scholarly journals Elastic-wave reverse-time migration based on decoupled elastic-wave equations and inner-product imaging condition

2016 ◽  
Vol 13 (6) ◽  
pp. 953-963 ◽  
Author(s):  
Peng Yong ◽  
Jianping Huang ◽  
Zhenchun Li ◽  
Wenyuan Liao ◽  
Luping Qu ◽  
...  
Keyword(s):  
Elastic Wave ◽  
Wave Equations ◽  
Inner Product ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Imaging Condition ◽  
Time Migration ◽  
Elastic Wave Equations

Source-free converted-wave reverse time migration: Formulation and limitations

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. S17-S27 ◽  
Author(s):  
Yue Du ◽  
Yunyue Elita Li ◽  
Jizhong Yang ◽  
Arthur Cheng ◽  
Xinding Fang
Keyword(s):  
Wave Equations ◽  
Mode Conversion ◽  
Objective Functions ◽  
Source Information ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Converted Wave ◽  
Imaging Condition ◽  
Time Migration ◽  
Elastic Wave Equations

The source-free converted-wave (SFCW) reverse time migration is an alternative way to image the subsurface when the source information is missing or the overburden velocities are complex. However, it is challenging due to the lack of source-wavefield constraints. We have derived the SFCW imaging condition from the first gradients of waveform matching objective functions using a set of coupled P- and S-potential equations and small-perturbation approximations. We found that the images obtained from this SFCW imaging condition are second-order approximations to the shear-modulus perturbations. The images produced by the proposed imaging condition are free of the polarity reversal effects and have clear physical meanings. We also find that the acoustic wave equations can be used to back propagate the recorded P- and S-potentials, and the resulting images have the same kinematic accuracy and fewer unphysical mode-conversion artifacts than the SFCW images obtained by the elastic wave equations. Using multiple numerical examples, we determine the accuracy of our formulations, analyze the resolution and artifacts on the resulting images, and develop the limitations of the proposed method.

Imaging conditions for elastic reverse time migration

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. S95-S111 ◽  
Author(s):  
Wei Zhang ◽  
Ying Shi
Keyword(s):  
Decomposition Method ◽  
Inner Product ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Imaging Condition ◽  
Subsurface Structures ◽  
Time Migration ◽  
Imaging Conditions ◽  
Wave Modes

Elastic reverse time migration (RTM) has the ability to retrieve accurately migrated images of complex subsurface structures by imaging the multicomponent seismic data. However, the imaging condition applied in elastic RTM significantly influences the quality of the migrated images. We evaluated three kinds of imaging conditions in elastic RTM. The first kind of imaging condition involves the crosscorrelation between the Cartesian components of the particle-velocity wavefields to yield migrated images of subsurface structures. An alternative crosscorrelation imaging condition between the separated pure wave modes obtained by a Helmholtz-like decomposition method could produce reflectivity images with explicit physical meaning and fewer crosstalk artifacts. A drawback of this approach, though, was that the polarity reversal of the separated S-wave could cause destructive interference in the converted-wave image after stacking over multiple shots. Unlike the conventional decomposition method, the elastic wavefields can also be decomposed in the vector domain using the decoupled elastic wave equation, which preserves the amplitude and phase information of the original elastic wavefields. We have developed an inner-product imaging condition to match the vector-separated P- and S-wave modes to obtain scalar reflectivity images of the subsurface. Moreover, an auxiliary P-wave stress image can supplement the elastic imaging. Using synthetic examples with a layered model, the Marmousi 2 model, and a fault model, we determined that the inner-product imaging condition has prominent advantages over the other two imaging conditions and generates images with preserved amplitude and phase attributes.

True-amplitude linearized waveform inversion with the quasi-elastic wave equation

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. R827-R844 ◽  
Author(s):  
Zongcai Feng ◽  
Gerard Schuster
Keyword(s):  
Wave Equation ◽  
Elastic Wave ◽  
Wave Equations ◽  
Waveform Inversion ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Elastic Wave Equation ◽  
P Waves ◽  
Time Migration

