Least-squares extended reverse time migration with randomly sampled space shifts

Geophysics ◽  
2020 ◽  
Vol 85 (6) ◽  
pp. S357-S369 ◽  
Author(s):  
Jizhong Yang ◽  
Yunyue Elita Li ◽  
Yuzhu Liu ◽  
Jingjing Zong
Keyword(s):  
Least Squares ◽  
Random Noise ◽  
Computational Cost ◽  
Extended Model ◽  
Memory Requirement ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Implicit Model ◽  
Geologic Interpretation

Because the velocity errors are inevitable in field data applications, direct implementation of conventional least-squares reverse time migration (LSRTM) would generate defocused migration images. Extending the model domain has the potential to preserve the data information, and reducing the extended model could provide a final image with more continuous subsurface structures for geologic interpretation. However, the computational cost and the memory requirement would be increased significantly compared to conventional LSRTM. To obtain an inversion image with better quality than conventional LSRTM, while maintaining the same computational cost and memory requirement, we have introduced random space shifts in LSRTM. The key point is to perform implicit model extension and immediate model reduction within each iteration of the inversion procedure. To be robust against the random noise during the random sampling process, we formulate the inverse problem based on a correlation objective function. Numerical examples on a simple layered model, the Marmousi model, and the SEAM model demonstrate that even when the bulk velocity errors are up to 10%, we still obtain reasonable results for subsurface geologic interpretation.

From acoustic to elastic inverse extended Born modeling: a first insight in the marine environment

Geophysics ◽  
2021 ◽  
pp. 1-73
Author(s):  
Milad Farshad ◽  
Hervé Chauris
Keyword(s):  
Least Squares ◽  
Marine Environment ◽  
Computational Cost ◽  
Physical Parameters ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
Physical Density ◽  
Acoustic Approximation

Elastic least-squares reverse time migration is the state-of-the-art linear imaging technique to retrieve high-resolution quantitative subsurface images. A successful application requires many migration/modeling cycles. To accelerate the convergence rate, various pseudoinverse Born operators have been proposed, providing quantitative results within a single iteration, while having roughly the same computational cost as reverse time migration. However, these are based on the acoustic approximation, leading to possible inaccurate amplitude predictions as well as the ignorance of S-wave effects. To solve this problem, we extend the pseudoinverse Born operator from acoustic to elastic media to account for the elastic amplitudes of PP reflections and provide an estimate of physical density, P- and S-wave impedance models. We restrict the extension to marine environment, with the recording of pressure waves at the receiver positions. Firstly, we replace the acoustic Green's functions by their elastic version, without modifying the structure of the original pseudoinverse Born operator. We then apply a Radon transform to the results of the first step to calculate the angle-dependent response. Finally, we simultaneously invert for the physical parameters using a weighted least-squares method. Through numerical experiments, we first illustrate the consequences of acoustic approximation on elastic data, leading to inaccurate parameter inversion as well as to artificial reflector inclusion. Then we demonstrate that our method can simultaneously invert for elastic parameters in the presence of complex uncorrelated structures, inaccurate background models, and Gaussian noisy data.

Mini-batch Least-Squares Reverse Time Migration In A Deep Learning Framework

Geophysics ◽  
2020 ◽  
pp. 1-61
Author(s):  
Janaki Vamaraju ◽  
Jeremy Vila ◽  
Mauricio Araya-Polo ◽  
Debanjan Datta ◽  
Mohamed Sidahmed ◽  
...  
Keyword(s):  
Deep Learning ◽  
Least Squares ◽  
Spatial Resolution ◽  
Data Science ◽  
Computational Cost ◽  
Computation Time ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Learning Framework ◽  
Time Migration

Migration techniques are an integral part of seismic imaging workflows. Least-squares reverse time migration (LSRTM) overcomes some of the shortcomings of conventional migration algorithms by compensating for illumination and removing sampling artifacts to increase spatial resolution. However, the computational cost associated with iterative LSRTM is high and convergence can be slow in complex media. We implement pre-stack LSRTM in a deep learning framework and adopt strategies from the data science domain to accelerate convergence. The proposed hybrid framework leverages the existing physics-based models and machine learning optimizers to achieve better and cheaper solutions. Using a time-domain formulation, we show that mini-batch gradients can reduce the computation cost by using a subset of total shots for each iteration. Mini-batch approach does not only reduce source cross-talk but also is less memory intensive. Combining mini-batch gradients with deep learning optimizers and loss functions can improve the efficiency of LSRTM. Deep learning optimizers such as the adaptive moment estimation are generally well suited for noisy and sparse data. We compare different optimizers and demonstrate their efficacy in mitigating migration artifacts. To accelerate the inversion, we adopt the regularised Huber loss function in conjunction. We apply these techniques to 2D Marmousi and 3D SEG/EAGE salt models and show improvements over conventional LSRTM baselines. The proposed approach achieves higher spatial resolution in less computation time measured by various qualitative and quantitative evaluation metrics.

