Direct vector-field method to obtain angle-domain common-image gathers from isotropic acoustic and elastic reverse time migration

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. WB135-WB149 ◽  
Author(s):  
Qunshan Zhang ◽  
George A. McMechan
Keyword(s):  
Direct Method ◽  
Incident Angle ◽  
Field Method ◽  
Propagation Direction ◽  
P Wave ◽  
Common Source ◽  
Spatial Gradient ◽  
Reverse Time ◽  
S Wave ◽  
Time Migration

We have developed an alternative (new) method to produce common-image gathers in the incident-angle domain by calculating wavenumbers directly from the P-wave polarization rather than using the dominant wavenumber as the normal to the source wavefront. In isotropic acoustic media, the wave propagation direction can be directly calculated as the spatial gradient direction of the acoustic wavefield, which is parallel to the wavenumber direction (the normal to the wavefront). Instantaneous wavenumber, obtained via a novel Hilbert transform approach, is used to calculate the local normal to the reflectors in the migrated image. The local incident angle is produced as the difference between the propagation direction and the normal to the reflector. By reordering the migrated images (over all common-source gathers) with incident angle, common-image gathers are produced in the incident-angle domain. Instantaneous wavenumber takes the place of the normal to the reflector in the migrated image. P- and S-wave separations allow both PP and PS common-image gathers to be calculated in the angle domain. Unlike the space-shift image condition for calculating the common-image gather in angle domain, we use the crosscorrelation image condition, which is substantially more efficient. This is a direct method, and is less dependent on the data quality than the space-shift method. The concepts were successfully implemented and tested with 2D synthetic acoustic and elastic examples, including a complicated (Marmousi2) model that illustrates effects of multipathing in angle-domain common-image gathers.

Scalar reverse‐time depth migration of prestack elastic seismic data

Geophysics ◽  
2001 ◽  
Vol 66 (5) ◽  
pp. 1519-1527 ◽  
Author(s):  
Robert Sun ◽  
George A. McMechan
Keyword(s):  
Seismic Waves ◽  
Velocity Model ◽  
P Wave ◽  
Common Source ◽  
Reverse Time ◽  
S Wave ◽  
Wave Source ◽  
Reflected Waves ◽  
S Waves ◽  
Elastic Data

Reflected P‐to‐P and P‐to‐S converted seismic waves in a two‐component elastic common‐source gather generated with a P‐wave source in a two‐dimensional model can be imaged by two independent scalar reverse‐time depth migrations. The inputs to migration are pure P‐ and S‐waves that are extracted by divergence and curl calculations during (shallow) extrapolation of the elastic data recorded at the earth’s surface. For both P‐to‐P and P‐to‐S converted reflected waves, the imaging time at each point is the P‐wave traveltime from the source to that point. The extracted P‐wave is reverse‐time extrapolated and imaged with a P‐velocity model, using a finite difference solution of the scalar wave equation. The extracted S‐wave is reverse‐time extrapolated and imaged similarly, but with an S‐velocity model. Converted S‐wave data requires a polarity correction prior to migration to ensure constructive interference between data from adjacent sources. Synthetic examples show that the algorithm gives satisfactory results for laterally inhomogeneous models.

3-D prestack migration in anisotropic media

Geophysics ◽  
1993 ◽  
Vol 58 (1) ◽  
pp. 79-90 ◽  
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.

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

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. R149-R159 ◽  
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.

