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.

scholarly journals Plane-wave least-squares reverse-time migration

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. S165-S177 ◽  
Author(s):  
Wei Dai ◽  
Gerard T. Schuster
Keyword(s):  
Phase Shift ◽  
Plane Wave ◽  
Least Squares ◽  
Plane Waves ◽  
Migration Velocity ◽  
Stable Convergence ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Time Migration

A plane-wave least-squares reverse-time migration (LSRTM) is formulated with a new parameterization, where the migration image of each shot gather is updated separately and an ensemble of prestack images is produced along with common image gathers. The merits of plane-wave prestack LSRTM are the following: (1) plane-wave prestack LSRTM can sometimes offer stable convergence even when the migration velocity has bulk errors of up to 5%; (2) to significantly reduce computation cost, linear phase-shift encoding is applied to hundreds of shot gathers to produce dozens of plane waves. Unlike phase-shift encoding with random time shifts applied to each shot gather, plane-wave encoding can be effectively applied to data with a marine streamer geometry. (3) Plane-wave prestack LSRTM can provide higher-quality images than standard reverse-time migration. Numerical tests on the Marmousi2 model and a marine field data set are performed to illustrate the benefits of plane-wave LSRTM. Empirical results show that LSRTM in the plane-wave domain, compared to standard reverse-time migration, produces images efficiently with fewer artifacts and better spatial resolution. Moreover, the prestack image ensemble accommodates more unknowns to makes it more robust than conventional least-squares migration in the presence of migration velocity errors.

scholarly journals Least-squares reverse time migration of marine data with frequency-selection encoding

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. S233-S242 ◽  
Author(s):  
Wei Dai ◽  
Yunsong Huang ◽  
Gerard T. Schuster
Keyword(s):  
Least Squares ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Frequency Selection ◽  
Time Migration ◽  
Order Of Magnitude ◽  
Marine Data ◽  
And Migration ◽  
Encoding Method

The phase-encoding technique can sometimes increase the efficiency of the least-squares reverse time migration (LSRTM) by more than one order of magnitude. However, traditional random encoding functions require all the encoded shots to share the same receiver locations, thus limiting the usage to seismic surveys with a fixed spread geometry. We implement a frequency-selection encoding strategy that accommodates data with a marine streamer geometry. The encoding functions are delta functions in the frequency domain, so that all the encoded shots have unique nonoverlapping frequency content, and the receivers can distinguish the wavefield from each shot with a unique frequency band. Because the encoding functions are orthogonal to each other, there will be no crosstalk between different shots during modeling and migration. With the frequency-selection encoding method, the computational efficiency of LSRTM is increased so that its cost is comparable to conventional RTM for the Marmousi2 model and a marine data set recorded in the Gulf of Mexico. With more iterations, the LSRTM image quality is further improved by suppressing migration artifacts, balancing reflector amplitudes, and enhancing the spatial resolution. We conclude that LSRTM with frequency-selection is an efficient migration method that can sometimes produce more focused images than conventional RTM.

3D acoustic least-squares reverse time migration using the energy norm

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. S261-S270 ◽  
Author(s):  
Daniel Rocha ◽  
Paul Sava ◽  
Antoine Guitton
Keyword(s):  
Least Squares ◽  
Convergence Rates ◽  
Energy Norm ◽  
Ocean Bottom ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Image Domain ◽  
Time Migration ◽  
And Migration

We have developed a least-squares reverse time migration (LSRTM) method that uses an energy-based imaging condition to obtain faster convergence rates when compared with similar methods based on conventional imaging conditions. To achieve our goal, we also define a linearized modeling operator that is the proper adjoint of the energy migration operator. Our modeling and migration operators use spatial and temporal derivatives that attenuate imaging artifacts and deliver a better representation of the reflectivity and scattered wavefields. We applied the method to two Gulf of Mexico field data sets: a 2D towed-streamer benchmark data set and a 3D ocean-bottom node data set. We found LSRTM resolution improvement relative to RTM images, as well as the superior convergence rate obtained by the linearized modeling and migration operators based on the energy norm, coupled with inversion preconditioning using image-domain nonstationary matching filters.

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.

Prestack correlative least-squares reverse time migration

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. S159-S172 ◽  
Author(s):  
Xuejian Liu ◽  
Yike Liu ◽  
Huiyi Lu ◽  
Hao Hu ◽  
Majid Khan
Keyword(s):  
Objective Function ◽  
Least Squares ◽  
Step Length ◽  
Inversion Algorithm ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Initial Image ◽  
Data Set ◽  
Time Migration ◽  
Gradient Descent Algorithm

In the correlative least-squares reverse time migration (CLSRTM) scheme, a stacked image is updated using a gradient-based inversion algorithm. However, CLSRTM experiences the incoherent stacking of different shots during each iteration due to the use of an imperfect velocity, which leads to image smearing. To reduce the sensitivity to velocity errors, we have developed prestack correlative least-squares reverse time migration (PCLSRTM), in which a gradient descent algorithm using a newly defined initial image and an efficiently defined analytical step length is developed to separately seek the optimal image for each shot gather before the final stacking. Furthermore, a weighted objective function is also designed for PCLSRTM, so that the data-domain gradient can avoid a strong truncation effect. Numerical experiments on a three-layer model as well as a marine synthetic and a field data set reveal the merits of PCLSRTM. In the presence of velocity errors, PCLSRTM shows better convergence and provides higher quality images as compared with CLSRTM. With the newly defined initial image, PCLSRTM can effectively handle observed data with unbalanced amplitudes. By using a weighted objective function, PCLSRTM can provide an image with enhanced resolution and balanced amplitude while avoiding many imaging artifacts.

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.

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.

Efficient Gather Domain Least-Squares Reverse Time Migration for Inaccurate Velocity Models

2020 ◽  
Author(s):  
M. Wang ◽  
S. Xu ◽  
H. Zhou ◽  
B. Tang ◽  
A. DeNosaquo ◽  
...  
Keyword(s):  
Least Squares ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Velocity Models ◽  
Time Migration

scholarly journals Elastic least-squares reverse time migration

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. S143-S157 ◽  
Author(s):  
Zongcai Feng ◽  
Gerard T. Schuster
Keyword(s):  
Least Squares ◽  
Synthetic Data ◽  
Adjoint Equations ◽  
Accurate Estimation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Velocity Models ◽  
Time Migration ◽  
Wave Migration

We use elastic least-squares reverse time migration (LSRTM) to invert for the reflectivity images of P- and S-wave impedances. Elastic LSRTM solves the linearized elastic-wave equations for forward modeling and the adjoint equations for backpropagating the residual wavefield at each iteration. Numerical tests on synthetic data and field data reveal the advantages of elastic LSRTM over elastic reverse time migration (RTM) and acoustic LSRTM. For our examples, the elastic LSRTM images have better resolution and amplitude balancing, fewer artifacts, and less crosstalk compared with the elastic RTM images. The images are also better focused and have better reflector continuity for steeply dipping events compared to the acoustic LSRTM images. Similar to conventional least-squares migration, elastic LSRTM also requires an accurate estimation of the P- and S-wave migration velocity models. However, the problem remains that, when there are moderate errors in the velocity model and strong multiples, LSRTM will produce migration noise stronger than that seen in the RTM images.

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