Attenuation compensation in anisotropic least-squares reverse time migration

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. S411-S423 ◽  
Author(s):  
Yingming Qu ◽  
Jianping Huang ◽  
Zhenchun Li ◽  
Zhe Guan ◽  
Jinli Li
Keyword(s):  
Wave Equation ◽  
Least Squares ◽  
Homogeneous Model ◽  
Seismic Wave Propagation ◽  
Negative Influence ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Wavenumber Domain ◽  
Time Migration ◽  
Numerical Noise

Anisotropic and attenuating properties of subsurface media cause amplitude loss and waveform distortion in seismic wave propagation, resulting in negative influence on seismic imaging. To correct the anisotropy effect and compensate amplitude attenuation, a compensated-amplitude vertical transverse isotropic (VTI) least-squares reverse time migration (LSRTM) method is adopted. In this method, the attenuation term of an attenuated acoustic wave equation is extended to a VTI quasi-differential wave equation, which takes care of effects from anisotropy and attenuation. The finite-difference method is used to solve the equation, in which attenuation terms are solved in the wavenumber domain, and other terms are solved in the space or wavenumber domain. Stable regularization operators are derived and introduced to the equations to eliminate severe numerical noise in high-frequency components during backward propagation. Meanwhile, a demigration operator, migration operator, and gradient formula for attenuated VTI media are derived to implement the amplitude-compensated VTI LSRTM. Test of a homogeneous model proves the accuracy of the attenuated VTI quasi-differential equations and the effectiveness of the regularization operators. A numerical example for a modified Marmousi model verifies the accuracy and superiority to the amplitude-compensated VTI LSRTM. Our results show that the sensitivity to anisotropic parameters is much higher than that to the [Formula: see text] parameters.

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.

Least-squares reverse time migration in TTI media using a pure qP-wave equation

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. S199-S216
Author(s):  
Xinru Mu ◽  
Jianping Huang ◽  
Jidong Yang ◽  
Xu Guo ◽  
Yundong Guo
Keyword(s):  
Wave Equation ◽  
Least Squares ◽  
Seismic Imaging ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
The Matrix ◽  
The Stability

Anisotropy is a common phenomenon in subsurface strata and should be considered in seismic imaging and inversion. Seismic imaging in a vertical transversely isotropic (VTI) medium does not take into account the effects of the tilt angles, which can lead to degraded migrated images in areas with strong anisotropy. To correct such waveform distortion, reduce related image artifacts, and improve migration resolution, a tilted transversely isotropic (TTI) least-squares reverse time migration (LSRTM) method is presented. In the LSRTM, a pure qP-wave equation is used and solved with the finite-difference method. We have analyzed the stability condition for the pure qP-wave equation using the matrix method, which is used to ensure the stability of wave propagation in the TTI medium. Based on this wave equation, we derive a corresponding demigration (Born modeling) and adjoint migration operators to implement TTI LSRTM. Numerical tests on the synthetic data show the advantages of TTI LSRTM over VTI RTM and VTI LSRTM when the recorded data contain strong effects caused by large tilt angles. Our numerical experiments illustrate that the sensitivity of the adopted TTI LSRTM to the migration velocity errors is much higher than that to the anisotropic parameters (including epsilon, delta, and tilted angle parameters), and its sensitivity to the epsilon model and tilt angle is higher than that to the delta model.

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.

Full Wavefield Least-Squares Reverse Time Migration

Geophysics ◽  
2021 ◽  
pp. 1-48
Author(s):  
Mikhail Davydenko ◽  
Eric Verschuur
Keyword(s):  
Wave Equation ◽  
Least Squares ◽  
Input Data ◽  
Waveform Inversion ◽  
Secondary Source ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Internal Multiples ◽  
The One

Waveform inversion based on Least-Squares Reverse Time Migration (LSRTM) usually involves Born modelling, which models the primary-only data. As a result the inversion process handles only primaries and corresponding multiple elimination pre-processing of the input data is required prior to imaging and inversion. Otherwise, multiples left in the input data are mapped as false reflectors, also known as crosstalk, in the final image. At the same time the developed Full Wavefield Migration (FWM) methodology can handle internal multiples in an inversion-based imaging process. However, because it is based on the framework of the one-way wave equation, it cannot image dips close to and beyond 90 degrees. Therefore, we aim at upgrading LSRTM framework by bringing functionality of FWM to handle internal multiples. We have discovered that the secondary source term, used in the original formulation of FWM to define a wavefield relationship that allows to model multiple scattering via reflectivity, can be injected into a pressure component when simulating the two-way wave equation using finite-difference modelling. We use this modified forward model for estimating the reflectivity model with automatic crosstalk supression and validate the method on both synthetic and field data containing visible internal multiples.

