is that the area over the target zone is smaller than that of the acquisition survey.

Reverse time migration of multiples: Eliminating migration artifacts in angle domain common image gathers

Geophysics ◽  
2014 ◽  
Vol 79 (6) ◽  
pp. S263-S270 ◽  
Author(s):  
Yibo Wang ◽  
Yikang Zheng ◽  
Lele Zhang ◽  
Xu Chang ◽  
Zhenxing Yao
Keyword(s):  
Free Surface ◽  
Radon Transform ◽  
Synthetic Data ◽  
Velocity Model ◽  
Migration Velocity ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Time Migration ◽  
Nonzero Curvature

Free-surface-related multiples are usually regarded as noise in conventional seismic processing. However, they can provide extra illumination of the subsurface and thus have been used in migration procedures, e.g., in one- and two-way wave-equation migrations. The disadvantage of the migration of multiples is the migration artifacts generated by the crosscorrelation of different seismic events, e.g., primaries and second-order free-surface-related multiples, so the effective elimination of migration artifacts is crucial for migration of multiples. The angle domain common image gather (ADCIG) is a suitable domain for testing the correctness of a migration velocity model. When the migration velocity model is correct, all the events in ADCIGs should be flat, and this provides a criterion for removing the migration artifacts. Our approach first obtains ADCIGs during reverse time migration and then applies a high-resolution parabolic Radon transform to all ADCIGs. By doing so, most migration artifacts will reside in the nonzero curvature regions in the Radon domain, and then a muting procedure can be implemented to remove the data components outside the vicinity of zero curvature. After the application of an adjoint Radon transform, the filtered ADCIGs are obtained and the final denoised migration result is generated by stacking all filtered ADCIGs. A three-flat-layer velocity model and the Marmousi synthetic data set are used for numerical experiments. The numerical results revealed that the proposed approach can eliminate most artifacts generated by migration of multiples when the migration velocity model is correct.

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.

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.

Dirty salt velocity inversion: The road to a clearer subsalt image

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. WB169-WB174 ◽  
Author(s):  
Shuo Ji ◽  
Tony Huang ◽  
Kang Fu ◽  
Zhengxue Li
Keyword(s):  
Model Building ◽  
Synthetic Data ◽  
Velocity Model ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Velocity Inversion ◽  
Time Migration ◽  
And Migration ◽  
Subsalt Imaging

For deep-water Gulf of Mexico, accurate salt geometry is critical to subsalt imaging. This requires the definition of both external and internal salt geometries. In recent years, external salt geometry (i.e., boundaries between allochthonous salt and background sediment) has improved a great deal due to advances in acquisition, velocity model building, and migration algorithms. But when it comes to defining internal salt geometry (i.e., intrasalt inclusions or dirty salt), no efficient method has yet been developed. In common industry practices, intrasalt inclusions (and thus their velocity anomalies) are generally ignored during the model building stages. However, as external salt geometries reach higher levels of accuracy, it becomes more important to consider the once-ignored effects of dirty salt. We have developed a reflectivity-based approach for dirty salt velocity inversion. This method takes true-amplitude reverse time migration stack volumes as input, then estimates the dirty salt velocity based on reflectivity under a 1D assumption. Results from a 2D synthetic data set and a real 3D Wide Azimuth data set demonstrated that the reflectivity inversion scheme significantly improves the subsalt image for certain areas. In general, we believe that this method produces a better salt model than the traditional clean salt velocity approach.

Simultaneous reverse time migration of primaries and free-surface related multiples without multiple prediction

Geophysics ◽  
2014 ◽  
Vol 79 (1) ◽  
pp. S1-S9 ◽  
Author(s):  
Yibo Wang ◽  
Xu Chang ◽  
Hao Hu
Keyword(s):  
Free Surface ◽  
Field Data ◽  
Synthetic Data ◽  
Velocity Model ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Imaging Condition ◽  
Time Migration ◽  
Multiple Prediction

Prestack reverse time migration (RTM) is usually regarded as an accurate imaging tool and has been widely used in exploration. Conventional RTM only uses primaries and treats free-surface related multiples as noise; however, free-surface related multiples can sometimes provide extra illumination of the subsurface, and this information could be used in migration procedures. There are many migration methods using free-surface related multiples, but most approaches need to predict multiples, which is time consuming and prone to error. We discovered a new RTM approach that uses the primaries and the free-surface related multiples simultaneously. Compared with migration methods that only use free-surface related multiples, the proposed approach can provide comparable migration results and does not need multiple predictions. In our approach, the source function in conventional RTM was replaced with recorded field data including primaries and free-surface related multiples, together with a synthetic wavelet; the back-propagated primaries in the conventional RTM were replaced with complete recorded field data. The imaging condition of the proposed approach was the same as the crosscorrelation imaging condition of conventional RTM. A three-layer velocity model with scatterers and the Sigsbee 2B synthetic data set were used for numerical experiments. The numerical results showed that the proposed approach can cover a wider range of the subsurface and provide better illumination compared with conventional RTM. The proposed approach was easy to implement and avoided tedious multiple prediction; it might be significant for general complex subsurface imaging.

