Two methods for computing the imaging condition for common‐shot prestack migration

Geophysics ◽  
1991 ◽  
Vol 56 (3) ◽  
pp. 378-381 ◽  
Author(s):  
D. Loewenthal ◽  
Liang‐zie Hu
Keyword(s):  
Seismic Data ◽  
Grid Point ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Imaging Condition ◽  
Prestack Migration ◽  
Time Zero ◽  
Time Migration ◽  
Excitation Time ◽  
The One

This note addresses two methods of computing the imaging condition for prestack migration of common‐shot seismic data; our work is based on the ideas from reverse‐time migration for both poststack (Loewenthal and Mufti, 1983; McMechan, 1983) and prestack data (Chang and McMechan, 1986). In reverse‐time migration of poststack data, the whole stacked section is backward‐extrapolated in time, with half of the medium velocity to time zero. All exploding reflectors are imaged at once at time zero. The time zero is referred to as the imaging condition. In prestack migration, the imaging condition is more involved. Each spatial grid point (treated as a point diffractor) has a different excitation time, which is equal to the one‐way traveltime from the source to that grid point. Each point diffractor is imaged separately at its excitation (the “imaging time”).

Reverse‐time migration of offset vertical seismic profiling data using the excitation‐time imaging condition

Geophysics ◽  
1986 ◽  
Vol 51 (1) ◽  
pp. 67-84 ◽  
Author(s):  
Wen‐Fong Chang ◽  
George A. McMechan
Keyword(s):  
Finite Difference ◽  
Wave Field ◽  
Image Space ◽  
Variable Velocity ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Imaging Condition ◽  
Time Zero ◽  
Time Migration ◽  
Excitation Time

To apply reverse‐time migration to prestack, finite‐offset data from variable‐velocity media, the standard (time zero) imaging condition must be generalized because each point in the image space has a different image time (or times). This generalization is the excitation‐time imaging condition, in which each point is imaged at the one‐way traveltime from the source to that point. Reverse‐time migration with the excitation‐time imaging condition consists of three elements: (1) computation of the imaging condition; (2) extrapolation of the recorder wave field; and (3) application of the imaging condition. Computation of the imaging condition for each point in the image is done by ray tracing from the source point; this is equivalent to extrapolation of the source wave field through the medium. Extrapolation of the recorded wave field is done by an acoustic finite‐difference algorithm. Imaging is performed at each step of the finite‐difference extrapolation by extracting, from the propagating wave field, the amplitude at each mesh point that is imaged at that time and adding these into the image space at the same spatial locations. The locus of all points imaged at one time step is a wavefront [a constant time (or phase) trajectory]. This prestack migration algorithm is very general. The excitation‐time imaging condition is applicable to all source‐receiver geometries and variable‐velocity media and reduces exactly to the usual time‐zero imaging condition when used with zero‐offset surface data. The algorithm is illustrated by application to both synthetic and real VSP data. The most interesting and potentially useful result in the processing of the synthetic data is imaging of the horizontal fluid interfaces within a reservoir even when the surrounding reservoir boundaries are not well imaged.

Source-receiver, reverse-time imaging of dual-source, vector-acoustic seismic data

Geophysics ◽  
2013 ◽  
Vol 78 (2) ◽  
pp. WA123-WA145 ◽  
Author(s):  
Ivan Vasconcelos
Keyword(s):  
Seismic Data ◽  
Super Resolution ◽  
Imaging Method ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Imaging Condition ◽  
Novel Technologies ◽  
Time Migration ◽  
Consistent Manner ◽  
Dual Source

Novel technologies in seismic data acquisition allow for recording full vector-acoustic (VA) data: pointwise recordings of pressure and its multicomponent gradient, excited by pressure only as well as dipole/gradient sources. Building on recent connections between imaging and seismic interferometry, we present a wave-equation-based, nonlinear, reverse-time imaging approach that takes full advantage of dual-source multicomponent data. The method’s formulation relies on source-receiver scattering reciprocity, thus making proper use of VA fields in the wavefield extrapolation and imaging condition steps in a self-consistent manner. The VA imaging method is capable of simultaneously focusing energy from all in- and outgoing waves: The receiver-side up- and downgoing (receiver ghosts) fields are handled by the VA receiver extrapolation, whereas source-side in- and outgoing (source ghosts) arrivals are accounted for when combining dual-source data at the imaging condition. Additionally, VA imaging handles image amplitudes better than conventional reverse-time migration because it properly handles finite-aperture directivity directly from dual-source, 4C data. For nonlinear imaging, we provide a complete source-receiver framework that relies only on surface integrals, thus being computationally applicable to practical problems. The nonlinear image can be implicitly interpreted as a superposition of several nonlinear interactions between scattering components of data with those corresponding to the extrapolators (i.e., to the model). We demonstrate various features of the method using synthetic examples with complex subsurface features. The numerical results show, e.g., that the dual-source, VA image retrieves subsurface features with “super-resolution”, i.e., with resolution higher than the limits of Born imaging, but at the cost of introducing image artifacts not present in the linear image. Although the method does not require any deghosting as a preprocessing step, it can use separated up- and downgoing fields to generate independent subsurface images.

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.

