Acoustic-elastic coupled equation for ocean bottom seismic data elastic reverse time migration

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. S333-S345 ◽  
Author(s):  
Pengfei Yu ◽  
Jianhua Geng ◽  
Xiaobo Li ◽  
Chenlong Wang
Keyword(s):  
Boundary Conditions ◽  
Particle Velocity ◽  
Ocean Bottom ◽  
Receiver Side ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
New Equation ◽  
Obs Data ◽  
Coupled Equation

Conventionally, multicomponent geophones used to record the elastic wavefields in the solid seabed are necessary for ocean bottom seismic (OBS) data elastic reverse time migration (RTM). Particle velocity components are usually injected directly as boundary conditions in the elastic-wave equation in the receiver-side wavefield extrapolation step, which causes artifacts in the resulting elastic images. We have deduced a first-order acoustic-elastic coupled equation (AECE) by substituting pressure fields into the elastic velocity-stress equation (EVSE). AECE has three advantages for OBS data over EVSE when performing elastic RTM. First, the new equation unifies wave propagation in acoustic and elastic media. Second, the new equation separates P-waves directly during wavefield propagation. Third, three approaches are identified when using the receiver-side multicomponent particle velocity records and pressure records in elastic RTM processing: (1) particle velocity components are set as boundary conditions in receiver-side vectorial extrapolation with the AECE, which is equal to the elastic RTM using the conventional EVSE; (2) the pressure component may also be used for receiver-side scalar extrapolation with the AECE, and with which we can accomplish PP and PS images using only the pressure records and suppress most of the artifacts in the PP image with vectorial extrapolation; and (3) ocean-bottom 4C data can be simultaneously used for elastic images with receiver-side tensorial extrapolation using the AECE. Thus, the AECE may be used for conventional elastic RTM, but it also offers the flexibility to obtain PP and PS images using only pressure records.

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 ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. C295-C307 ◽  
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.

Acoustic-elastic coupled equations in vertical transverse isotropic media for pseudoacoustic-wave reverse time migration of ocean-bottom 4C seismic data

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. S317-S327 ◽  
Author(s):  
Pengfei Yu ◽  
Jianhua Geng
Keyword(s):  
Seismic Data ◽  
Ocean Bottom ◽  
Receiver Side ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Coupled Equations ◽  
Wave Separation ◽  
Time Migration ◽  
Transverse Isotropic ◽  
Vti Media

Quasi-P (qP)-wave separation and receiver-side records back extrapolation are two key technologies commonly applied in vertical transverse isotropic (VTI) media for ocean-bottom 4C seismic data pseudoacoustic-wave reverse time migration (RTM). However, it remains problematic to quickly and accurately separate the qP-wave in VTI media. The qP-wave can be fast separated by synthesizing pressure in weakly anisotropic media. Like the derivation of acoustic-elastic coupled equations (AECEs) in an isotropic medium, novel AECEs can also be obtained in VTI media. Based on these novel coupled equations, we have developed a method for pseudoacoustic-wave RTM of ocean-bottom 4C seismic data. Three synthetic examples are provided to illustrate the validity and effectiveness of our method. The results indicate that our method possesses three advantages for ocean-bottom 4C data compared with the conventional method when conducting pseudoacoustic-wave RTM in VTI media. First, these new coupled equations are able to obtain a qP-wave during wavefield propagation. Second, ocean-bottom 4C records can be implemented strictly for receiver-side tensorial extrapolation with undulating topography of the seafloor, which brings benefits for suppressing artifacts in pseudoacoustic-wave RTM and improving imaging quality. Finally, our method is fairly robust to coarse sampling.

scholarly journals Analytic Acoustic–Elastic Coupled Equations and Their Application in Vector-Wave-Based Imaging of Ocean Bottom 4C Data

2019 ◽  
Vol 177 (2) ◽  
pp. 961-975
Author(s):  
Pengfei Yu ◽  
Jianhua Geng
Keyword(s):  
Synthetic Data ◽  
Ocean Bottom ◽  
Receiver Side ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Vector Wave ◽  
Coupled Equations ◽  
Time Migration ◽  
Vector Decomposition

