Least-squares reverse time migration with sparse regularization in the 2D wavelet domain

Geophysics ◽  
2020 ◽  
Vol 85 (6) ◽  
pp. S313-S325
Author(s):  
Feipeng Li ◽  
Jinghuai Gao ◽  
Zhaoqi Gao ◽  
Xiudi Jiang ◽  
Wenbo Sun
Keyword(s):  
Wavelet Transform ◽  
Image Quality ◽  
Least Squares ◽  
Conjugate Gradient ◽  
Seismic Data ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Sparse Constraint ◽  
Sparse Regularization ◽  
Time Migration

The inadequate sampling of seismic data in the spatial dimension results in migration artifacts. Conventional least-squares reverse time migration (LSRTM) could improve the image quality. However, even LSRTM will not work in some inadequately sampling situations. To mitigate the impact of migration artifacts, we have developed a new LSRTM method with a sparse regularization, which takes advantage of the effective sparse representation of the subsurface reflectivity model in the 2D undecimated wavelet transform (UWT) domain. Different from other sparse regularizations, a sparseness constraint in the 2D UWT domain is applied on the angle slices of the image. To efficiently solve the least-squares inversion problem, we employ an inversion scheme using the conjugate gradient method that uses a soft threshold method to achieve sparse constraint in updating the conjugate gradient direction. Compared with the sparse constraint based on the discrete wavelet transform (DWT), the threshold in this method is angle-dependent and is determined according to the energy distribution of each angle slice. To avoid overregularization that can lead to instability and increase the number of iterations, we also apply an exponential threshold strategy. Numerical tests on synthetic datasets demonstrate that our method is capable of improving the image quality by enhancing the resolution and suppressing migration artifacts caused by inadequately sampled seismic data. The method can converge more rapidly than conventional LSRTM. Because this method performs sparse regularization on several slopes, it achieves better performance on enhancing complex structures with discontinuities such as the steeply dipping faults compared to DWT-based regularization.

Plane-wave least-squares reverse time migration with a preconditioned stochastic conjugate gradient method

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. S33-S46 ◽  
Author(s):  
Chuang Li ◽  
Jianping Huang ◽  
Zhenchun Li ◽  
Rongrong Wang
Keyword(s):  
Plane Wave ◽  
Least Squares ◽  
Conjugate Gradient ◽  
Sampling Method ◽  
Singular Spectrum Analysis ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Numerical Tests ◽  
Time Migration

This study derives a preconditioned stochastic conjugate gradient (CG) method that combines stochastic optimization with singular spectrum analysis (SSA) denoising to improve the efficiency and image quality of plane-wave least-squares reverse time migration (PLSRTM). This method reduces the computational costs of PLSRTM by applying a controlled group-sampling method to a sufficiently large number of plane-wave sections and accelerates the convergence using a hybrid of stochastic descent (SD) iteration and CG iteration. However, the group sampling also produces aliasing artifacts in the migration results. We use SSA denoising as a preconditioner to remove the artifacts. Moreover, we implement the preconditioning on the take-off angle-domain common-image gathers (CIGs) for better results. We conduct numerical tests using the Marmousi model and Sigsbee2A salt model and compare the results of this method with those of the SD method and the CG method. The results demonstrate that our method efficiently eliminates the artifacts and produces high-quality images and CIGs.

Periodic plane-wave least-squares reverse time migration for diffractions

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. S185-S198
Author(s):  
Chuang Li ◽  
Jinghuai Gao ◽  
Zhaoqi Gao ◽  
Rongrong Wang ◽  
Tao Yang
Keyword(s):  
Inverse Problem ◽  
Image Quality ◽  
Plane Wave ◽  
Least Squares ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Diffraction Imaging ◽  
Periodic Plane