We present a quasi-elastic wave equation as a function of the pressure variable, which can accurately model PP reflections with elastic amplitude variation with offset effects under the first-order Born approximation. The kinematic part of the quasi-elastic wave equation accurately models the propagation of P waves, whereas the virtual-source part, which models the amplitudes of reflections, is a function of the perturbations of density and Lamé parameters [Formula: see text] and [Formula: see text]. The quasi-elastic wave equation generates a scattering radiation pattern that is exactly the same as that for the elastic wave equation, and only requires the solution of two acoustic wave equations for each shot gather. This means that the quasi-elastic wave equation can be used for true-amplitude linearized waveform inversion (also known as least-squares reverse time migration) of elastic PP reflections, in which the corresponding misfit gradients are with respect to the perturbations of density and the P- and S-wave impedances. The perturbations of elastic parameters are iteratively updated by minimizing the [Formula: see text]-norm of the difference between the recorded PP reflections and the predicted pressure data modeled from the quasi-elastic wave equation. Numerical tests on synthetic and field data indicate that true-amplitude linearized waveform inversion using the quasi-elastic wave equation can account for the elastic PP amplitudes and provide a robust estimate of the perturbations of P- and S-wave impedances and, in some cases, the density. In addition, true-amplitude linearized waveform inversion provides images with a wider bandwidth and fewer artifacts because the PP amplitudes are accurately explained. We also determine the 2D scalar quasi-elastic wave equation for P-SV reflections and the 3D vector equation for PS reflections.

Isotropic elastic wavefield imaging using the energy norm

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. S207-S219 ◽  
Author(s):  
Daniel Rocha ◽  
Nicolay Tanushev ◽  
Paul Sava
Keyword(s):  
Normal Incidence ◽  
Spatial Location ◽  
Energy Norm ◽  
Inner Product ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Elastic Wave Equation ◽  
Imaging Condition ◽  
Time Migration

From the elastic-wave equation and the energy conservation principle, we have derived an energy norm that is applicable to imaging with elastic wavefields. Extending the concept of the norm to an inner product enables us to compare two related wavefields. For example, the inner product of source and receiver wavefields at each spatial location leads to an imaging condition. This new imaging condition outputs a single image representing the total reflection energy, and it contains individual terms related to the kinetic and potential energy (strain energy) from both extrapolated wavefields. An advantage of the proposed imaging condition compared with alternatives is that it does not suffer from polarity reversal at normal incidence, as do conventional images obtained using converted waves. Our imaging condition also accounted for the directionality of the wavefields in space and time. Based on this information, we have modified the imaging condition for attenuation of backscattering artifacts in elastic reverse time migration images. We performed numerical experiments that revealed the improved quality of the energy images compared with their conventional counterparts and the effectiveness of the imaging condition in attenuating backscattering artifacts even in media characterized by high spatial variability.

Multi-Component Seismic Wave Field Prestack Reverse-Time Depth Migration

2013 ◽  
Vol 868 ◽  
pp. 11-14
Author(s):  
Jia Jia Yang ◽  
Bing Shou He ◽  
Jian Zhong Zhang
Keyword(s):  
Wave Equation ◽  
Elastic Wave ◽  
Cross Correlation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Elastic Wave Equation ◽  
Imaging Condition ◽  
Depth Migration ◽  
Time Migration ◽  
Excitation Time

Based on the elastic wave equation, high-order finite-difference schemes for reverse-time extrapolation in the space of staggered grid and the perfectly matched layer (PML) absorbing boundary condition for the equation are derived. Prestack reverse-time depth migration (RTM) of elastic wave equation using the excitation time imaging condition and normalized cross-correlation imaging condition is carried out. Numerical experiments show that reverse-time migration is not limited for the angle of incidence and dramatic changes in lateral velocity. The reverse-time migration results of normalized cross-correlation imaging condition give the better effect than that of excitation time imaging condition.

Acoustic wavefield imaging using the energy norm

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. S151-S163 ◽  
Author(s):  
Daniel Rocha ◽  
Nicolay Tanushev ◽  
Paul Sava
Keyword(s):  
Waveform Inversion ◽  
Spatial Location ◽  
Energy Norm ◽  
Inner Product ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Imaging Condition ◽  
Time Migration ◽  
Head Waves ◽  
Complex Models

Wavefield energy can be measured by the so-called energy norm. We have extended the concept of “norm” to obtain the energy inner product between two related wavefields. Considering an imaging condition as an inner product between the source and receiver wavefields at each spatial location, we have developed a new imaging condition that represents the total reflection energy. Investigating this imaging condition further, we have found that it accounts for wavefield directionality in space time. Based on the directionality discrimination provided by this imaging condition, we have applied it to attenuate backscattering artifacts in reverse time migration (RTM). This imaging condition can be designed not only to attenuate backscattering artifacts, but also to attenuate any selected reflection angle. By exploiting the flexibility of this imaging condition for attenuating certain angles, we have developed a procedure to preserve the type of events that propagate along the same path, i.e., backscattered, diving, and head waves, leading to a suitable application for full-waveform- inversion (FWI). This application involves filtering the FWI gradient to preserve the tomographic term (waves propagating in the same path) and attenuate the migration term (reflections) of the gradient. We have developed the energy imaging condition applications for RTM and FWI using numerical experiments in simple (horizontal reflector) and complex models (Sigsbee and Marmousi).

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