3D coupled acoustic-elastic migration with topography and bathymetry based on spectral-element and adjoint methods

In the context of the adjoint method, we considered 3D coupled acoustic-elastic migration in the presence of surface topography and/or bathymetry. Isotropic elastic imaging involves three primary kernels, related to mass density and shear and bulk moduli, and various secondary kernels, for example, related to P-wave impedance and compressional and shear-wave speeds. Similar to reverse-time migration, these kernels reflect the constructive interference between a forward wavefield generated by active sources and an adjoint wavefield triggered by simultaneously back propagating recorded reflections from all receivers. Forward and adjoint wavefields were simulated using a spectral-element method, which, due to its weak nature, captures free-surface topography in land surveys and bathymetry in marine acquisition. To avoid storing the entire 3D forward wavefield, required for calculating its interaction with the adjoint wavefield, we only saved information on domain boundaries and reconstructed the forward wavefield while simulating the adjoint wavefield. Their interactions were calculated and integrated on the fly, thereby eliminating storage issues but doubling memory and CPU requirements. Our 3D images confirmed a previous conclusion based on 2D simulations, namely, that the impedance kernel best highlights reflectors, whereas wave-speed kernels constrain large-scale structures, i.e., the background model.

Download Full-text

Q least-squares reverse time migration based on the first-order viscoacoustic quasidifferential equations

Geophysics ◽

10.1190/geo2020-0712.1 ◽

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.

Download Full-text

Quasi-P wave Reverse Time Migration on SEAM dataset

10.1190/segam2015-5870250.1 ◽

2015 ◽

Author(s):

Jun Mu ◽

Bing Tang ◽

Sheng Xu ◽

Hongbo Zhou ◽

Aaron DeNosaquo

Keyword(s):

P Wave ◽

Reverse Time ◽

Reverse Time Migration ◽

Time Migration

Download Full-text

3-D prestack migration in anisotropic media

Geophysics ◽

10.1190/1.1443353 ◽

1993 ◽

Vol 58 (1) ◽

pp. 79-90 ◽

Cited By ~ 16

Author(s):

Zhengxin Dong ◽

George A. McMechan

Keyword(s):

A Priori ◽

Three Dimensional ◽

Synthetic Data ◽

Anisotropic Media ◽

P Wave ◽

Common Source ◽

Reverse Time ◽

Reverse Time Migration ◽

Prestack Migration ◽

Time Migration

A three‐dimensional (3-D) prestack reverse‐time migration algorithm for common‐source P‐wave data from anisotropic media is developed and illustrated by application to synthetic data. Both extrapolation of the data and computation of the excitation‐time imaging condition are implemented using a second‐order finite‐ difference solution of the 3-D anisotropic scalar‐wave equation. Poorly focused, distorted images are obtained if data from anisotropic media are migrated using isotropic extrapolation; well focused, clear images are obtained using anisotropic extrapolation. A priori estimation of the 3-D anisotropic velocity distribution is required. Zones of anomalous, directionally dependent reflectivity associated with anisotropic fracture zones are detectable in both the 3-D common‐ source data and the corresponding migrated images.

Download Full-text

Tensorial elastodynamics for isotropic media

Geophysics ◽

10.1190/geo2020-0074.1 ◽

2020 ◽

Vol 85 (6) ◽

pp. T359-T373

Author(s):

Jeffrey Shragge ◽

Tugrul Konuk

Keyword(s):

Free Surface ◽

Surface Topography ◽

Numerical Solutions ◽

Waveform Inversion ◽

Real Life ◽

Staggered Grid ◽

Surface Boundary ◽

Reverse Time ◽

Reverse Time Migration ◽

Time Migration

Numerical solutions of 3D isotropic elastodynamics form the key computational kernel for many isotropic elastic reverse time migration and full-waveform inversion applications. However, real-life scenarios often require computing solutions for computational domains characterized by non-Cartesian geometry (e.g., free-surface topography). One solution strategy is to compute the elastodynamic response on vertically deformed meshes designed to incorporate irregular topology. Using a tensorial formulation, we have developed and validated a novel system of semianalytic equations governing 3D elastodynamics in a stress-velocity formulation for a family of vertically deformed meshes defined by Bézier interpolation functions between two (or more) nonintersecting surfaces. The analytic coordinate definition also leads to a corresponding analytic free-surface boundary condition (FSBC) as well as expressions for wavefield injection and extraction. Theoretical examples illustrate the utility of the tensorial approach in generating analytic equations of 3D elastodynamics and the corresponding FSBCs for scenarios involving free-surface topography. Numerical examples developed using a fully staggered grid with a mimetic finite-difference formulation demonstrate the ability to model the expected full-wavefield behavior, including complex free-surface interactions.

