Improved subsalt images with least-squares reverse time migration

2017 ◽  
Vol 5 (3) ◽  
pp. SN25-SN32 ◽  
Author(s):  
Ping Wang ◽  
Shouting Huang ◽  
Ming Wang
Keyword(s):  
Least Squares ◽  
Field Data ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Lateral Velocity ◽  
Image Domain ◽  
Time Migration ◽  
Iterative Inversion ◽  
Velocity Variations ◽  
Subsalt Imaging

Complex overburdens often distort reservoir images in terms of structural positioning, stratigraphic resolution, and amplitude fidelity. One prime example of a complex overburden is in the deepwater Gulf of Mexico, where thick and irregular layers of remobilized (i.e., allochthonous) salt are situated above prospective reservoir intervals. The highly variant salt layers create large lateral velocity variations that distort wave propagation and the illumination of deeper reservoir targets. In subsalt imaging, tools such as reflection tomography, full-waveform inversion, and detailed salt interpretation are needed to derive a high-resolution velocity model that captures the lateral velocity variations. Once a velocity field is obtained, reverse time migration (RTM) can be applied to restore structural positioning of events below and around the salt. However, RTM by nature is unable to fully recover the reflectivity for desired amplitudes and resolution. This shortcoming is well-recognized by the imaging community, and it has propelled the emergence of least-squares RTM (LSRTM) in recent years. We have investigated how current LSRTM methods perform on subsalt images. First, we compared the formulation of data-domain versus image-domain least-squares migration, as well as methods using single-iteration approximation versus iterative inversion. Then, we examined the resulting subsalt images of several LSRTM methods applied on the synthetic and field data. Among our tests, we found that image-domain single-iteration LSRTM methods, including an extension of an approximate inverse Hessian method in the curvelet domain, not only compensated for amplitude loss due to poor illumination caused by complex salt bodies, but it also produced subsalt images with fewer migration artifacts in the field data. In contrast, an iterative inversion method showed its potential for broadening the bandwidth in the subsalt, but it was less effective in reducing migration artifacts and noise. Based on our understanding, we evaluated the current state of LSRTM for subsalt imaging.

Elastic least-squares reverse time migration in the image domain

2017 ◽  
Author(s):  
Bruno Pereira-Dias ◽  
André Bulcão ◽  
Djalma Soares Filho ◽  
Roberto Dias ◽  
Felipe Duarte ◽  
...  
Keyword(s):  
Least Squares ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Image Domain ◽  
Time Migration

A guide to least-squares reverse time migration for subsalt imaging: Challenges and solutions

2017 ◽  
Vol 5 (3) ◽  
pp. SN1-SN11 ◽  
Author(s):  
Chong Zeng ◽  
Shuqian Dong ◽  
Bin Wang
Keyword(s):  
Least Squares ◽  
Confidence Level ◽  
Input Data ◽  
Convergence Rates ◽  
Depth Image ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Area Of Interest ◽  
Time Migration ◽  
Subsalt Imaging

Least-squares reverse time migration (LSRTM) overcomes the shortcomings of conventional migration algorithms by iteratively fitting the demigrated synthetic data and the input data to refine the initial depth image toward true reflectivity. It gradually enhances the effective signals and removes the migration artifacts such as swing noise during conventional migration. When imaging the subsalt area with complex structures, many practical issues have to be considered to ensure the convergence of the inversion. We tackle those practical issues such as an unknown source wavelet, inaccurate migration velocity, and slow convergence to make LSRTM applicable to subsalt imaging in geologic complex areas such as the Gulf of Mexico. Dynamic warping is used to realign the modeled and input data to compensate for minor velocity errors in the subsalt sediments. A windowed crosscorrelation-based confidence level is used to control the quality of the residual computation. The confidence level is further used as an inverse weighting to precondition the data residual so that the convergence rates in shallow and deep images are automatically balanced. It also helps suppress the strong artifacts related to the salt boundary. The efficiency of the LSRTM is improved so that interpretable images in the area of interest can be obtained in only a few iterations. After removing the artifacts near the salt body using LSRTM, the image better represents the true geology than the outcome of conventional RTM; thus, it facilitates the interpretation. Synthetic and field data examples examine and demonstrate the effectiveness of the adaptive strategies.

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%.

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.

