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 controlled-order multiple reflections

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. S347-S357 ◽  
Author(s):  
Yike Liu ◽  
Xuejian Liu ◽  
Are Osen ◽  
Yu Shao ◽  
Hao Hu ◽  
...  
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Multiple Reflections ◽  
Numerical Tests ◽  
Elimination Algorithm ◽  
Reflection Data ◽  
Time Migration ◽  
Least Squares Migration

Reverse time migration (RTM) using multiples generates inherent crosstalk artifacts due to the interference among multiples of different orders. We have developed a method to remove such crosstalk. This approach first separates the recorded seismic data into primary reflections and multiples using the surface-related multiples elimination algorithm and then isolates the multiples into different orders. We can take any specified, say the [Formula: see text]th, order of multiples data as the incident wave and the next higher order multiples data, ([Formula: see text])th order, as the corresponding primary reflection data for imaging. We have applied the least-squares migration scheme to these two successive orders of multiples. Our method is denoted as least-squares RTM using controlled-order multiples (LSRTM-CM). Our numerical tests demonstrated that LSRTM-CM can significantly improve imaging quality compared with straightforward seismic imaging using multiples without multiples separation.

An exact adjoint operation pair in time extrapolation and its application in least-squares reverse-time migration

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. H27-H33 ◽  
Author(s):  
Jun Ji
Keyword(s):  
Least Squares ◽  
Adjoint Operator ◽  
Synthetic Data ◽  
Forward Modeling ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Product Test ◽  
Least Squares Migration ◽  
Time Extrapolation

To reduce the migration artifacts arising from incomplete data or inaccurate operators instead of migrating data with the adjoint of the forward-modeling operator, a least-squares migration often is considered. Least-squares migration requires a forward-modeling operator and its adjoint. In a derivation of the mathematically correct adjoint operator to a given forward-time-extrapolation modeling operator, the exact adjoint of the derived operator is obtained by formulating an explicit matrix equation for the forward operation and transposing it. The programs that implement the exact adjoint operator pair are verified by the dot-product test. The derived exact adjoint operator turns out to differ from the conventional reverse-time-migration (RTM) operator, an implementation of wavefield extrapolation backward in time. Examples with synthetic data show that migration using the exact adjoint operator gives similar results for a conventional RTM operator and that least-squares RTM is quite successful in reducing most migration artifacts. The least-squares solution using the exact adjoint pair produces a model that fits the data better than one using a conventional RTM operator pair.

Least-squares reverse time migration of multiples

Geophysics ◽  
2014 ◽  
Vol 79 (1) ◽  
pp. S11-S21 ◽  
Author(s):  
Dongliang Zhang ◽  
Gerard T. Schuster
Keyword(s):  
Free Surface ◽  
Least Squares ◽  
Synthetic Data ◽  
Time History ◽  
Ocean Bottom ◽  
Virtual Source ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Sea Bed

The theory of least-squares reverse time migration of multiples (RTMM) is presented. In this method, least squares migration (LSM) is used to image free-surface multiples where the recorded traces are used as the time histories of the virtual sources at the hydrophones and the surface-related multiples are the observed data. For a single source, the entire free-surface becomes an extended virtual source where the downgoing free-surface multiples more fully illuminate the subsurface compared to the primaries. Since each recorded trace is treated as the time history of a virtual source, knowledge of the source wavelet is not required and the ringy time series for each source is automatically deconvolved. If the multiples can be perfectly separated from the primaries, numerical tests on synthetic data for the Sigsbee2B and Marmousi2 models show that least-squares reverse time migration of multiples (LSRTMM) can significantly improve the image quality compared to RTMM or standard reverse time migration (RTM) of primaries. However, if there is imperfect separation and the multiples are strongly interfering with the primaries then LSRTMM images show no significant advantage over the primary migration images. In some cases, they can be of worse quality. Applying LSRTMM to Gulf of Mexico data shows higher signal-to-noise imaging of the salt bottom and top compared to standard RTM images. This is likely attributed to the fact that the target body is just below the sea bed so that the deep water multiples do not have strong interference with the primaries. Migrating a sparsely sampled version of the Marmousi2 ocean bottom seismic data shows that LSM of primaries and LSRTMM provides significantly better imaging than standard RTM. A potential liability of LSRTMM is that multiples require several round trips between the reflector and the free surface, so that high frequencies in the multiples suffer greater attenuation compared to the primary reflections. This can lead to lower resolution in the migration image compared to that computed from primaries. Another liability is that the multiple migration image is more down-dip limited than the standard primaries migration image. Finally, if the surface-related multiple elimination method is imperfect and there are strong multiples interfering with the primaries, then the resulting LSRTMM image can be significantly degraded. We conclude that LSRTMM can be a useful complement, not a replacement, for RTM of primary reflections.