Download Full-text

Accurate source-wavefield reconstruction for large-scale 3D reverse-time migration

10.1190/segam2014-1272.1 ◽

2014 ◽

Author(s):

Sirui Tan ◽

Lianjie Huang

Keyword(s):

Large Scale ◽

Reverse Time ◽

Reverse Time Migration ◽

Time Migration

Download Full-text

Elastic inversion of near- and postcritical reflections using phase variation with angle

Geophysics ◽

10.1190/geo2011-0230.1 ◽

2012 ◽

Vol 77 (4) ◽

pp. R149-R159 ◽

Cited By ~ 29

Author(s):

Xinfa Zhu ◽

George A. McMechan

Keyword(s):

Wave Velocity ◽

Spherical Wave ◽

Phase Variation ◽

P Wave ◽

Wide Angle ◽

Reverse Time ◽

Reverse Time Migration ◽

S Wave ◽

Time Migration ◽

Elastic Inversion

Near- and postcritical (wide-angle) reflections provide the potential for velocity and density inversion because of their large amplitudes and phase-shifted waveforms. We tested using phase variation with angle (PVA) data in addition to, or instead of, amplitude variation with angle (AVA) data for elastic inversion. Accurate PVA test data were generated using the reflectivity method. Two other forward modeling methods were also investigated, including plane-wave and spherical-wave reflection coefficients. For a two half-space model, linearized least squares was used to invert PVA and AVA data for the P-wave velocity, S-wave velocity, and the density of the lower space and the S-wave velocity of the upper space. Inversion tests showed the feasibility and robustness of PVA inversion. A reverse-time migration test demonstrated better preservation of PVA information than AVA information during wavefield propagation through a layered overburden. Phases of deeper reflections were less affected than amplitudes by the transmission losses, which makes the results of PVA inversion more accurate than AVA inversion in multilayered media. PVA brings useful information to the elastic inversion of wide-angle reflections.

Download Full-text

Separating quasi-P-wave in transversely isotropic media with a vertical symmetry axis by synthesized pressure applied to ocean-bottom seismic data elastic reverse time migration

Geophysics ◽

10.1190/geo2016-0108.1 ◽

2016 ◽

Vol 81 (6) ◽

pp. C295-C307 ◽

Cited By ~ 3

Author(s):

Pengfei Yu ◽

Jianhua Geng ◽

Chenlong Wang

Keyword(s):

Transversely Isotropic ◽

P Wave ◽

Ocean Bottom ◽

Receiver Side ◽

Reverse Time ◽

Reverse Time Migration ◽

Time Migration ◽

Isotropic Media ◽

Wave Imaging ◽

Obs Data

Quasi-P (qP)-wavefield separation is a crucial step for elastic P-wave imaging in anisotropic media. It is, however, notoriously challenging to quickly and accurately obtain separated qP-wavefields. Based on the concepts of the trace of the stress tensor and the pressure fields defined in isotropic media, we have developed a new method to rapidly separate the qP-wave in a transversely isotropic medium with a vertical symmetry axis (VTI) by synthesized pressure from ocean-bottom seismic (OBS) data as a preprocessing step for elastic reverse time migration (ERTM). Another key aspect of OBS data elastic wave imaging is receiver-side 4C records back extrapolation. Recent studies have revealed that receiver-side tensorial extrapolation in isotropic media with ocean-bottom 4C records can sufficiently suppress nonphysical waves produced during receiver-side reverse time wavefield extrapolation. Similarly, the receiver-side 4C records tensorial extrapolation was extended to ERTM in VTI media in our studies. Combining a separated qP-wave by synthesizing pressure and receiver-side wavefield reverse time tensorial extrapolation with the crosscorrelation imaging condition, we have developed a robust, fast, flexible, and elastic imaging quality improved method in VTI media for OBS data.

Download Full-text

Amplitude-preserving scalar PP and PS imaging condition for elastic reverse time migration based on a wavefield decoupling method

Geophysics ◽

10.1190/geo2017-0840.1 ◽

2019 ◽

Vol 84 (3) ◽

pp. S113-S125 ◽

Cited By ~ 1

Author(s):

Xiyan Zhou ◽

Xu Chang ◽

Yibo Wang ◽

Zhenxing Yao

Keyword(s):

Wave Vector ◽

Numerical Models ◽

P Wave ◽

Imaging Method ◽

Reverse Time ◽

Reverse Time Migration ◽

S Wave ◽

Decoupling Method ◽

Time Migration ◽

Imaging Results

To eliminate crosstalk within the imaging results of elastic reverse time migration (ERTM), we can separate the coupled P- and S-waves from the forward source wavefield and the backpropagated receiver wavefield. The P- and S-wave decoupling method retains the original phase, amplitude, and physical meaning in the separated wavefields. Thus, it is a vital wavefield separation method in ERTM. However, because these decomposed wavefields are vectors, we could consider how to retrieve scalar images that reveal the real reflectivity of the subsurface. For this purpose, we derive a scalar P-wave equation from the velocity-stress relationship for PP imaging. The phase and amplitude of this scalar P-wave are consistent with the scalarized P-wave. Therefore, this scalar P-wave can be exploited to perform PP imaging directly, with the imaging result retaining the amplitude characteristics. For PS imaging, it is difficult to calculate a dynamic preserved scalar S-wave. However, we have developed a scalar PS imaging method that divides the PS image into energy and sign components according to the geometric relationship between the wavefield vibration and propagation directions. The energy is calculated through the amplitude crosscorrelation of the forward P-wave and backpropagated S-wave from the receivers. The sign is obtained from the dot product of the forward P-wave vector and the backpropagated S-wave vector. These PP and PS imaging methods are suitable for 2D and 3D isotropic media and maintain the correct amplitude information while eliminating polarity-reversal phenomena. Several numerical models are used to verify the robustness and effectiveness of our method.

Download Full-text