Least-squares reverse time migration method using the factorization of the Hessian matrix

2021 ◽  
Vol 18 (1) ◽  
pp. 94-100
Author(s):  
Sun Xiao-Dong ◽  
Teng Hou-Hua ◽  
Ren Li-Juan ◽  
Wang Wei-Qi ◽  
Li Zhen-Chun
Keyword(s):  
Least Squares ◽  
Hessian Matrix ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Migration Method

scholarly journals Least-Squares Reverse Time Migration Using the Gradient Preconditioning Based on Transmitted Wave Energy

2021 ◽  
Vol 9 ◽  
Author(s):  
Chuang Xie ◽  
Peng Song ◽  
Xishuang Li ◽  
Jun Tan ◽  
Shaowen Wang ◽  
...  
Keyword(s):  
Least Squares ◽  
Wave Energy ◽  
Hessian Matrix ◽  
Transmitted Wave ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Reflected Waves ◽  
Time Migration ◽  
Acoustic Equation ◽  
And Storage

A gradient preconditioning approach based on transmitted wave energy for least-squares reverse time migration (LSRTM) is proposed in this study. The gradient is preconditioned by using the energy of “approximate transmission wavefield,” which is calculated based on the non-reflecting acoustic equation. The proposed method can effectively avoid a huge amount of calculation and storage required by the Hessian matrix or approximated Hessian matrix and can overcome the influence of reflected waves, multiples, and other wavefields on the gradient in gradient preconditioning based on seismic wave energy (GPSWE). The numerical experiments, compared with that using GPSWE, show that LSRTM using the gradient preconditioning based on transmitted wave energy (GPTWE) can significantly improve the imaging accuracy of deep target and accelerate the convergence rate without trivial increased calculation.

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.

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.

Decoupled elastic least-squares reverse time migration and its application in tunnel geological forward-prospecting

Geophysics ◽  
2021 ◽  
pp. 1-136
Author(s):  
Bin Liu ◽  
Jiansen Wang ◽  
Yuxiao Ren ◽  
Xu Guo ◽  
Lei Chen ◽  
...  
Keyword(s):  
Least Squares ◽  
Tunnel Construction ◽  
Stable Convergence ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Migration Imaging ◽  
Imaging Results ◽  
Geological Conditions ◽  
Migration Method

Accurate seismic imaging can ensure safe and efficient tunnel construction under complex geological conditions. As a high-precision migration method, reverse time migration (RTM) has been introduced into tunnel seismic forward-prospecting. However, the resolution of traditional RTM imaging results may not meet the requirements in a complex tunnel environment, which affects the interpretation of tunnel seismic forward-prospecting results. In this study, we propose a least-squares RTM method based on the decoupled elastic wave equation in tunnels. The Born forward modeling operator and its exact adjoint migration imaging operator are derived to ensure a stable convergence of the conjugate gradient method. Moreover, a pseudo-Hessian based preconditioning operator is adopted to accelerate the convergence. Numerical examples are provided to verify the efficiency of the proposed scheme. A field test in a traffic tunnel construction site is performed to show the good application effect of the decoupled elastic least-squares RTM in practical situations.

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

Reverse time migration

Geophysics ◽  
1983 ◽  
Vol 48 (11) ◽  
pp. 1514-1524 ◽  
Author(s):  
Edip Baysal ◽  
Dan D. Kosloff ◽  
John W. C. Sherwood
Keyword(s):  
Wave Amplitude ◽  
Synthetic Data ◽  
Data Sets ◽  
Field Observations ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Migration Method ◽  
Zero Offset ◽  
Time Extrapolation

Migration of stacked or zero‐offset sections is based on deriving the wave amplitude in space from wave field observations at the surface. Conventionally this calculation has been carried out through a depth extrapolation. We examine the alternative of carrying out the migration through a reverse time extrapolation. This approach may offer improvements over existing migration methods, especially in cases of steeply dipping structures with strong velocity contrasts. This migration method is tested using appropriate synthetic data sets.

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.

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