Angle- and azimuth-domain common-image gathers by reverse time migration for 3D elastic isotropic media

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. S151-S167
Author(s):  
Zabihollah Khaksar ◽  
George A. McMechan
Keyword(s):  
Incident Angle ◽  
Migration Velocity ◽  
Spatial Gradient ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Disk Storage ◽  
Time Migration ◽  
Isotropic Media ◽  
The Hilbert Transform ◽  
Elastic Particle

A 2D algorithm for angle-domain common-image gather (CIG) calculation is extended and modified to produce 3D elastic angle and azimuth CIGs. The elastic seismic data are propagated with the elastic particle displacement wave equation, and then the PP-reflected and PS-converted waves are separated by divergence and curl calculations during application of the excitation-time imaging condition. The incident angles and azimuths are calculated using source propagation directions and the reflector normals. The source propagation direction vector is computed as the spatial gradient of the incident 3C P-wavefield. The vector normal to the reflector is calculated using the Hilbert transform. Ordering the migrated images with respect to incident angles for a fixed azimuth bin, or with respect to azimuths for a fixed incident angle bin, creates angle- or azimuth-domain CIGs, respectively. Sorting the azimuth gathers by the incident angle bins causes a shift to a greater depth for too-high migration velocity and to a smaller depth for too-low migration velocity. For the sorted incident angle gathers, the velocity-dependent depth moveout is within the angle gathers and across the azimuth gathers. This method is compared with three other 3D CIG algorithms with respect to the number of calculations and their disk storage and RAM requirements; it is three to six orders of magnitude faster and requires two to three orders of magnitude less disk space. The method is successfully tested with data for a modified part of the SEG/EAGE overthrust model.

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

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. S113-S125 ◽  
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.

Elastic reflection waveform inversion based on the decomposition of sensitivity kernels

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. R235-R250 ◽  
Author(s):  
Zhiming Ren ◽  
Zhenchun Li ◽  
Bingluo Gu
Keyword(s):  
Wave Velocity ◽  
Waveform Inversion ◽  
Velocity Model ◽  
P Wave ◽  
Background Model ◽  
Reverse Time ◽  
S Wave ◽  
Velocity Models ◽  
Time Migration ◽  
Starting Model

Full-waveform inversion (FWI) has the potential to obtain an accurate velocity model. Nevertheless, it depends strongly on the low-frequency data and the initial model. When the starting model is far from the real model, FWI tends to converge to a local minimum. Based on a scale separation of the model (into the background model and reflectivity model), reflection waveform inversion (RWI) can separate out the tomography term in the conventional FWI kernel and invert for the long-wavelength components of the velocity model by smearing the reflected wave residuals along the transmission (or “rabbit-ear”) paths. We have developed a new elastic RWI method to build the P- and S-wave velocity macromodels. Our method exploits a traveltime-based misfit function to highlight the contribution of tomography terms in the sensitivity kernels and a sensitivity kernel decomposition scheme based on the P- and S-wave separation to suppress the high-wavenumber artifacts caused by the crosstalk of different wave modes. Numerical examples reveal that the gradients of the background models become sufficiently smooth owing to the decomposition of sensitivity kernels and the traveltime-based misfit function. We implement our elastic RWI in an alternating way. At each loop, the reflectivity model is generated by elastic least-squares reverse time migration, and then the background model is updated using the separated traveltime kernels. Our RWI method has been successfully applied in synthetic and real reflection seismic data. Inversion results demonstrate that the proposed method can retrieve preferable low-wavenumber components of the P- and S-wave velocity models, which are reliable to serve as a starting model for conventional elastic FWI. Also, our method with a two-stage inversion workflow, first updating the P-wave velocity using the PP kernels and then updating the S-wave velocity using the PS kernels, is feasible and robust even when P- and S-wave velocities have different structures.

