Improving the least-squares image by using angle information to avoid cycle skipping

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. S581-S598 ◽  
Author(s):  
Bin He ◽  
Yike Liu ◽  
Yanbao Zhang
Keyword(s):  
Least Squares ◽  
Real Data ◽  
Velocity Model ◽  
Migration Velocity ◽  
Common Source ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Propagation Angle ◽  
Time Migration ◽  
The Common

In the past few decades, the least-squares reverse time migration (LSRTM) algorithm has been widely used to enhance images of complex subsurface structures by minimizing the data misfit function between the predicted and observed seismic data. However, this algorithm is sensitive to the accuracy of the migration velocity model, which, in the case of real data applications (generally obtained via tomography), always deviates from the true velocity model. Therefore, conventional LSRTM faces a cycle-skipping problem caused by a smeared image when using an inaccurate migration velocity model. To address the cycle-skipping problem, we have introduced an angle-domain LSRTM algorithm. Unlike the conventional LSRTM algorithm, our method updates the common source-propagation angle image gathers rather than the stacked image. An extended Born modeling operator in the common source-propagation angle domain is was derived, which reproduced kinematically accurate data in the presence of velocity errors. Our method can provide more focused images with high resolution as well as angle-domain common-image gathers (ADCIGs) with enhanced resolution and balanced amplitudes. However, because the velocity model is not updated, the provided image can have errors in depth. Synthetic and field examples are used to verify that our method can robustly improve the quality of the ADCIGs and the finally stacked images with affordable computational costs in the presence of velocity errors.

Least-squares reverse time migration in the presence of velocity errors

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. S567-S580 ◽  
Author(s):  
Jizhong Yang ◽  
Yunyue Elita Li ◽  
Arthur Cheng ◽  
Yuzhu Liu ◽  
Liangguo Dong
Keyword(s):  
Least Squares ◽  
Velocity Model ◽  
Migration Velocity ◽  
Resolution Limit ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Large Velocity ◽  
Iterative Inversion ◽  
Inversion Procedure

Least-squares reverse time migration (LSRTM), which aims to match the modeled data with the observed data in an iterative inversion procedure, is very sensitive to the accuracy of the migration velocity model. If the migration velocity model contains errors, the final migration image may be defocused and incoherent. We have used an LSRTM scheme based on the subsurface offset extended imaging condition, least-squares extended reverse time migration (LSERTM), to provide a better solution when large velocity errors exist. By introducing an extra dimension in the image space, LSERTM can fit the observed data even when significant errors are present in the migration velocity model. We further investigate this property and find that after stacking the extended migration images along the subsurface offset axis within the theoretical lateral resolution limit, we can obtain an image with better coherency and fewer migration artifacts. Using multiple numerical examples, we demonstrate that our method provides superior inversion results compared to conventional LSRTM when the bulk velocity errors are as large as 10%.

Least-squares reverse time migration of multiples in viscoacoustic media

Geophysics ◽  
2020 ◽  
Vol 85 (5) ◽  
pp. S285-S297
Author(s):  
Zhina Li ◽  
Zhenchun Li ◽  
Qingqing Li ◽  
Qingyang Li ◽  
Miaomiao Sun ◽  
...  
Keyword(s):  
Least Squares ◽  
Signal To Noise Ratio ◽  
Real Data ◽  
Velocity Model ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Q Model ◽  
Standard Linear Solid ◽  
Standard Linear

The migration of multiples can provide complementary information about the subsurface, but crosstalk artifacts caused by the interference between different-order multiples reduce its reliability. To mitigate the crosstalk artifacts, least-squares reverse time migration (LSRTM) of multiples is suggested by some researchers. Multiples are more affected by attenuation than primaries because of the longer travel path. To avoid incorrect waveform matching during the inversion, we propose to include viscosity in the LSRTM implementation. A method of LSRTM of multiples is introduced based on a viscoacoustic wave equation, which is derived from the generalized standard linear solid model. The merit of the proposed method is that it not only compensates for the amplitude loss and phase change, which cannot be achieved by traditional RTM and LSRTM of multiples, but it also provides more information about the subsurface with fewer crosstalk artifacts by using multiples compared with the viscoacoustic LSRTM of primaries. Tests on sensitivity to the errors in the velocity model, the Q model, and the separated multiples reveal that accurate models and input multiples are vital to the image quality. Numerical tests on synthetic models and real data demonstrate the advantages of our approach in improving the quality of the image in terms of amplitude balancing and signal-to-noise ratio.