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.

An implicit stabilization strategy for Q-compensated reverse time migration

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. S169-S183
Author(s):  
Hanming Chen ◽  
Hui Zhou ◽  
Ying Rao
Keyword(s):  
Robust Stabilization ◽  
Synthetic Data ◽  
Frequency Noise ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Time Migration ◽  
Wavefield Extrapolation ◽  
Amplitude Compensation ◽  
Seismic Images

Reverse time migration with [Formula: see text] compensation ([Formula: see text]-RTM) is an effective approach to enhance the resolution of seismic images because it retrieves the amplitude loss and phase distortion induced by the viscosity of media. According to the crosscorrelation imaging condition, [Formula: see text]-RTM requires compensation for the amplitude loss in the propagation paths of source and receiver wavefields, which can be realized by solving an amplitude-boosted wave equation. However, the amplitude-boosted simulations suffer from numerical instability due to the amplification of high-frequency noise. We have developed a robust stabilization strategy for [Formula: see text]-RTM by incorporating a time-variant filter into the amplitude-boosted wavefield extrapolation step. We modify the Fourier spectrum of the operator that controls the amplitude compensation to be time variant, and we add to the spectrum a stabilization factor. Doing so, we integrate the time-variant filter into the viscoacoustic wave propagator implicitly, and we avoid any explicit filtering operation in [Formula: see text]-RTM. We verify the robustness of this stabilized [Formula: see text]-RTM with two synthetic data examples. We also apply this technique to a field data set to demonstrate the imaging improvements compared to an acoustic RTM and a more traditional [Formula: see text]-RTM method.

Reverse time migration in tilted transversely isotropic media

2020 ◽  
Vol 38 (2) ◽  
Author(s):  
Razec Cezar Sampaio Pinto da Silva Torres ◽  
Leandro Di Bartolo
Keyword(s):  
Seismic Anisotropy ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Computer Clusters ◽  
Time Migration ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Tti Media

ABSTRACT. Reverse time migration (RTM) is one of the most powerful methods used to generate images of the subsurface. The RTM was proposed in the early 1980s, but only recently it has been routinely used in exploratory projects involving complex geology – Brazilian pre-salt, for example. Because the method uses the two-way wave equation, RTM is able to correctly image any kind of geological environment (simple or complex), including those with anisotropy. On the other hand, RTM is computationally expensive and requires the use of computer clusters. This paper proposes to investigate the influence of anisotropy on seismic imaging through the application of RTM for tilted transversely isotropic (TTI) media in pre-stack synthetic data. This work presents in detail how to implement RTM for TTI media, addressing the main issues and specific details, e.g., the computational resources required. A couple of simple models results are presented, including the application to a BP TTI 2007 benchmark model.Keywords: finite differences, wave numerical modeling, seismic anisotropy. Migração reversa no tempo em meios transversalmente isotrópicos inclinadosRESUMO. A migração reversa no tempo (RTM) é um dos mais poderosos métodos utilizados para gerar imagens da subsuperfície. A RTM foi proposta no início da década de 80, mas apenas recentemente tem sido rotineiramente utilizada em projetos exploratórios envolvendo geologia complexa, em especial no pré-sal brasileiro. Por ser um método que utiliza a equação completa da onda, qualquer configuração do meio geológico pode ser corretamente tratada, em especial na presença de anisotropia. Por outro lado, a RTM é dispendiosa computacionalmente e requer o uso de clusters de computadores por parte da indústria. Este artigo apresenta em detalhes uma implementação da RTM para meios transversalmente isotrópicos inclinados (TTI), abordando as principais dificuldades na sua implementação, além dos recursos computacionais exigidos. O algoritmo desenvolvido é aplicado a casos simples e a um benchmark padrão, conhecido como BP TTI 2007.Palavras-chave: diferenças finitas, modelagem numérica de ondas, anisotropia sísmica.

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