Image-domain least-squares reverse-time migration through point spread functions

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.

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

Geophysics ◽

10.1190/geo2017-0466.1 ◽

2018 ◽

Vol 83 (3) ◽

pp. S261-S270 ◽

Cited By ~ 9

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.

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

Geophysics ◽

10.1190/geo2019-0254.1 ◽

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.

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

Geophysics ◽

10.1190/geo2018-0033.1 ◽

2018 ◽

Vol 83 (6) ◽

pp. A81-A86 ◽

Cited By ~ 3

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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Improving Image-domain Least-squares Reverse Time Migration Close to High Velocity Contrasts

80th EAGE Conference and Exhibition 2018 ◽

10.3997/2214-4609.201800974 ◽

2018 ◽

Author(s):

R. Fletcher ◽

M. Cavalca

Keyword(s):

Least Squares ◽

High Velocity ◽

Reverse Time ◽

Reverse Time Migration ◽

Image Domain ◽

Time Migration

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Migration of viscoacoustic data using acoustic reverse time migration with hybrid deblurring filters

Geophysics ◽

10.1190/geo2018-0256.1 ◽

2019 ◽

Vol 84 (3) ◽

pp. S127-S136 ◽

Cited By ~ 5

Author(s):

Yuqing Chen ◽

Bowen Guo ◽

Gerard T. Schuster

Keyword(s):

Least Squares ◽

Computation Time ◽

Phase Distortion ◽

Storage Space ◽

Reverse Time ◽

Reverse Time Migration ◽

Image Domain ◽

Time Migration ◽

The Cost ◽

Least Squares Migration

Viscoacoustic migration can significantly compensate for the amplitude loss and phase distortion in migration images computed from highly attenuated data. However, solving the viscoacoustic wave equation requires a significant amount of storage space and computation time, especially for least-squares migration methods. To mitigate this problem, we used acoustic reverse time migration (RTM) instead of viscoacoustic migration to migrate the viscoacoustic data and then we correct the amplitude and phase distortion by hybrid deblurring filters in the image domain. Numerical tests on synthetic and field data demonstrate that acoustic RTM combined with hybrid deblurring filters can compensate for the attenuation effects and produce images with high resolution and balanced amplitudes. This procedure requires less than one-third of the storage space and is [Formula: see text] times faster compared with the viscoacoustic migration, but at the cost of mildly reduced accuracy. Here, [Formula: see text] represents the number of iterations used for least-squares migration method. This method can be extended to 3D migration at even a greater cost saving.

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