Joint least-squares reverse time migration of primary and prismatic waves

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. S29-S40 ◽  
Author(s):  
Jizhong Yang ◽  
Yuzhu Liu ◽  
Yunyue Elita Li ◽  
Arthur Cheng ◽  
Liangguo Dong ◽  
...  
Keyword(s):  
Least Squares ◽  
Nonlinear Least Squares ◽  
Velocity Model ◽  
Migration Velocity ◽  
Gradient Algorithm ◽  
Normal Equation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Recorded Data

Direct imaging of the steeply dipping structures is challenging for conventional reverse time migration (RTM), especially when there are no strong reflectors in the migration velocity model. To address this issue, we have enhanced the imaging of the steeply dipping structures by incorporating the prismatic waves. We formulate the imaging problem in a nonlinear least-squares optimization framework because the prismatic waves cannot be linearly mapped from the model perturbation. Primary and prismatic waves are jointly imaged to provide a single consistent image that includes structures illuminated by both types of waves, avoiding the complexities in scaling and/or interpreting primary and prismatic images separately. A conjugate gradient algorithm is used to iteratively solve the least-squares normal equation. This inversion procedure can become unstable if directly using the recorded data for migration because it is hindered by the crosstalk caused by imaging primary waves with the prismatic imaging operator. Therefore, we isolate the prismatic waves from the recorded data and image them with the prismatic imaging operator. Our scheme only requires a kinematically accurate and smooth migration velocity model, without the need to explicitly embed the strong reflectors in the migration velocity model. Realistic 2D numerical examples demonstrate that our method can resolve the steeply dipping structures much better than conventional least-squares RTM of primary waves.

Benefits of inserting salt stratification to detail velocity model prior to least-squares reverse-time migration

2021 ◽  
pp. 104469
Author(s):  
A. Maul ◽  
A. Bulcão ◽  
R.M. Dias ◽  
B. Pereira-Dias ◽  
L. Teixeira ◽  
...  
Keyword(s):  
Least Squares ◽  
Velocity Model ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration

Angle-domain common-image gathers from plane-wave least-squares reverse time migration

Geophysics ◽  
2021 ◽  
pp. 1-60
Author(s):  
Chuang Li ◽  
Zhaoqi Gao ◽  
Jinghuai Gao ◽  
Feipeng Li ◽  
Tao Yang
Keyword(s):  
Inverse Problem ◽  
Plane Wave ◽  
Least Squares ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Migration Velocity Analysis ◽  
Amplitude Versus

Angle-domain common-image gathers (ADCIGs) that can be used for migration velocity analysis and amplitude versus angle analysis are important for seismic exploration. However, because of limited acquisition geometry and seismic frequency band, the ADCIGs extracted by reverse time migration (RTM) suffer from illumination gaps, migration artifacts, and low resolution. We have developed a reflection angle-domain pseudo-extended plane-wave least-squares RTM method for obtaining high-quality ADCIGs. We build the mapping relations between the ADCIGs and the plane-wave sections using an angle-domain pseudo-extended Born modeling operator and an adjoint operator, based on which we formulate the extraction of ADCIGs as an inverse problem. The inverse problem is iteratively solved by a preconditioned stochastic conjugate gradient method, allowing for reduction in computational cost by migrating only a subset instead of the whole dataset and improving image quality thanks to preconditioners. Numerical tests on synthetic and field data verify that the proposed method can compensate for illumination gaps, suppress migration artifacts, and improve resolution of the ADCIGs and the stacked images. Therefore, compared with RTM, the proposed method provides a more reliable input for migration velocity analysis and amplitude versus angle analysis. Moreover, it also provides much better stacked images for seismic interpretation.

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.

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.

