Accelerating least-squares Kirchhoff time migration using beam methodology

Geophysics ◽  
2021 ◽  
pp. 1-70
Author(s):  
Yubo Yue ◽  
Yujin Liu ◽  
Samuel H. Gray
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Correction Term ◽  
Computational Cost ◽  
Least Square ◽  
Computational Accuracy ◽  
Time Migration ◽  
Time Modeling ◽  
Slant Stacking ◽  
Least Squares Migration

Least-squares migration is an advanced imaging technique capable of producing images with improved spatial resolution, balanced illumination and reduced migration artifacts; however, the prohibitive computational cost poses a great challenge for its practical application. We have incorporated the beam methodology into the implementation of Kirchhoff time modeling/ migration and developed a fast common-offset least-squares Kirchhoff beam time migration (LSKBTM). Different from conventional Kirchhoff time modeling/migration in which the seismic data are modeled/migrated trace by trace, the mapping operation in Kirchhoff beam time modeling/migration is performed in terms of beam components and performed only at sparsely sampled beam centers. Therefore, the computational cost of LSKBTM is significantly reduced in comparison with that of least-square Kirchhoff time migration (LSKTM). In addition, based on the second-order Taylor expansion of the diffraction traveltime, we introduce a quadratic correction term into the inverse/forward local slant stacking, effectively enhancing the computational accuracy of LSKBTM. We have used both 2D synthetic and 3D field data examples to verify the effectiveness of the proposed method. The results show that LSKBTM can produce images comparable to that of LSKTM, but at considerably reduced computational cost.

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.

Compressive least-squares migration with on-the-fly Fourier transforms

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. R655-R672 ◽  
Author(s):  
Philipp A. Witte ◽  
Mathias Louboutin ◽  
Fabio Luporini ◽  
Gerard J. Gorman ◽  
Felix J. Herrmann
Keyword(s):  
Objective Function ◽  
Least Squares ◽  
Fourier Transforms ◽  
Computational Cost ◽  
Reverse Time ◽  
Helmholtz Equations ◽  
Data Movement ◽  
Computational Costs ◽  
Time Migration ◽  
Least Squares Migration

Least-squares reverse time migration is a powerful approach for true-amplitude seismic imaging of complex geologic structures, but the successful application of this method is currently hindered by its enormous computational cost, as well as its high memory requirements for computing the gradient of the objective function. We have tackled these problems by introducing an algorithm for low-cost sparsity-promoting least-squares migration using on-the-fly Fourier transforms. We formulate the least-squares migration objective function in the frequency domain (FD) and compute gradients for randomized subsets of shot records and frequencies, thus significantly reducing data movement and the number of overall wave equations solves. By using on-the-fly Fourier transforms, we can compute an arbitrary number of monochromatic FD wavefields with a time-domain (TD) modeling code, instead of having to solve individual Helmholtz equations for each frequency, which becomes computationally infeasible when moving to high frequencies. Our numerical examples demonstrate that compressive imaging with on-the-fly Fourier transforms provides a fast and memory-efficient alternative to TD imaging with optimal checkpointing, whose memory requirements for a fixed background model and source wavelet are independent of the number of time steps. Instead, the memory and additional computational costs grow with the number of frequencies and determine the amount of subsampling artifacts and crosstalk. In contrast to optimal checkpointing, this offers the possibility to trade the memory and computational costs for image quality or a larger number of iterations and is advantageous in new computing environments such as the cloud, where computing is often cheaper than memory and data movement.

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.

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.

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.

