Source-independent elastic least-squares reverse time migration

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. S1-S16 ◽  
Author(s):  
Jinwei Fang ◽  
Hui Zhou ◽  
Hanming Chen ◽  
Ning Wang ◽  
Yufeng Wang ◽  
...  
Keyword(s):  
Objective Function ◽  
Least Squares ◽  
Noisy Data ◽  
Simulated Data ◽  
High Accuracy ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Numerical Examples ◽  
Time Migration ◽  
Seismic Images

Elastic least-squares reverse time migration (LSRTM) has been developed recently for its high accuracy imaging ability. The theory is based on minimizing the misfit between the observed and simulated data by an iterative algorithm to refine seismic images toward the true reflectivity. We have developed a new elastic LSRTM with the same modeling equations for source and receiver wavefield extrapolations, except for their source terms. The LSRTM has a natural advantage to solve the source and receiver wavefields using the same modeling system; thus, it is easy to implement LSRTM. In practice, it is difficult to obtain an accurate source wavelet, so a convolution-based objective function is used in our source-independent elastic LSRTM. Such an objective function can relax the requirement of an accurate wavelet, and improve the robustness of the inverse problem in the presence of noise. The numerical examples indicate that our method has the ability to recover the reflectivity models with an incorrect source wavelet from noisy data.

scholarly journals Sparse Constrained Least-Squares Reverse Time Migration Based on Kirchhoff Approximation

2021 ◽  
Vol 9 ◽  
Author(s):  
Xu Hong-Qiao ◽  
Wang Xiao-Yi ◽  
Wang Chen-Yuan ◽  
Zhang Jiang-Jie
Keyword(s):  
Least Squares ◽  
Kirchhoff Approximation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
L1 Norm ◽  
Constrained Least Squares ◽  
Geological Structures ◽  
Numerical Examples ◽  
Time Migration ◽  
The Difference

Least-squares reverse time migration (LSRTM) is powerful for imaging complex geological structures. Most researches are based on Born modeling operator with the assumption of small perturbation. However, studies have shown that LSRTM based on Kirchhoff approximation performs better; in particular, it generates a more explicit reflected subsurface and fits large offset data well. Moreover, minimizing the difference between predicted and observed data in a least-squares sense leads to an average solution with relatively low quality. This study applies L1-norm regularization to LSRTM (L1-LSRTM) based on Kirchhoff approximation to compensate for the shortcomings of conventional LSRTM, which obtains a better reflectivity image and gets the residual and resolution in balance. Several numerical examples demonstrate that our method can effectively mitigate the deficiencies of conventional LSRTM and provide a higher resolution image profile.

Prestack correlative least-squares reverse time migration

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. S159-S172 ◽  
Author(s):  
Xuejian Liu ◽  
Yike Liu ◽  
Huiyi Lu ◽  
Hao Hu ◽  
Majid Khan
Keyword(s):  
Objective Function ◽  
Least Squares ◽  
Step Length ◽  
Inversion Algorithm ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Initial Image ◽  
Data Set ◽  
Time Migration ◽  
Gradient Descent Algorithm

In the correlative least-squares reverse time migration (CLSRTM) scheme, a stacked image is updated using a gradient-based inversion algorithm. However, CLSRTM experiences the incoherent stacking of different shots during each iteration due to the use of an imperfect velocity, which leads to image smearing. To reduce the sensitivity to velocity errors, we have developed prestack correlative least-squares reverse time migration (PCLSRTM), in which a gradient descent algorithm using a newly defined initial image and an efficiently defined analytical step length is developed to separately seek the optimal image for each shot gather before the final stacking. Furthermore, a weighted objective function is also designed for PCLSRTM, so that the data-domain gradient can avoid a strong truncation effect. Numerical experiments on a three-layer model as well as a marine synthetic and a field data set reveal the merits of PCLSRTM. In the presence of velocity errors, PCLSRTM shows better convergence and provides higher quality images as compared with CLSRTM. With the newly defined initial image, PCLSRTM can effectively handle observed data with unbalanced amplitudes. By using a weighted objective function, PCLSRTM can provide an image with enhanced resolution and balanced amplitude while avoiding many imaging artifacts.