A stable and practical implementation of least-squares reverse time migration

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. V23-V31 ◽  
Author(s):  
Yu Zhang ◽  
Lian Duan ◽  
Yi Xie
Keyword(s):  
Least Squares ◽  
Real Data ◽  
Descent Method ◽  
Steepest Descent Method ◽  
Practical Implementation ◽  
Reverse Time ◽  
Crosstalk Noise ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Enhanced Resolution

By adapting reverse time migration (RTM) and demigration as the migration and modeling operators to maximize the crosscorrelation between the simulated and the acquired seismic data, we introduced a new practical least-squares RTM (LSRTM) scheme and derived a steepest descent method in seeking the optimal image. Through synthetic and real data experiments, we determined that the proposed LSRTM provided high-quality images with balanced amplitudes, improved focusing, and enhanced resolution. The method was also capable of removing free surface ghosts caused by towed streamer acquisition, filling the structures and reducing crosstalk noise associated with simultaneous shooting.

Least-squares migration with primary- and multiple-guided weighting matrices

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. S171-S185 ◽  
Author(s):  
Chuang Li ◽  
Jianping Huang ◽  
Zhenchun Li ◽  
Han Yu ◽  
Rongrong Wang
Keyword(s):  
Free Surface ◽  
Least Squares ◽  
Seismic Data ◽  
Synthetic Data ◽  
Velocity Model ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Multiple Reflections ◽  
Time Migration ◽  
Least Squares Migration

Least-squares migration (LSM) of seismic data is supposed to produce images of subsurface structures with better quality than standard migration if we have an accurate migration velocity model. However, LSM suffers from data mismatch problems and migration artifacts when noise pollutes the recorded profiles. This study has developed a reweighted least-squares reverse time migration (RWLSRTM) method to overcome the problems caused by such noise. We first verify that spiky noise and free-surface multiples lead to the mismatch problems and should be eliminated from the data residual. The primary- and multiple-guided weighting matrices are then derived for RWLSRTM to reduce the noise in the data residual. The weighting matrices impose constraints on the data residual such that spiky noise and free-surface multiple reflections are reduced whereas primary reflections are preserved. The weights for spiky noise and multiple reflections are controlled by a dynamic threshold parameter decreasing with iterations for better results. Finally, we use an iteratively reweighted least-squares algorithm to minimize the weighted data residual. We conduct numerical tests using the synthetic data and compared the results of this method with the results of standard LSRTM. The results suggest that RWLSRTM is more robust than standard LSRTM when the seismic data contain spiky noise and multiple reflections. Moreover, our method not only suppresses the migration artifacts, but it also accelerates the convergence.

Least-squares reverse time migration using convolutional neural networks

Geophysics ◽  
2021 ◽  
pp. 1-92
Author(s):  
Wei Zhang ◽  
Jinghuai Gao ◽  
Tao Yang ◽  
Xiudi Jiang ◽  
Wenbo Sun
Keyword(s):  
Neural Networks ◽  
High Resolution ◽  
Least Squares ◽  
Convolutional Neural Networks ◽  
Input Data ◽  
Velocity Model ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Reflection Image

Least-squares reverse time migration (LSRTM) has the potential to reconstruct a high-resolution image of subsurface reflectivity. However, the current data-domain LSRTM approach, which iteratively updates the subsurface reflectivity by minimizing the data residuals, is a computationally expensive task. To alleviate this problem and improve imaging quality, we develop a LSRTM approach using convolutional neural networks (CNNs), which is referred to as CNN-LSRTM. Specifically, the LSRTM problem can be implemented via a gradient-like iterative scheme, in which the updating component in each iteration is learned via a CNN model. In order to make the most of observation data and migration velocity model at hand, we utilize the common-source RTM image, the stacked RTM image, and the migration velocity model rather than only the stacked RTM image as the input data of CNN. We have successfully trained the constructed CNN model on the training data sets with a total of 5000 randomly layered and fault models. Based on the well-trained CNN model, we have proved that the proposed approach can efficiently recover the high-resolution reflection image for the layered, fault, and overthrust models. Through a marine field data experiment, it can determine the benefit of our constructed CNN model in terms of computational efficiency. In addition, we analyze the influence of input data of the constructed CNN model on the reconstruction quality of the reflection image.

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