Abstract In conventional vector-wave-based elastic reverse-time migration, there are two types of artifacts: low-frequency artifacts and nonphysical artifacts. Vector-decomposition-based acoustic–elastic coupled equations are effective in suppressing nonphysical artifacts by using ocean bottom four component (4C) seismic data for receiver-side tensorial extrapolation. We introduce up/down-going wave separation into the vector-decomposition-based acoustic–elastic coupled equations, and deduce novel analytic acoustic–elastic coupled equations. With these novel equations, we can obtain the source-side and receiver-side up-going and down-going P/S-wave vectors in wavefield propagation, and effectively suppress both of the artifacts in vector-wave-based elastic reverse-time migration by combining receiver-side tensorial extrapolation and the decomposed vector-wave-based imaging conditions. Examples using synthetic data and field data are presented to illustrate the validity and effectiveness of our method.

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.

Multiparameter least-squares reverse time migration for acoustic—elastic coupling media based on ocean bottom cable data

2019 ◽  
Vol 16 (3) ◽  
pp. 327-337
Author(s):  
Ying-Ming Qu ◽  
Chong-Peng Huang ◽  
Chang Liu ◽  
Chang Zhou ◽  
Zhen-Chun Li ◽  
...  
Keyword(s):  
Least Squares ◽  
Ocean Bottom ◽  
Elastic Coupling ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration

Reverse time migration with an exact two way illumination compensation

Geophysics ◽  
2021 ◽  
pp. 1-67
Author(s):  
Yuzhu Liu ◽  
Weigang Liu ◽  
Zheng Wu ◽  
Jizhong Yang
Keyword(s):  
Side Effects ◽  
Oil And Gas ◽  
Computational Cost ◽  
Receiver Side ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Subsurface Structures ◽  
Time Migration ◽  
Hessian Operator

Reverse time migration (RTM) has been widely used for imaging complex subsurface structures in oil and gas exploration. However, because only the adjoint of the forward Born modeling operator is applied to the seismic data in RTM, the output migration profile is biased in terms of the amplitude. To help partially balance the amplitude performance, the RTM image can be preconditioned with the inverse of the diagonal of the Hessian operator. Yet, existing preconditioning methods do not correctly consider the receiver-side effects, assuming that the receiver coverage is infinite or the velocity model is constant. We therefore provide a comparative study aiming to give a clearer understanding on the importance of incorporating the receiver-side effects by developing a frequency-domain scattering-integral reverse time migration (SI-RTM). In the proposed SI-RTM, the diagonal of the Hessian operator is explicitly computed in its exact formulation, and the source-side wavefield and receiver-side Green’s functions are obtained by solving the two-way wave equation. The computational cost is relatively affordable when compared with the more expensive least-squares RTM. In the comparative counterpart, the diagonal of the Hessian operator is approximated by the source-side illumination. We perform two synthetic numerical examples using an overthrust model and a complex reservoir model; the final migration images were significantly improved when the receiver-side effects were accurately considered. A third application of SI-RTM on one field data set acquired from the East China Sea further demonstrates the importance of incorporating the receiver-side effects in normalizing the RTM image. Findings of this study are expected to provide a theoretical basis for improving the ability of RTM imaging of subsurface structures, thereby critically advancing the application of geophysical techniques for imaging complex environments.

Least-squares reverse time migration of multiples

Geophysics ◽  
2014 ◽  
Vol 79 (1) ◽  
pp. S11-S21 ◽  
Author(s):  
Dongliang Zhang ◽  
Gerard T. Schuster
Keyword(s):  
Free Surface ◽  
Least Squares ◽  
Synthetic Data ◽  
Time History ◽  
Ocean Bottom ◽  
Virtual Source ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Sea Bed