An efficient step-length formula for correlative least-squares reverse time migration

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. S221-S238 ◽  
Author(s):  
Youshan Liu ◽  
Jiwen Teng ◽  
Tao Xu ◽  
Zhiming Bai ◽  
Haiqiang Lan ◽  
...  
Keyword(s):  
Objective Function ◽  
Least Squares ◽  
Step Length ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Step Size ◽  
Time Migration ◽  
Seismic Records ◽  
Complex Models ◽  
Analytical Step

In correlative least-squares reverse time migration (CLSRTM), the estimation of the optimal step size is usually determined by fitting a parabola and finding its minimum; it involves at least two times extra reading of all seismic records, which significantly lowers the efficiency of the algorithm. To improve the efficiency of the CLSRTM algorithm, we have deduced an analytical step-length (ASL) formula based on the linear property of the demigration operator. Numerical examples performed with the data synthetized by the Marmousi and Sigsbee2A models were used to test its validity. In complex models with imperfect migration velocity, such as the Sigabee2A model, our formula makes the value of the objective function converges to a much smaller minimum. Additional numerical tests performed with the data either acquired irregularly or contaminated by different noise levels verify the robustness of the ASL formula. Compared with the commonly used parabolic search method, the ASL formula is much more efficient because it is free from an extra estimation of the value of the objective function.

Least-squares reverse time migration in the presence of density variations

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. S497-S509 ◽  
Author(s):  
Jizhong Yang ◽  
Yuzhu Liu ◽  
Liangguo Dong
Keyword(s):  
Least Squares ◽  
Simulated Data ◽  
Integral Approach ◽  
Constant Density ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Density Assumption ◽  
Density Perturbations ◽  
Least Squares Migration

Least-squares migration (LSM) is commonly regarded as an amplitude-preserving or true amplitude migration algorithm that, compared with conventional migration, can provide migrated images with reduced migration artifacts, balanced amplitudes, and enhanced spatial resolution. Most applications of LSM are based on the constant-density assumption, which is not the case in the real earth. Consequently, the amplitude performance of LSM is not appropriate. To partially remedy this problem, we have developed a least-squares reverse time migration (LSRTM) scheme suitable for density variations in the acoustic approximation. An improved scattering-integral approach is adopted for implementation of LSRTM in the frequency domain. LSRTM images associated with velocity and density perturbations are simultaneously used to generate the simulated data, which better matches the recorded data in amplitudes. Summation of these two images provides a reflectivity model related to impedance perturbation that is in better accordance with the true one, than are the velocity and density images separately. Numerical examples based on a two-layer model and a small part of the Sigsbee2A model verify the effectiveness of our method.

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

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.

Q least-squares reverse time migration based on the first-order viscoacoustic quasidifferential equations

Geophysics ◽  
2021 ◽  
pp. 1-65
Author(s):  
Yingming Qu ◽  
Yixin Wang ◽  
Zhenchun Li ◽  
Chang Liu
Keyword(s):  
Wave Equation ◽  
Least Squares ◽  
Surface Topography ◽  
Density Perturbation ◽  
Second Order ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
First Order ◽  
Time Migration ◽  
Grid Scheme

Seismic wave attenuation caused by subsurface viscoelasticity reduces the quality of migration and the reliability of interpretation. A variety of Q-compensated migration methods have been developed based on the second-order viscoacoustic quasidifferential equations. However, these second-order wave-equation-based methods are difficult to handle with density perturbation and surface topography. In addition, the staggered grid scheme, which has an advantage over the collocated grid scheme because of its reduced numerical dispersion and enhanced stability, works in first-order wave-equation-based methods. We have developed a Q least-squares reverse time migration method based on the first-order viscoacoustic quasidifferential equations by deriving Q-compensated forward-propagated operators, Q-compensated adjoint operators, and Q-attenuated Born modeling operators. Besides, our method using curvilinear grids is available even when the attenuating medium has surface topography and can conduct Q-compensated migration with density perturbation. The results of numerical tests on two synthetic and a field data sets indicate that our method improves the imaging quality with iterations and produces better imaging results with clearer structures, higher signal-to-noise ratio, higher resolution, and more balanced amplitude by correcting the energy loss and phase distortion caused by Q attenuation. It also suppresses the scattering and diffracted noise caused by the surface topography.

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