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.

An exact adjoint operation pair in time extrapolation and its application in least-squares reverse-time migration

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. H27-H33 ◽  
Author(s):  
Jun Ji
Keyword(s):  
Least Squares ◽  
Adjoint Operator ◽  
Synthetic Data ◽  
Forward Modeling ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Product Test ◽  
Least Squares Migration ◽  
Time Extrapolation

To reduce the migration artifacts arising from incomplete data or inaccurate operators instead of migrating data with the adjoint of the forward-modeling operator, a least-squares migration often is considered. Least-squares migration requires a forward-modeling operator and its adjoint. In a derivation of the mathematically correct adjoint operator to a given forward-time-extrapolation modeling operator, the exact adjoint of the derived operator is obtained by formulating an explicit matrix equation for the forward operation and transposing it. The programs that implement the exact adjoint operator pair are verified by the dot-product test. The derived exact adjoint operator turns out to differ from the conventional reverse-time-migration (RTM) operator, an implementation of wavefield extrapolation backward in time. Examples with synthetic data show that migration using the exact adjoint operator gives similar results for a conventional RTM operator and that least-squares RTM is quite successful in reducing most migration artifacts. The least-squares solution using the exact adjoint pair produces a model that fits the data better than one using a conventional RTM operator pair.

Least-squares migration with primary- and multiple-guided weighting matrices

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. S171-S185 ◽  
Author(s):  
Chuang Li ◽  
Jianping Huang ◽  
Zhenchun Li ◽  
Han Yu ◽  
Rongrong Wang
Keyword(s):  
Free Surface ◽  
Least Squares ◽  
Seismic Data ◽  
Synthetic Data ◽  
Velocity Model ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Multiple Reflections ◽  
Time Migration ◽  
Least Squares Migration

Least-squares migration (LSM) of seismic data is supposed to produce images of subsurface structures with better quality than standard migration if we have an accurate migration velocity model. However, LSM suffers from data mismatch problems and migration artifacts when noise pollutes the recorded profiles. This study has developed a reweighted least-squares reverse time migration (RWLSRTM) method to overcome the problems caused by such noise. We first verify that spiky noise and free-surface multiples lead to the mismatch problems and should be eliminated from the data residual. The primary- and multiple-guided weighting matrices are then derived for RWLSRTM to reduce the noise in the data residual. The weighting matrices impose constraints on the data residual such that spiky noise and free-surface multiple reflections are reduced whereas primary reflections are preserved. The weights for spiky noise and multiple reflections are controlled by a dynamic threshold parameter decreasing with iterations for better results. Finally, we use an iteratively reweighted least-squares algorithm to minimize the weighted data residual. We conduct numerical tests using the synthetic data and compared the results of this method with the results of standard LSRTM. The results suggest that RWLSRTM is more robust than standard LSRTM when the seismic data contain spiky noise and multiple reflections. Moreover, our method not only suppresses the migration artifacts, but it also accelerates the convergence.

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.

Least-squares reverse time migration using controlled-order multiple reflections

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. S347-S357 ◽  
Author(s):  
Yike Liu ◽  
Xuejian Liu ◽  
Are Osen ◽  
Yu Shao ◽  
Hao Hu ◽  
...  
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Multiple Reflections ◽  
Numerical Tests ◽  
Elimination Algorithm ◽  
Reflection Data ◽  
Time Migration ◽  
Least Squares Migration

Reverse time migration (RTM) using multiples generates inherent crosstalk artifacts due to the interference among multiples of different orders. We have developed a method to remove such crosstalk. This approach first separates the recorded seismic data into primary reflections and multiples using the surface-related multiples elimination algorithm and then isolates the multiples into different orders. We can take any specified, say the [Formula: see text]th, order of multiples data as the incident wave and the next higher order multiples data, ([Formula: see text])th order, as the corresponding primary reflection data for imaging. We have applied the least-squares migration scheme to these two successive orders of multiples. Our method is denoted as least-squares RTM using controlled-order multiples (LSRTM-CM). Our numerical tests demonstrated that LSRTM-CM can significantly improve imaging quality compared with straightforward seismic imaging using multiples without multiples separation.