The theory of least-squares reverse time migration of multiples (RTMM) is presented. In this method, least squares migration (LSM) is used to image free-surface multiples where the recorded traces are used as the time histories of the virtual sources at the hydrophones and the surface-related multiples are the observed data. For a single source, the entire free-surface becomes an extended virtual source where the downgoing free-surface multiples more fully illuminate the subsurface compared to the primaries. Since each recorded trace is treated as the time history of a virtual source, knowledge of the source wavelet is not required and the ringy time series for each source is automatically deconvolved. If the multiples can be perfectly separated from the primaries, numerical tests on synthetic data for the Sigsbee2B and Marmousi2 models show that least-squares reverse time migration of multiples (LSRTMM) can significantly improve the image quality compared to RTMM or standard reverse time migration (RTM) of primaries. However, if there is imperfect separation and the multiples are strongly interfering with the primaries then LSRTMM images show no significant advantage over the primary migration images. In some cases, they can be of worse quality. Applying LSRTMM to Gulf of Mexico data shows higher signal-to-noise imaging of the salt bottom and top compared to standard RTM images. This is likely attributed to the fact that the target body is just below the sea bed so that the deep water multiples do not have strong interference with the primaries. Migrating a sparsely sampled version of the Marmousi2 ocean bottom seismic data shows that LSM of primaries and LSRTMM provides significantly better imaging than standard RTM. A potential liability of LSRTMM is that multiples require several round trips between the reflector and the free surface, so that high frequencies in the multiples suffer greater attenuation compared to the primary reflections. This can lead to lower resolution in the migration image compared to that computed from primaries. Another liability is that the multiple migration image is more down-dip limited than the standard primaries migration image. Finally, if the surface-related multiple elimination method is imperfect and there are strong multiples interfering with the primaries, then the resulting LSRTMM image can be significantly degraded. We conclude that LSRTMM can be a useful complement, not a replacement, for RTM of primary reflections.

scholarly journals Elastic imaging with exact wavefield extrapolation for application to ocean-bottom 4C seismic data

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. S265-S284 ◽  
Author(s):  
Matteo Ravasi ◽  
Andrew Curtis
Keyword(s):  
Model Simulation ◽  
P Wave ◽  
Solid Boundary ◽  
Central Component ◽  
Ocean Bottom ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
True Time ◽  
Wavefield Extrapolation

A central component of imaging methods is receiver-side wavefield backpropagation or extrapolation in which the wavefield from a physical source scattered at any point in the subsurface is estimated from data recorded by receivers located near or at the Earth’s surface. Elastic reverse-time migration usually accomplishes wavefield extrapolation by simultaneous reversed-time ‘injection’ of the particle displacements (or velocities) recorded at each receiver location into a wavefield modeling code. Here, we formulate an exact integral expression based on reciprocity theory that uses a combination of velocity-stress recordings and quadrupole-dipole backpropagating sources, rather than the commonly used approximate formula involving only particle velocity data and dipole backpropagating sources. The latter approximation results in two types of nonphysical waves in the scattered wavefield estimate: First, each arrival contained in the data is injected upward and downward rather than unidirectionally as in the true time-reversed experiment; second, all injected energy emits compressional and shear propagating modes in the model simulation (e.g., if a recorded P-wave is injected, both P and S propagating waves result). These artifacts vanish if the exact wavefield extrapolation integral is used. Finally, we show that such a formula is suitable for extrapolation of ocean-bottom 4C data: Due to the fluid-solid boundary conditions at the seabed, the data recorded in standard surveys are sufficient to perform backpropagation using the exact equations. Synthetic examples provide numerical evidence of the importance of correcting such errors.

3D acoustic least-squares reverse time migration using the energy norm

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. S261-S270 ◽  
Author(s):  
Daniel Rocha ◽  
Paul Sava ◽  
Antoine Guitton
Keyword(s):  
Least Squares ◽  
Convergence Rates ◽  
Energy Norm ◽  
Ocean Bottom ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Image Domain ◽  
Time Migration ◽  
And Migration

We have developed a least-squares reverse time migration (LSRTM) method that uses an energy-based imaging condition to obtain faster convergence rates when compared with similar methods based on conventional imaging conditions. To achieve our goal, we also define a linearized modeling operator that is the proper adjoint of the energy migration operator. Our modeling and migration operators use spatial and temporal derivatives that attenuate imaging artifacts and deliver a better representation of the reflectivity and scattered wavefields. We applied the method to two Gulf of Mexico field data sets: a 2D towed-streamer benchmark data set and a 3D ocean-bottom node data set. We found LSRTM resolution improvement relative to RTM images, as well as the superior convergence rate obtained by the linearized modeling and migration operators based on the energy norm, coupled with inversion preconditioning using image-domain nonstationary matching filters.

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