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.

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.

Least-squares migration of multisource data with a deblurring filter

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. R135-R146 ◽  
Author(s):  
Wei Dai ◽  
Xin Wang ◽  
Gerard T. Schuster
Keyword(s):  
Wave Equation ◽  
Least Squares ◽  
Computational Efficiency ◽  
Computational Cost ◽  
Processing Technique ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Migration Method ◽  
Least Squares Migration

Least-squares migration (LSM) has been shown to be able to produce high-quality migration images, but its computational cost is considered to be too high for practical imaging. We have developed a multisource least-squares migration algorithm (MLSM) to increase the computational efficiency by using the blended sources processing technique. To expedite convergence, a multisource deblurring filter is used as a preconditioner to reduce the data residual. This MLSM algorithm is applicable with Kirchhoff migration, wave-equation migration, or reverse time migration, and the gain in computational efficiency depends on the choice of migration method. Numerical results with Kirchhoff LSM on the 2D SEG/EAGE salt model show that an accurate image is obtained by migrating a supergather of 320 phase-encoded shots. When the encoding functions are the same for every iteration, the input/output cost of MLSM is reduced by 320 times. Empirical results show that the crosstalk noise introduced by blended sources is more effectively reduced when the encoding functions are changed at every iteration. The analysis of signal-to-noise ratio (S/N) suggests that not too many iterations are needed to enhance the S/N to an acceptable level. Therefore, when implemented with wave-equation migration or reverse time migration methods, the MLSM algorithm can be more efficient than the conventional migration method.

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.

scholarly journals Fast Least-Squares Reverse Time Migration of OBN Down-Going Multiples

2021 ◽  
Vol 9 ◽  
Author(s):  
Yanbao Zhang ◽  
Yike Liu ◽  
Jia Yi ◽  
Xuejian Liu
Keyword(s):  
Least Squares ◽  
Oil And Gas ◽  
Computational Cost ◽  
Ocean Bottom ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Subsurface Structures ◽  
Time Migration ◽  
Resource Exploration ◽  
Imaging Algorithms

Nowadays the ocean bottom node (OBN) acquisition is widely used in oil and gas resource exploration and seismic monitoring. Conventional imaging algorithms of OBN data mainly focus on the processing of up-going primaries and down-going first-order multiples. Up-going multiples and higher-order down-going multiples are generally regarded as noise and should be eliminated or ignored in conventional migration methods. However, multiples carry abundant information about subsurface structures where primaries cannot achieve. To take full advantage of multiples, we propose a migration method using OBN down-going all-order multiples. And then the least-squares optimization algorithm is used to suppress crosstalks. Finally, a phase-encoding-based migration algorithm is developed to cut down the computational cost by blending several common receiver gathers together using random time delays and polarity reversals. Numerical experiments on the complex Marmousi model illustrate that the developed approach can enlarge the imaging area evidently, reduce the computational cost effectively, and enhance the image quality by suppressing crosstalks and improving the resolution.

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

First-order particle velocity equations of decoupled P- and S-wavefields and their application in elastic reverse time migration

Geophysics ◽  
2021 ◽  
pp. 1-78
Author(s):  
Zhiyuan Li ◽  
Youshan Liu ◽  
Guanghe Liang ◽  
Guoqiang Xue ◽  
Runjie Wang
Keyword(s):  
Particle Velocity ◽  
Computational Cost ◽  
Staggered Grid ◽  
Additional Stress ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Computational Accuracy ◽  
First Order ◽  
Time Migration ◽  
Stress Variable

The separation of P- and S-wavefields is considered to be an effective approach for eliminating wave-mode cross-talk in elastic reverse-time migration. At present, the Helmholtz decomposition method is widely used for isotropic media. However, it tends to change the amplitudes and phases of the separated wavefields compared with the original wavefields. Other methods used to obtain pure P- and S-wavefields include the application of the elastic wave equations of the decoupled wavefields. To achieve a high computational accuracy, staggered-grid finite-difference (FD) schemes are usually used to numerically solve the equations by introducing an additional stress variable. However, the computational cost of this method is high because a conventional hybrid wavefield (P- and S-wavefields are mixed together) simulation must be created before the P- and S-wavefields can be calculated. We developed the first-order particle velocity equations to reduce the computational cost. The equations can describe four types of particle velocity wavefields: the vector P-wavefield, the scalar P-wavefield, the vector S-wavefield, and the vector S-wavefield rotated in the direction of the curl factor. Without introducing the stress variable, only the four types of particle velocity variables are used to construct the staggered-grid FD schemes, so the computational cost is reduced. We also present an algorithm to calculate the P and S propagation vectors using the four particle velocities, which is simpler than the Poynting vector. Finally, we applied the velocity equations and propagation vectors to elastic reverse-time migration and angle-domain common-image gather computations. These numerical examples illustrate the efficiency of the proposed methods.

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