Implicit static corrections in prestack migration of common‐source data

Geophysics ◽  
1990 ◽  
Vol 55 (6) ◽  
pp. 757-760 ◽  
Author(s):  
G. A. McMechan ◽  
H. W. Chen
Keyword(s):  
Surface Velocity ◽  
Common Source ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Near Surface ◽  
Prestack Migration ◽  
Time Migration ◽  
Excitation Time ◽  
Source Data ◽  
Static Corrections

Static effects due to surface topography and near‐surface velocity variations may be accurately compensated for, in an implicit way, during prestack reverse‐time migration of common‐source gathers, obviating the need for explicit static corrections. Receiver statics are incorporated by extrapolating the observed data from the actual recorder positions; source statics are incorporated by computing the excitation‐time imaging conditions from the actual source positions.

Excitation amplitude imaging condition for prestack reverse-time migration

Geophysics ◽  
2013 ◽  
Vol 78 (1) ◽  
pp. S37-S46 ◽  
Author(s):  
Bao D. Nguyen ◽  
George A. McMechan
Keyword(s):  
Signal To Noise Ratio ◽  
Grid Point ◽  
Synthetic Data ◽  
Cost Effective ◽  
Excitation Amplitude ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Step ◽  
Imaging Condition ◽  
Time Migration

An implicitly stable ratio imaging condition for prestack reverse-time migration (RTM) was defined using excitation criteria. Amplitude maxima and their corresponding occurrence times were saved at each grid point during forward source wavefield extrapolation. Application of the imaging condition involves dividing the amplitudes of the back-propagated receiver wavefield by the precomputed maximum source wavefield amplitude only at the grid points that satisfy the image time at each time step. The division normalizes by the source amplitude, so only the highest signal-to-noise ratio portion of the data is used. Provided that the source and receiver wavefield amplitudes are accurate at the reflection points, the peak wavelet amplitudes in the migrated image are the angle-dependent reflection coefficients and low wavenumber artifacts are significantly reduced compared to those in images calculated by crosscorrelation. Using excitation information and time-binning for the imaging condition improves computational and storage efficiency by three or more orders of magnitude when compared to crosscorrelation with the full source wavefield. Numerical tests with synthetic data for the Marmousi2 model have shown this method to be a cost-effective and practical imaging condition for use in prestack RTM.

Vector-based elastic reverse time migration based on scalar imaging condition

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. S111-S127 ◽  
Author(s):  
Qizhen Du ◽  
ChengFeng Guo ◽  
Qiang Zhao ◽  
Xufei Gong ◽  
Chengxiang Wang ◽  
...  
Keyword(s):  
Alternative Methods ◽  
Polarity Reversal ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Converted Wave ◽  
Imaging Condition ◽  
Time Migration ◽  
Wavefield Separation ◽  
Wave Modes

The scalar images (PP, PS, SP, and SS) of elastic reverse time migration (ERTM) can be generated by applying an imaging condition as crosscorrelation of pure wave modes. In conventional ERTM, Helmholtz decomposition is commonly applied in wavefield separation, which leads to a polarity reversal problem in converted-wave images because of the opposite polarity distributions of the S-wavefields. Polarity reversal of the converted-wave image will cause destructive interference when stacking over multiple shots. Besides, in the 3D case, the curl calculation generates a vector S-wave, which makes it impossible to produce scalar PS, SP, and SS images with the crosscorrelation imaging condition. We evaluate a vector-based ERTM (VB-ERTM) method to address these problems. In VB-ERTM, an amplitude-preserved wavefield separation method based on decoupled elastic wave equation is exploited to obtain the pure wave modes. The output separated wavefields are both vectorial. To obtain the scalar images, the scalar imaging condition in which the scalar product of two vector wavefields with source-normalized illumination is exploited to produce scalar images instead of correlating Cartesian components or magnitude of the vector P- and S-wave modes. Compared with alternative methods for correcting the polarity reversal of PS and SP images, our ERTM solution is more stable and simple. Besides these four scalar images, the VB-ERTM method generates another PP-mode image by using the auxiliary stress wavefields. Several 2D and 3D numerical examples are evaluated to demonstrate the potential of our ERTM method.

Reducing artifacts of elastic reverse time migration by the deprimary technique

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. S569-S577 ◽  
Author(s):  
Yang Zhao ◽  
Houzhu Zhang ◽  
Jidong Yang ◽  
Tong Fei
Keyword(s):  
Complex Function ◽  
Noise Removal ◽  
Pure Mode ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Imaging Condition ◽  
Velocity Models ◽  
Time Migration ◽  
Wavefield Decomposition

Using the two-way elastic-wave equation, elastic reverse time migration (ERTM) is superior to acoustic RTM because ERTM can handle mode conversions and S-wave propagations in complex realistic subsurface. However, ERTM results may not only contain classical backscattering noises, but they may also suffer from false images associated with primary P- and S-wave reflections along their nonphysical paths. These false images are produced by specific wave paths in migration velocity models in the presence of sharp interfaces or strong velocity contrasts. We have addressed these issues explicitly by introducing a primary noise removal strategy into ERTM, in which the up- and downgoing waves are efficiently separated from the pure-mode vector P- and S-wavefields during source- and receiver-side wavefield extrapolation. Specifically, we investigate a new method of vector wavefield decomposition, which allows us to produce the same phases and amplitudes for the separated P- and S-wavefields as those of the input elastic wavefields. A complex function involved with the Hilbert transform is used in up- and downgoing wavefield decomposition. Our approach is cost effective and avoids the large storage of wavefield snapshots that is required by the conventional wavefield separation technique. A modified dot-product imaging condition is proposed to produce multicomponent PP-, PS-, SP-, and SS-images. We apply our imaging condition to two synthetic models, and we demonstrate the improvement on the image quality of ERTM.

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.

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