Plane-wave domain least-squares reverse time migration with free-surface multiples

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. S477-S487 ◽  
Author(s):  
Xuejian Liu ◽  
Yike Liu
Keyword(s):  
Free Surface ◽  
Plane Wave ◽  
Least Squares ◽  
Computational Time ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Multiple Reflections ◽  
Time Migration ◽  
Computationally Intensive ◽  
Dynamic Plane

Free-surface multiples have been used in the reverse time migration (RTM) procedure to provide additional subsurface illumination. However, imaging multiple reflections with conventional RTM operators generates many crosstalk artifacts. Least-squares RTM (LSRTM) can be used to iteratively suppress crosstalk artifacts of multiples; however, the method is computationally intensive. By applying the linear Radon transformation to hundreds of shots of acquired data to produce dozens of plane-wave gathers, we have developed plane-wave domain LSRTM with free-surface multiples, which could efficiently provide images from the multiples with the crosstalk artifacts effectively suppressed. The proposed method has high computational efficiency when the dynamic plane-wave encoding scheme is used, in which only one or two plane-wave gathers of multiples are migrated at each iteration. We apply the method to numerical Pluto1.5 data and find that the proposed method can reduce most crosstalk artifacts and enhance spatial resolution, using even less computational time relative to RTM with multiples. Furthermore, joint imaging of primaries and multiples by plane-wave LSRTM can provide broader illumination and higher fold for the subsurface when compared with the imaging process with primaries only.

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.

Elastic least-squares reverse time migration with hybrid l1/l2 misfit function

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. S271-S291 ◽  
Author(s):  
Bingluo Gu ◽  
Zhenchun Li ◽  
Peng Yang ◽  
Wencai Xu ◽  
Jianguang Han
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Synthetic Data ◽  
Adjoint Equations ◽  
P Wave ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
Wave Image

We have developed the theory and synthetic tests of elastic least-squares reverse time migration (ELSRTM). In this method, a least-squares reverse time migration algorithm is used to image multicomponent seismic data based on the first-order elastic velocity-stress wave equation, in which the linearized elastic modeling equations are used for forward modeling and its adjoint equations are derived based on the adjoint-state method for back propagating the data residuals. Also, we have developed another ELSRTM scheme based on the wavefield separation technique, in which the P-wave image is obtained using P-wave forward and adjoint wavefields and the S-wave image is obtained using P-wave forward and S-wave adjoint wavefields. In this way, the crosstalk artifacts can be minimized to a significant extent. In general, seismic data inevitably contain noise. We apply the hybrid [Formula: see text] misfit function to the ELSRTM algorithm to improve the robustness of our ELSRTM to noise. Numerical tests on synthetic data reveal that our ELSRTM, when compared with elastic reverse time migration, can produce images with higher spatial resolution, more-balanced amplitudes, and fewer artifacts. Moreover, the hybrid [Formula: see text] misfit function makes the ELSRTM more robust than the [Formula: see text] misfit function in the presence of noise.

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.

Fast least-squares reverse time migration of VSP free-surface multiples with dynamic phase-encoding schemes

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. S321-S332 ◽  
Author(s):  
Xuejian Liu ◽  
Yike Liu ◽  
Majid Khan
Keyword(s):  
Free Surface ◽  
Least Squares ◽  
Computational Cost ◽  
Seismic Profile ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Multiple Reflections ◽  
Phase Encoding ◽  
Time Migration ◽  
Migration Method

For vertical seismic profile (VSP), free-surface multiples can provide much wider subsurface illumination when compared with primaries. However, migration of multiple reflections generates not only the desired image of reflection interfaces but also many crosstalk artifacts. Therefore, the least-squares reverse time migration method is used to image the VSP downgoing free-surface multiples (receiver-side ghosts) and iteratively suppress crosstalks, in which full downgoing data (including direct waves) and downgoing multiples are used as sources and observed data, respectively. To reduce the computational cost, we have developed the simultaneous imaging of different common-receiver gathers that are dynamically blended together with iterations through the altered realizations of the phase-encoding function. Relative to the popular encoding function with a combination of random time delays and polarities, only the random polarities can be applied for further increasing the computational efficiency. Synthetic experiments on Sigsbee2B and Pluto1.5 models indicate that the proposed method can effectively eliminate crosstalk artifacts and improve imaging resolution while calculated even more efficiently than reverse time migration of VSP ghosts.

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

Least-squares reverse time migration via linearized waveform inversion using a Wasserstein metric

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. S411-S423
Author(s):  
Peng Yong ◽  
Jianping Huang ◽  
Zhenchun Li ◽  
Wenyuan Liao ◽  
Luping Qu
Keyword(s):  
Least Squares ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Gradient Algorithm ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Wasserstein Metric ◽  
Time Migration ◽  
Imaging Results ◽  
Primal Dual

Least-squares reverse time migration (LSRTM), an effective tool for imaging the structures of the earth from seismograms, can be characterized as a linearized waveform inversion problem. We have investigated the performance of three minimization functionals as the [Formula: see text] norm, the hybrid [Formula: see text] norm, and the Wasserstein metric ([Formula: see text] metric) for LSRTM. The [Formula: see text] metric used in this study is based on the dynamic formulation of transport problems, and a primal-dual hybrid gradient algorithm is introduced to efficiently compute the [Formula: see text] metric between two seismograms. One-dimensional signal analysis has demonstrated that the [Formula: see text] metric behaves like the [Formula: see text] norm for two amplitude-varied signals. Unlike the [Formula: see text] norm, the [Formula: see text] metric does not suffer from the differentiability issue for null residuals. Numerical examples of the application of three misfit functions to LSRTM on synthetic data have demonstrated that, compared to the [Formula: see text] norm, the hybrid [Formula: see text] norm and [Formula: see text] metric can accelerate LSRTM and are less sensitive to non-Gaussian noise. For the field data application, the [Formula: see text] metric produces the most reliable imaging results. The hybrid [Formula: see text] norm requires tedious trial-and-error tests for the judicious threshold parameter selection. Hence, the more automatic [Formula: see text] metric is recommended as a robust alternative to the customary [Formula: see text] norm for time-domain LSRTM.

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