A new decoupling and elastic propagator for efficient elastic reverse time migration

Geophysics ◽  
2020 ◽  
Vol 85 (5) ◽  
pp. A31-A36
Author(s):  
Qizhen Du ◽  
Qiang Zhao ◽  
Qingqing Li ◽  
Liyun Fu ◽  
Qifeng Sun
Keyword(s):  
Heterogeneous Media ◽  
Compressional Wave ◽  
Wave Mode ◽  
P Wave ◽  
Receiver Side ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
Energy Leakage

Methods to decompose the elastic wavefield into compressional wave (P-wave) and shear wave (S-wave) components in heterogeneous media without wavefield distortions or energy leakage are the key issues in elastic imaging and inversion. We have introduced a decoupled P- and S-wave propagator to form an efficient elastic reverse time migration (RTM) framework, without assuming homogeneous Lamé parameters. Also, no wave-mode conversions occur using the proposed propagator in the presence of strong heterogeneities, which avoids the potential imaging artifacts caused by wave-mode conversions in the receiver-side backward extrapolation. In the proposed elastic RTM framework, the source-side forward wavefield is simulated with a P-wave propagator. The receiver-side wavefield is back extrapolated with the proposed propagator, using the recorded multicomponent seismic data as input. Compared to the conventional elastic RTM, the proposed framework reduces the computational complexity while preserving the imaging accuracy. We have determined its accuracy and efficiency using two synthetic examples.

Common-image gathers in the incident phase-angle domain from reverse time migration in 2D elastic VTI media

Geophysics ◽  
2011 ◽  
Vol 76 (6) ◽  
pp. S197-S206 ◽  
Author(s):  
Qunshan Zhang ◽  
George A. McMechan
Keyword(s):  
Phase Angle ◽  
Incident Angle ◽  
Image Point ◽  
Common Source ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Wave Phase ◽  
Time Migration ◽  
Imaging Time ◽  
Vti Media

Reverse time migration (RTM) was implemented with a modified crosscorrelation imaging condition for data from 2D elastic vertically transversely isotropy (VTI) media. The computation cost was reduced because scalar qP- and qS-wavefield separations are performed in VTI media, for the source and receiver wavefields only at the RTM imaging time, to calculate the migrated qP and qS images. Angle-domain common-image gathers (CIGs) were extracted from qPqP and qPqS common-source RTM images. The local incident angle was produced as the difference between the qP-wave phase angle, obtained directly from the source wavefield polarization, and the normal to the reflector, calculated as the instantaneous wavenumber direction via a directional Hilbert transform of the stacked image. Angle-domain CIGs were extracted by reordering the prestack-migrated images by local incident phase angle, source by source. Vector decomposition of the source qP-wavefield was required to calculate the qP-wave phase polarization direction for each image point at its imaging time. RTM and angle-domain CIG extraction were successfully implemented and illustrated with a synthetic 2D elastic VTI example.

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.

A wavefield-separation-based elastic least-squares reverse time migration

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. S279-S297 ◽  
Author(s):  
Bingluo Gu ◽  
Zhenchun Li ◽  
Jianguang Han
Keyword(s):  
Least Squares ◽  
Synthetic Data ◽  
P Wave ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
S Waves ◽  
Numerical Tests ◽  
Time Migration

Elastic least-squares reverse time migration (ELSRTM) has the potential to provide improved subsurface reflectivity estimation. Compared with elastic RTM (ERTM), ELSRTM can produce images with higher spatial resolution, more balanced amplitudes, and fewer artifacts. However, the crosstalk between P- and S-waves can significantly degrade the imaging quality of ELSRTM. We have developed an ELSRTM method to suppress the crosstalk artifacts. This method includes three crucial points. The first is that the forward and backward wavefields are extrapolated based on the separated elastic velocity-stress equation of P- and S-waves. The second is that the separated vector P- and S-wave residuals are migrated to form reflectivity images of Lamé constants [Formula: see text] and [Formula: see text] independently. The third is that the reflectivity images of [Formula: see text] and [Formula: see text] are obtained by the vector P-wave wavefields achieved in the backward extrapolation of the separated vector P-wave residuals and the vector S-wave wavefields achieved in the backward extrapolation of the separated vector S-wave residuals, respectively. Numerical tests with synthetic data demonstrate that our ELSRTM method can produce images free of crosstalk artifacts. Compared with ELSRTM based on the coupled wavefields, our ELSRTM method has better convergence and higher accuracy.

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