Fast least-squares reverse time migration via a superposition of Kronecker products

Geophysics ◽  
2020 ◽  
Vol 85 (2) ◽  
pp. S115-S134
Author(s):  
Wenlei Gao ◽  
Gian Matharu ◽  
Mauricio D. Sacchi
Keyword(s):  
Least Squares ◽  
Computational Cost ◽  
Low Rank ◽  
Fast Method ◽  
Kronecker Products ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Major Drawback ◽  
Image Domain ◽  
Time Migration

Least-squares reverse time migration (LSRTM) has become increasingly popular for complex wavefield imaging due to its ability to equalize image amplitudes, attenuate migration artifacts, handle incomplete and noisy data, and improve spatial resolution. The major drawback of LSRTM is the considerable computational cost incurred by performing migration/demigration at each iteration of the optimization. To ameliorate the computational cost, we introduced a fast method to solve the LSRTM problem in the image domain. Our method is based on a new factorization that approximates the Hessian using a superposition of Kronecker products. The Kronecker factors are small matrices relative to the size of the Hessian. Crucially, the factorization is able to honor the characteristic block-band structure of the Hessian. We have developed a computationally efficient algorithm to estimate the Kronecker factors via low-rank matrix completion. The completion algorithm uses only a small percentage of preferentially sampled elements of the Hessian matrix. Element sampling requires computation of the source and receiver Green’s functions but avoids explicitly constructing the entire Hessian. Our Kronecker-based factorization leads to an imaging technique that we name Kronecker-LSRTM (KLSRTM). The iterative solution of the image-domain KLSRTM is fast because we replace computationally expensive migration/demigration operations with fast matrix multiplications involving small matrices. We first validate the efficacy of our method by explicitly computing the Hessian for a small problem. Subsequent 2D numerical tests compare LSRTM with KLSRTM for several benchmark models. We observe that KLSRTM achieves near-identical images to LSRTM at a significantly reduced computational cost (approximately 5–15× faster); however, KLSRTM has an increased, yet manageable, memory cost.

scholarly journals Q-least-squares reverse time migration with viscoacoustic deblurring filters

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. S425-S438 ◽  
Author(s):  
Yuqing Chen ◽  
Gaurav Dutta ◽  
Wei Dai ◽  
Gerard T. Schuster
Keyword(s):  
Convergence Rate ◽  
Least Squares ◽  
Field Data ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Acoustic Data ◽  
Numerical Tests ◽  
Time Migration ◽  
Preconditioning Method ◽  
Number Of Iterations

Viscoacoustic least-squares reverse time migration, also denoted as Q-LSRTM, linearly inverts for the subsurface reflectivity model from lossy data. Compared with conventional migration methods, it can compensate for the amplitude loss in the migrated images due to strong subsurface attenuation and can produce reflectors that are accurately positioned in depth. However, the adjoint [Formula: see text] propagators used for backward propagating the residual data are also attenuative. Thus, the inverted images from [Formula: see text]-LSRTM with a small number of iterations are often observed to have lower resolution when compared with the benchmark acoustic LSRTM images from acoustic data. To increase the resolution and accelerate the convergence of [Formula: see text]-LSRTM, we used viscoacoustic deblurring filters as a preconditioner for [Formula: see text]-LSRTM. These filters can be estimated by matching a simulated migration image to its reference reflectivity model. Numerical tests on synthetic and field data demonstrate that [Formula: see text]-LSRTM combined with viscoacoustic deblurring filters can produce images with higher resolution and more balanced amplitudes than images from acoustic RTM, acoustic LSRTM, and [Formula: see text]-LSRTM when there is strong attenuation in the background medium. Our preconditioning method is also shown to improve the convergence rate of [Formula: see text]-LSRTM by more than 30% in some cases and significantly compensate for the lossy artifacts in RTM images.

Pure qP-wave least-squares reverse time migration in vertically transverse isotropic media and its application to field data

2020 ◽  
Vol 17 (2) ◽  
pp. 208-220
Author(s):  
Jian-Ping Huang ◽  
Xin-Ru Mu ◽  
Zhen-Chun Li ◽  
Qing-Yang Li ◽  
Shuang-Qi Yuan ◽  
...  
Keyword(s):  
Least Squares ◽  
Field Data ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Isotropic Media ◽  
Transverse Isotropic

Fast image-domain target-oriented least-squares reverse time migration

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. A81-A86 ◽  
Author(s):  
Zeyu Zhao ◽  
Mrinal K. Sen
Keyword(s):  
Plane Wave ◽  
Least Squares ◽  
Large Scale ◽  
Green's Functions ◽  
Green’S Functions ◽  
Hessian Matrix ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Image Domain ◽  
Time Migration

We have developed a fast image-domain target-oriented least-squares reverse time migration (LSRTM) method based on applying the inverse or pseudoinverse of a target-oriented Hessian matrix to a migrated image. The image and the target-oriented Hessian matrix are constructed using plane-wave Green’s functions that are computed by solving the two-way wave equation. Because the number of required plane-wave Green’s functions is small, the proposed method is highly efficient. We exploit the sparsity of the Hessian matrix by computing only a couple of off-diagonal terms for the target-oriented Hessian, which further improves the computational efficiency. We examined the proposed LSRTM method using the 2D Marmousi model. We demonstrated that our method correctly recovers the reflectivity model, and the retrieved results have more balanced illumination and higher spatial resolution than traditional images. Because of the low cost of computing the target-oriented Hessian matrix, the proposed method has the potential to be applied to large-scale problems.

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