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 step-length formula for correlative least-squares reverse time migration

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. S221-S238 ◽  
Author(s):  
Youshan Liu ◽  
Jiwen Teng ◽  
Tao Xu ◽  
Zhiming Bai ◽  
Haiqiang Lan ◽  
...  
Keyword(s):  
Objective Function ◽  
Least Squares ◽  
Step Length ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Step Size ◽  
Time Migration ◽  
Seismic Records ◽  
Complex Models ◽  
Analytical Step

In correlative least-squares reverse time migration (CLSRTM), the estimation of the optimal step size is usually determined by fitting a parabola and finding its minimum; it involves at least two times extra reading of all seismic records, which significantly lowers the efficiency of the algorithm. To improve the efficiency of the CLSRTM algorithm, we have deduced an analytical step-length (ASL) formula based on the linear property of the demigration operator. Numerical examples performed with the data synthetized by the Marmousi and Sigsbee2A models were used to test its validity. In complex models with imperfect migration velocity, such as the Sigabee2A model, our formula makes the value of the objective function converges to a much smaller minimum. Additional numerical tests performed with the data either acquired irregularly or contaminated by different noise levels verify the robustness of the ASL formula. Compared with the commonly used parabolic search method, the ASL formula is much more efficient because it is free from an extra estimation of the value of the objective function.

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.

Comparison between Born and Kirchhoff operators for least-squares reverse time migration and the constraint of the propagation of the background wavefield

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. R725-R739 ◽  
Author(s):  
Kai Yang ◽  
Jianfeng Zhang
Keyword(s):  
Least Squares ◽  
Born Approximation ◽  
Computational Cost ◽  
Stopping Time ◽  
Step Length ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Recording Time ◽  
Time Migration ◽  
Computational Strategy

The Born approximation and the Kirchhoff approximation are two frameworks that are extensively used in solving seismic migration/inversion problems. Both approximations assume a linear relationship between the primary reflected/scattered data to the corresponding physical model. However, different approximations result in different behaviors. For least-squares reverse time migration (LSRTM), most of the algorithms are constructed based on Born approximation. We have constructed a pair of Kirchhoff modeling and migration operators based on the Born modeling operator and the connection between the perturbation model and the reflectivity model, and then we compared the different performances between Born and Kirchhoff operators for LSRTM. Numerical examples on Marmousi model and SEAM 2D salt model indicate that LSRTM with Kirchhoff operators is a better alternative to that with Born operators for imaging complex structures. To reduce the computational cost, we also investigate a strategy by restricting the propagation of the background wavefield to a stopping time rather than the maximum recording time. And this stopping time can be chosen as half of the maximum recording time. This computational strategy can be used in LSRTM procedures of predicting the primary reflected data, calculating the step length, and computing the gradient. Theoretical analyses and numerical experiments are given to justify this computational strategy for LSRTM.

Source-independent elastic least-squares reverse time migration

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. S1-S16 ◽  
Author(s):  
Jinwei Fang ◽  
Hui Zhou ◽  
Hanming Chen ◽  
Ning Wang ◽  
Yufeng Wang ◽  
...  
Keyword(s):  
Objective Function ◽  
Least Squares ◽  
Noisy Data ◽  
Simulated Data ◽  
High Accuracy ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Numerical Examples ◽  
Time Migration ◽  
Seismic Images

Elastic least-squares reverse time migration (LSRTM) has been developed recently for its high accuracy imaging ability. The theory is based on minimizing the misfit between the observed and simulated data by an iterative algorithm to refine seismic images toward the true reflectivity. We have developed a new elastic LSRTM with the same modeling equations for source and receiver wavefield extrapolations, except for their source terms. The LSRTM has a natural advantage to solve the source and receiver wavefields using the same modeling system; thus, it is easy to implement LSRTM. In practice, it is difficult to obtain an accurate source wavelet, so a convolution-based objective function is used in our source-independent elastic LSRTM. Such an objective function can relax the requirement of an accurate wavelet, and improve the robustness of the inverse problem in the presence of noise. The numerical examples indicate that our method has the ability to recover the reflectivity models with an incorrect source wavelet from noisy data.

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.

Least-squares reverse time migration with an angle-dependent weighting factor

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. S299-S310 ◽  
Author(s):  
Kai Yang ◽  
Jianfeng Zhang
Keyword(s):  
Least Squares ◽  
Step Length ◽  
Weighting Factor ◽  
Deep Part ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Pass Filter ◽  
Time Migration ◽  
L2 Norm ◽  
The Right

Least-squares reverse time migration (LSRTM) produces higher quality images than conventional RTM. However, directly using the standard gradient formula, the inverted images suffer from low-wavenumber noise. Using a simple high-pass filter on the gradient can alleviate the effect of the low-wavenumber noise. But, owing to the illumination issue, the amplitudes are not balanced and in the deep part they are often weak. These two issues can be mitigated by the iterative approach, but it needs more iterations. We introduced an angle-dependent weighting factor to weight the gradient of LSRTM to suppress the low-wavenumber noise and also to emphasize the gradient in the deep part. An optimal step length for the L2-norm objective function is also presented to scale the gradient to the right order. Two numerical examples performed with the data synthesized on the Sigsbee2A and Marmousi models indicate that when using this weighted gradient combined with the preconditioned [Formula: see text]-BFGS algorithm with the optimal step length, only a few iterations can achieve satisfying results.

scholarly journals One-step data-domain least-squares reverse time migration

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. R361-R368 ◽  
Author(s):  
Qiancheng Liu ◽  
Daniel Peter
Keyword(s):  
Least Squares ◽  
Wiener Filter ◽  
Real Data ◽  
Image Resolution ◽  
Inversion Algorithm ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Iterative Inversion ◽  
One Step

Least-squares reverse time migration (LSRTM) is an iterative inversion algorithm for estimating the broadband-wavenumber reflectivity model. Although it produces superior results compared with conventional reverse time migration (RTM), LSRTM is computationally expensive. We have developed a one-step LSRTM method by considering the demigrated and observed data to design a deblurring preconditioner in the data domain using the Wiener filter. For the Wiener filtering, we further use a stabilized division algorithm via the Taylor expansion. The preconditioned observed data are then remigrated to obtain a deblurred image. The total cost of this method is about two RTMs. Through synthetic and real data experiments, we see that one-step LSRTM is able to enhance image resolution and balance source illumination at low computational costs.

scholarly journals A GPU implementation of least-squares reverse time migration

2021 ◽  
Vol 1719 (1) ◽  
pp. 012030
Author(s):  
Phudit Sombutsirinun ◽  
Chaiwoot Boonyasiriwat
Keyword(s):  
Least Squares ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Gpu Implementation
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