Kirchhoff modeling, inversion for reflectivity, and subsurface illumination

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1195-1209 ◽  
Author(s):  
Bertrand Duquet ◽  
Kurt J. Marfurt ◽  
Joe A. Dellinger
Keyword(s):  
Least Squares ◽  
A Priori ◽  
Computational Cost ◽  
Image Point ◽  
Surface Sampling ◽  
Constrained Least Squares ◽  
Amplitude Variation With Offset ◽  
Depth Migration ◽  
Kirchhoff Migration ◽  
Least Squares Migration

Because of its computational efficiency, prestack Kirchhoff depth migration is currently one of the most popular algorithms used in 2-D and 3-D subsurface depth imaging. Nevertheless, Kirchhoff algorithms in their typical implementation produce less than ideal results in complex terranes where multipathing from the surface to a given image point may occur, and beneath fast carbonates, salt, or volcanics through which ray‐theoretical energy cannot penetrate to illuminate underlying slower‐velocity sediments. To evaluate the likely effectiveness of a proposed seismic‐acquisition program, we could perform a forward‐modeling study, but this can be expensive. We show how Kirchhoff modeling can be defined as the mathematical transpose of Kirchhoff migration. The resulting Kirchhoff modeling algorithm has the same low computational cost as Kirchhoff migration and, unlike expensive full acoustic or elastic wave‐equation methods, only models the events that Kirchhoff migration can image. Kirchhoff modeling is also a necessary element of constrained least‐squares Kirchhoff migration. We show how including a simple a priori constraint during the inversion (that adjacent common‐offset images should be similar) can greatly improve the resulting image by partially compensating for irregularities in surface sampling (including missing data), as well as for irregularities in ray coverage due to strong lateral variations in velocity and our failure to account for multipathing. By allowing unstacked common‐offset gathers to become interpretable, the additional cost of constrained least‐squares migration may be justifiable for velocity analysis and amplitude‐variation‐with‐offset studies. One useful by‐product of least‐squares migration is an image of the subsurface illumination for each offset. If the data are sufficiently well sampled (so that including the constraint term is not necessary), the illumination can instead be calculated directly and used to balance the result of conventional migration, obtaining most of the advantages of least‐squares migration for only about twice the cost of conventional migration.

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.

scholarly journals Imaging Complex Subsurface Structures for Geothermal Exploration at Pirouette Mountain and Eleven-Mile Canyon in Nevada

2021 ◽  
Vol 9 ◽  
Author(s):  
Yunsong Huang ◽  
Miao Zhang ◽  
Kai Gao ◽  
Andrew Sabin ◽  
Lianjie Huang
Keyword(s):  
High Resolution ◽  
Least Squares ◽  
Seismic Data ◽  
Seismic Wave Propagation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Geothermal Exploration ◽  
Subsurface Structures ◽  
Time Migration ◽  
Ground Roll

Accurate imaging of subsurface complex structures with faults is crucial for geothermal exploration because faults are generally the primary conduit of hydrothermal flow. It is very challenging to image geothermal exploration areas because of complex geologic structures with various faults and noisy surface seismic data with strong and coherent ground-roll noise. In addition, fracture zones and most geologic formations behave as anisotropic media for seismic-wave propagation. Properly suppressing ground-roll noise and accounting for subsurface anisotropic properties are essential for high-resolution imaging of subsurface structures and faults for geothermal exploration. We develop a novel wavenumber-adaptive bandpass filter to suppress the ground-roll noise without affecting useful seismic signals. This filter adaptively exploits both characteristics of the lower frequency and the smaller velocity of the ground-roll noise than those of the signals. Consequently, this filter can effectively differentiate the ground-roll noise from the signal. We use our novel filter to attenuate the ground-roll noise in seismic data along five survey lines acquired by the U.S. Navy Geothermal Program Office at Pirouette Mountain and Eleven-Mile Canyon in Nevada, United States. We then apply our novel anisotropic least-squares reverse-time migration algorithm to the resulting data for imaging subsurface structures at the Pirouette Mountain and Eleven-Mile Canyon geothermal exploration areas. The migration method employs an efficient implicit wavefield-separation scheme to reduce image artifacts and improve the image quality. Our results demonstrate that our wavenumber-adaptive bandpass filtering method successfully suppresses the strong and coherent ground-roll noise in the land seismic data, and our anisotropic least-squares reverse-time migration produces high-resolution subsurface images of Pirouette Mountain and Eleven-Mile Canyon, facilitating accurate fault interpretation for geothermal exploration.

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