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.

Elastic least-squares reverse time migration with density variations

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. S533-S547 ◽  
Author(s):  
Minao Sun ◽  
Liangguo Dong ◽  
Jizhong Yang ◽  
Chao Huang ◽  
Yuzhu Liu
Keyword(s):  
Least Squares ◽  
Wave Velocity ◽  
Constant Density ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
Velocity Images ◽  
Density Image ◽  
Elastic Impedance

Elastic least-squares reverse time migration (ELSRTM) is a powerful tool to retrieve high-resolution subsurface images of the earth’s interior. By minimizing the differences between synthetic and observed data, ELSRTM can improve spatial resolution and reduce migration artifacts. However, conventional ELSRTM methods usually assume constant density models, which cause inaccurate amplitude performance in resulting images. To partially remedy this problem, we have developed a new ELSRTM method that considers P- and S-wave velocity and density variations. Our method can simultaneously obtain P- and S-wave velocity and density images with enhanced amplitude fidelity and suppressed parameter crosstalk. In addition, it can provide subsurface elastic impedance images by summing the inverted velocity images with the density image. Compared with the conventional ELSRTM method, our method can improve the quality of final images and provide more accurate reflectivity estimates. Numerical experiments on a horizontal reflector model and a Marmousi-II model demonstrate the effectiveness of this method.

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

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. S127-S136 ◽  
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.

Elastic least-squares reverse time migration

Geophysics ◽  
2017 ◽  
Vol 82 (4) ◽  
pp. S315-S325 ◽  
Author(s):  
Yuting Duan ◽  
Antoine Guitton ◽  
Paul Sava
Keyword(s):  
Least Squares ◽  
Reservoir Characterization ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Imaging Condition ◽  
Time Migration ◽  
Energy Focusing ◽  
Polarity Reversals ◽  
New Perturbation ◽  
Least Squares Migration

Least-squares migration can produce images with improved resolution and reduced migration artifacts, compared with conventional imaging. We have developed a method for elastic least-squares reverse time migration (LSRTM) based on a new perturbation imaging condition that yields scalar images of squared P- and S-velocity perturbations. These perturbation images do not suffer from polarity reversals that are common for more conventional elastic imaging methods. We use 2D synthetic and field-data examples to demonstrate the proposed LSRTM algorithm using the perturbation imaging condition. Our results show that elastic LSRTM improves the energy focusing and illumination of the elastic images and it attenuates artifacts resulting, for instance, from sparseness in the wavefield sampling and crosstalk of the P- and S-modes. Compared with RTM images, the LSRTM images provide more accurate relative amplitude information that is useful for reservoir characterization.

scholarly journals Extracting angle domain common image gather with variable density acoustic-wave equation

2021 ◽  
Vol 18 (2) ◽  
pp. 1-8
Author(s):  
Yuzhu Liu ◽  
Weigang Liu ◽  
Jizhong Yang ◽  
Liangguo Dong
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Velocity Model ◽  
Variable Density ◽  
Constant Density ◽  
Acoustic Wave Equation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Density Perturbations

Abstract Angle domain common image gathers (ADCIGs), commonly regarded as important prestacked gathers, provide the information required for velocity model construction and the phase and amplitude information needed for subsurface structures in oil/gas exploration. Based on the constant-density acoustic-wave equation assumption, the ADCIGs generated from reverse time migration ignore the fact that the subsurface density varies with location. Consequently, the amplitude versus angle (AVA) analysis extracted from these ADCIGs is not accurate. To partially solve this problem and to improve the accuracy of the AVA analysis, we developed amplitude-preserving ADCIGs suitable for density variations with the assumption of acoustic approximation. The Poynting vector approach, which is efficient and computationally inexpensive, was used to calculate the high-resolution wavefield propagation. The ADCIGs generated from the velocity and density perturbations match the theoretical AVA relationship better than ADCIGs with constant density. The extraction of the AVA analysis of the various combinations of the subsurface medium indicates that the density is non-negligible, especially when the density contrast is sharp. Numerical examples based on a layered model verify our conclusions.

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