Diffraction imaging is important for high-resolution characterization of small subsurface heterogeneities. However, due to geometry limitations and noise distortion, conventional diffraction imaging methods may produce low-quality images. We have adopted a periodic plane-wave least-squares reverse time migration method for diffractions to improve the image quality of heterogeneities. The method reformulates diffraction imaging as an inverse problem using the Born modeling operator and its adjoint operator derived in the periodic plane-wave domain. The inverse problem is implemented for diffractions separated by a plane-wave destruction filter from the periodic plane-wave sections. Because the plane-wave destruction filter may fail to eliminate hyperbolic reflections and noise, we adopt a hyperbolic misfit function to minimize a weighted residual using an iteratively reweighted least-squares algorithm and thereby reduce residual reflections and noise. Synthetic and field data tests show that the adopted method can significantly improve the image quality of subsalt and deep heterogeneities. Compared with reverse time migration, it produces better images with fewer artifacts, higher resolution, and more balanced amplitude. Therefore, the adopted method can accurately characterize small heterogeneities and provide a reliable input for seismic interpretation in the prediction of hydrocarbon reservoirs.

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.

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.

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.

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.

2D least-squares elastic reverse time migration of multicomponent seismic data

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. S523-S538 ◽  
Author(s):  
Bingluo Gu ◽  
Jianguang Han ◽  
Zhiming Ren ◽  
Zhenchun Li
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Signal To Noise Ratio ◽  
Adjoint Operator ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Multicomponent Seismic ◽  
Isotropic Media ◽  
Wavefield Decomposition

Elastic reverse time migration (ERTM) is a state-of-the-art imaging technique used for determining complicated subsurface structures. However, the migrated images often suffer from low spatial resolution, low signal-to-noise ratio (S/N), and unbalanced amplitudes because the theoretical hypothesis of ERTM cannot be satisfied in practice. Although elastic least-squares reverse time migration (ELSRTM) has been proposed to address the issues of ERTM, the resulting images are generally represented by parameter perturbations such as P- and S-velocity perturbations, which have the different physical meanings from the ERTM images. To produce improved ERTM images, we used a least-squares RTM method for elastic data in isotropic media by applying least-squares inversion to ERTM. In the least-squares ERTM method, the forward operator generates multicomponent seismic data from the migrated images by applying elastic wavefield decomposition, scalar wavefield extrapolation, and wavefield recomposition operators. Additionally, the adjoint operator generates PP and PS images using ERTM, at which point the wavefield decomposition operator and scalar imaging condition are applied in the imaging process. Compared to conventional ERTM, our least-squares ERTM method enables us to produce improved ERTM images with higher resolution, more balanced amplitudes, and fewer artifacts. Several synthetic and field data examples were used to validate the effectiveness of the proposed least-squares ERTM method.

Elastic least-squares reverse time migration of steeply dipping structures using prismatic reflections

Geophysics ◽  
2022 ◽  
pp. 1-130
Author(s):  
Zheng Wu ◽  
Yuzhu Liu ◽  
Jizhong Yang
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Oil And Gas ◽  
Normal Equation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
Multicomponent Seismic ◽  
Imaging Conditions

The migration of prismatic reflections can be used to delineate steeply dipping structures, which is crucial for oil and gas exploration and production. Elastic least-squares reverse time migration (ELSRTM), which considers the effects of elastic wave propagation, can be used to obtain reasonable subsurface reflectivity estimations and interpret multicomponent seismic data. In most cases, we can only obtain a smooth migration model. Thus, conventional ELSRTM, which is based on the first-order Born approximation, considers only primary reflections and cannot resolve steeply dipping structures. To address this issue, we develop an ELSRTM framework, called Pris-ELSRTM, which can jointly image primary and prismatic reflections in multicomponent seismic data. When Pris-ELSRTM is directly applied to multicomponent records, near-vertical structures can be resolved. However, the application of imaging conditions established for prismatic reflections to primary reflections destabilizes the process and leads to severe contamination of the results. Therefore, we further improve the Pris-ELSRTM framework by separating prismatic reflections from recorded multicomponent data. By removing artificial imaging conditions from the normal equation, primary and prismatic reflections can be imaged based on unique imaging conditions. The results of synthetic tests and field data applications demonstrate that the improved Pris-ELSRTM framework produces high-quality images of steeply dipping P- and S-wave velocity structures. However, it is difficult to delineate steep density structures because of the insensitivity of the density to prismatic reflections.

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