scholarly journals Attenuation compensation for least-squares reverse time migration using the viscoacoustic-wave equation

Geophysics ◽  
2014 ◽  
Vol 79 (6) ◽  
pp. S251-S262 ◽  
Author(s):  
Gaurav Dutta ◽  
Gerard T. Schuster
Keyword(s):  
Least Squares ◽  
Seismic Waves ◽  
Adjoint Equations ◽  
Inversion Method ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Adjoint State ◽  
Attenuation Models ◽  
Adjoint State Method

Strong subsurface attenuation leads to distortion of amplitudes and phases of seismic waves propagating inside the earth. Conventional acoustic reverse time migration (RTM) and least-squares reverse time migration (LSRTM) do not account for this distortion, which can lead to defocusing of migration images in highly attenuative geologic environments. To correct for this distortion, we used a linearized inversion method, denoted as [Formula: see text]-LSRTM. During the least-squares iterations, we used a linearized viscoacoustic modeling operator for forward modeling. The adjoint equations were derived using the adjoint-state method for back propagating the residual wavefields. The merit of this approach compared with conventional RTM and LSRTM was that [Formula: see text]-LSRTM compensated for the amplitude loss due to attenuation and could produce images with better balanced amplitudes and more resolution below highly attenuative layers. Numerical tests on synthetic and field data illustrated the advantages of [Formula: see text]-LSRTM over RTM and LSRTM when the recorded data had strong attenuation effects. Similar to standard LSRTM, the sensitivity tests for background velocity and [Formula: see text] errors revealed that the liability of this method is the requirement for smooth and accurate migration velocity and attenuation models.

scholarly journals Reverse time migration with optimal checkpointing

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. SM213-SM221 ◽  
Author(s):  
William W. Symes
Keyword(s):  
Wave Equation ◽  
Reverse Order ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Adjoint State ◽  
Forward Computation ◽  
State Method ◽  
Adjoint State Method

Reverse time migration (RTM) requires that fields computed in forward time be accessed in reverse order. Such out-of-order access, to recursively computed fields, requires that some part of the recursion history be stored (checkpointed), with the remainder computed by repeating parts of the forward computation. Optimal checkpointing algorithms choose checkpoints in such a way that the total storage is minimized for a prescribed level of excess computation, or vice versa. Optimal checkpointing dramatically reduces the storage required by RTM, compared to that needed for nonoptimal implementations, at the price of a small increase in computation. This paper describes optimal checkpointing in a form which applies both to RTM and other applications of the adjoint state method, such as construction of velocity updates from prestack wave equation migration.

Elastic least-squares reverse time migration with hybrid l1/l2 misfit function

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. S271-S291 ◽  
Author(s):  
Bingluo Gu ◽  
Zhenchun Li ◽  
Peng Yang ◽  
Wencai Xu ◽  
Jianguang Han
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Synthetic Data ◽  
Adjoint Equations ◽  
P Wave ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
Wave Image

We have developed the theory and synthetic tests of elastic least-squares reverse time migration (ELSRTM). In this method, a least-squares reverse time migration algorithm is used to image multicomponent seismic data based on the first-order elastic velocity-stress wave equation, in which the linearized elastic modeling equations are used for forward modeling and its adjoint equations are derived based on the adjoint-state method for back propagating the data residuals. Also, we have developed another ELSRTM scheme based on the wavefield separation technique, in which the P-wave image is obtained using P-wave forward and adjoint wavefields and the S-wave image is obtained using P-wave forward and S-wave adjoint wavefields. In this way, the crosstalk artifacts can be minimized to a significant extent. In general, seismic data inevitably contain noise. We apply the hybrid [Formula: see text] misfit function to the ELSRTM algorithm to improve the robustness of our ELSRTM to noise. Numerical tests on synthetic data reveal that our ELSRTM, when compared with elastic reverse time migration, can produce images with higher spatial resolution, more-balanced amplitudes, and fewer artifacts. Moreover, the hybrid [Formula: see text] misfit function makes the ELSRTM more robust than the [Formula: see text] misfit function in the presence of noise.

scholarly journals Elastic least-squares reverse time migration

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. S143-S157 ◽  
Author(s):  
Zongcai Feng ◽  
Gerard T. Schuster
Keyword(s):  
Least Squares ◽  
Synthetic Data ◽  
Adjoint Equations ◽  
Accurate Estimation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Velocity Models ◽  
Time Migration ◽  
Wave Migration

We use elastic least-squares reverse time migration (LSRTM) to invert for the reflectivity images of P- and S-wave impedances. Elastic LSRTM solves the linearized elastic-wave equations for forward modeling and the adjoint equations for backpropagating the residual wavefield at each iteration. Numerical tests on synthetic data and field data reveal the advantages of elastic LSRTM over elastic reverse time migration (RTM) and acoustic LSRTM. For our examples, the elastic LSRTM images have better resolution and amplitude balancing, fewer artifacts, and less crosstalk compared with the elastic RTM images. The images are also better focused and have better reflector continuity for steeply dipping events compared to the acoustic LSRTM images. Similar to conventional least-squares migration, elastic LSRTM also requires an accurate estimation of the P- and S-wave migration velocity models. However, the problem remains that, when there are moderate errors in the velocity model and strong multiples, LSRTM will produce migration noise stronger than that seen in the RTM images.

Elastic least-squares reverse time migration based on decoupled wave equations

Geophysics ◽  
2021 ◽  
pp. 1-72
Author(s):  
Yu Zhong ◽  
Hanming Gu ◽  
Yangting Liu ◽  
QingHui Mao
Keyword(s):  
Least Squares ◽  
Wave Equations ◽  
Wave Mode ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Waves ◽  
Limited Bandwidth ◽  
Time Migration ◽  
Adjoint State ◽  
Isotropic Media

Elastic reverse time migration (ERTM) is developed for better characterization of complex structures by imaging multicomponent seismic data. However, conventional ERTM is subject to limitations such as finite recording aperture, limited bandwidth, and imperfect illumination. Elastic least-squares reverse time migration (ELSRTM) can improve imaging accuracy gradually with iterations by minimizing the residuals between observed and calculated multicomponent data. Conventional ELSRTM suffers from crosstalk artifacts caused by coupled elastic wavefields with different wave modes. Decomposing the coupled elastic wavefields into pure P- and S-waves is an effective method to suppress these crosstalk artifacts. Considering the trade-off between calculation accuracy and efficiency, we have developed a new ELSRTM scheme for isotropic media based on decoupled wave equations to suppress these wave mode-related crosstalk artifacts in the images of conventional ELSRTM. Pure wavefields are obtained by solving the decoupled wave equations using the finite-difference (FD) method in our new ELSRTM method. We also derive new decoupled adjoint-state wave equations, which are suitable for the elastic velocity-stress equations in isotropic media. We further propose the gradient equations based on pure wavefields to update the reflectivity images. Synthetic examples demonstrate that our new ELSRTM method can generate images that better represent the subsurface when compared with conventional ERTM and conventional ELSRTM.

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.

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