Preconditioned acoustic least-squares two-way wave-equation migration with exact adjoint operator

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. S1-S13 ◽  
Author(s):  
Linan Xu ◽  
Mauricio D. Sacchi
Keyword(s):  
Wave Equation ◽  
Least Squares ◽  
Adjoint Operator ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Product Test ◽  
Dot Product ◽  
The Time Domain ◽  
Adjoint Operators

We have investigated the problem of designing the forward operator and its exact adjoint for two-way wave-equation least-squares migration. We study the problem in the time domain and pay particular attention to the individual operators that are required by the algorithm. We derive our algorithm using the language of linear algebra and establish a simple path to design forward and adjoint operators that pass the dot-product test. We also found that the exact adjoint operator is not equal to the classic reverse time migration algorithm. For instance, one must pay particular attention to boundary conditions to compute the exact adjoint that accurately passes the dot-product test. Forward and adjoint operators are adopted to solve the so-called least-squares reverse time migration problem via the method of conjugate gradients. We also examine a preconditioning strategy to invert extended images.

Anisotropic least-squares reverse time migration based on first-order velocity-stress wave equation

2018 ◽  
Author(s):  
Xu Guo ◽  
JianPing Huang ◽  
JinQiang Huang ◽  
Qingyang Li ◽  
Feng Zhu
Keyword(s):  
Wave Equation ◽  
Least Squares ◽  
Stress Wave ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
First Order ◽  
Time Migration

Least-squares reverse time migration based on pure qP-wave equation in TTI media

2019 ◽  
Author(s):  
Xinru Mu ◽  
Jianping Huang ◽  
Xu Guo ◽  
Yingming Qu
Keyword(s):  
Wave Equation ◽  
Least Squares ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Tti Media

Elastic least-squares reverse time migration in vertical transverse isotropic media

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. S539-S553 ◽  
Author(s):  
Jidong Yang ◽  
Hejun Zhu ◽  
George McMechan ◽  
Houzhu Zhang ◽  
Yang Zhao
Keyword(s):  
Wave Equation ◽  
Least Squares ◽  
Transversely Isotropic ◽  
Image Resolution ◽  
Total Variation Regularization ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Isotropic Media ◽  
Band Limited

Using adjoint-based elastic reverse time migration, it is difficult to produce high-quality reflectivity images due to the limited acquisition apertures, band-limited source time function, and irregular subsurface illumination. Through iteratively computing the Hessian inverse, least-squares migration enables us to reduce the point-spread-function effects and improve the image resolution and amplitude fidelity. By incorporating anisotropy in the 2D elastic wave equation, we have developed an elastic least-squares reverse time migration (LSRTM) method for multicomponent data from the vertically transversely isotropic (VTI) media. Using the perturbed stiffness parameters [Formula: see text] and [Formula: see text] as PP and PS reflectivities, we linearize the elastic VTI wave equation and obtain a Born modeling (demigration) operator. Then, we use the Lagrange multiplier method to derive the corresponding adjoint wave equation and reflectivity kernels. With linearized forward modeling and adjoint migration operators, we solve a linear inverse problem to estimate the subsurface reflectivity models for [Formula: see text] and [Formula: see text]. To reduce the artifacts caused by data over-fitting, we introduce total-variation regularization into the reflectivity inversion, which promotes a sparse solution in terms of the model derivatives. To accelerate the convergence of LSRTM, we use source illumination to approximate the diagonal Hessian and use it as a preconditioner for the misfit gradient. Numerical examples help us determine that our elastic VTI LSRTM method can improve the spatial resolution and amplitude fidelity in comparison to adjoint migration.

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