scholarly journals Nonlinear scattering based imaging in elastic media: Theory, theorems, and imaging conditions

Geophysics ◽  
2013 ◽  
Vol 78 (3) ◽  
pp. S137-S155 ◽  
Author(s):  
Matteo Ravasi ◽  
Andrew Curtis
Keyword(s):  
Representation Theorem ◽  
Time Lag ◽  
Seismic Exploration ◽  
Elastic Media ◽  
Type Representation ◽  
Imaging Condition ◽  
Time Migration ◽  
Starting Point ◽  
Wavefield Extrapolation ◽  
Imaging Conditions

With the more widespread introduction of multicomponent recording devices in land and marine ocean-bottom seismic acquisition, elastic imaging may become mainstream in coming years. We have derived new, nonlinear, elastic imaging conditions. A correlation-type representation theorem for perturbed elastic media, commonly used in seismic interferometry to explain how a scattered wave response between two receivers/sources may be predicted given a boundary of sources/receivers, can be considered as a starting point for the derivation. Here, we use this theorem to derive and interpret imaging conditions for elastic migration by wavefield extrapolation (e.g., elastic reverse-time migration). Some approximations lead to a known, heuristically derived imaging condition that crosscorrelates P- and S-wave potentials that are separated in the subsurface after full-wavefield extrapolation. This formal connection reveals that the nonapproximated correlation-type representation theorem can be interpreted as a nonlinear imaging condition, that accounts also for multiply scattered and multiply converted waves, properly focusing such energy at each image point. We present a synthetic data example using either an ideal (acquisition on a full, closed boundary) or a real (partial boundary) seismic exploration survey, and we demonstrate the importance of nonlinearities in pure- and converted-mode imaging. In PP imaging, they result in better illumination and artifact reduction, whereas in PS imaging they show how zero time-lag and zero space-lag crosscorrelation imaging conditions are not ideal for imaging of converted-mode waves because no conversion arises from zero-offset experiments.

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.

Reverse time migration for microseismic sources using the geometric mean as an imaging condition

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. KS51-KS60 ◽  
Author(s):  
Nori Nakata ◽  
Gregory C. Beroza
Keyword(s):  
Time Reversal ◽  
Geometric Mean ◽  
Time Lag ◽  
Computational Cost ◽  
Velocity Model ◽  
Seismic Sources ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Imaging Condition ◽  
Time Migration

Time reversal is a powerful tool used to image directly the location and mechanism of passive seismic sources. This technique assumes seismic velocities in the medium and propagates time-reversed observations of ground motion at each receiver location. Assuming an accurate velocity model and adequate array aperture, the waves will focus at the source location. Because we do not know the location and the origin time a priori, we need to scan the entire 4D image (3D in space and 1D in time) to localize the source, which makes time-reversal imaging computationally demanding. We have developed a new approach of time-reversal imaging that reduces the computational cost and the scanning dimensions from 4D to 3D (no time) and increases the spatial resolution of the source image. We first individually extrapolate wavefields at each receiver, and then we crosscorrelate these wavefields (the product in the frequency domain: geometric mean). This crosscorrelation creates another imaging condition, and focusing of the seismic wavefields occurs at the zero time lag of the correlation provided the velocity model is sufficiently accurate. Due to the analogy to the active-shot reverse time migration (RTM), we refer to this technique as the geometric-mean RTM or GmRTM. In addition to reducing the dimension from 4D to 3D compared with conventional time-reversal imaging, the crosscorrelation effectively suppresses the side lobes and yields a spatially high-resolution image of seismic sources. The GmRTM is robust for random and coherent noise because crosscorrelation enhances signal and suppresses noise. An added benefit is that, in contrast to conventional time-reversal imaging, GmRTM has the potential to be used to retrieve velocity information by analyzing time and/or space lags of crosscorrelation, which is similar to what is done in active-source imaging.

Elastic wavefield separation based on the Helmholtz decomposition

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. S173-S183 ◽  
Author(s):  
Hejun Zhu
Keyword(s):  
Vector Fields ◽  
Helmholtz Decomposition ◽  
Elastic Media ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
S Waves ◽  
Poisson Solver ◽  
Time Migration ◽  
Imaging Conditions

Divergence and curl operators used for the decomposition of P- and S-wave modes in elastic reverse time migration (RTM) change the amplitudes, units, and phases of extrapolated wavefields. I separate the P- and S-waves in elastic media based on the Helmholtz decomposition. The decomposed wavefields based on this approach have the same amplitudes, units, and phases as the extrapolated wavefields. To avoid expensive multidimensional integrals in the Helmholtz decomposition, I introduce a fast Poisson solver to efficiently solve the vector Poisson’s equation. This fast algorithm allows us to reduce computational complexity from [Formula: see text] to [Formula: see text], where [Formula: see text] is the total number of grid points. Because the decomposed P- and S-waves are vector fields, I use vector imaging conditions to construct PP-, PS-, SS-, and SP-images. Several 2D numerical examples demonstrate that this approach allows us to accurately and efficiently decompose P- and S-waves in elastic media. In addition, elastic RTM images based on the vector imaging conditions have better quality and avoid polarity reversal in comparison with images based on the divergence and curl separation or direct component-by-component crosscorrelation.

Polarity-reversal correction for vector-based elastic reverse time migration

Geophysics ◽  
2021 ◽  
Vol 86 (1) ◽  
pp. S45-S58
Author(s):  
Kai Yang ◽  
Xingpeng Dong ◽  
Jianfeng Zhang
Keyword(s):  
Polarity Reversal ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Reversal Problem ◽  
Imaging Condition ◽  
Time Migration ◽  
Sign Change ◽  
Large Opening ◽  
Dot Product ◽  
Imaging Conditions

Polarity reversal is a well-known problem in elastic reverse time migration, and it is closely related to the imaging conditions. The dot product of source and receiver wavefields is a stable and efficient way to construct scalar imaging conditions for decomposed elastic vector wavefields. However, for PP images, the dot product introduces an angle-dependent factor that will change the polarity of image amplitudes at large opening angles, and it is also contaminated by low-wavenumber artifacts when sharp contrasts exist in the velocity model. Those two problems can be suppressed by muting the reflections with large opening angles at the expense of losing useful information. We have developed an elastic inverse-scattering imaging condition that can retain the initial polarity of the image amplitude and significantly reduce the low-wavenumber noise. For PS images, much attention is paid to the polarity-reversal problem at the normal incidence, and the dot-product-based imaging condition successfully avoids this kind of polarity reversal. There is another polarity-reversal problem arising from the sign change of the PS reflection coefficient at the Brewster angle. However, this sign change is often neglected in the construction of a stacked PS image, which will lead to reversed or distorted phases after stacking. We suggested using the S-wave impedance kernel used in elastic full-waveform inversion but only in the PS mode as an alternative to the dot-product imaging condition to alleviate this kind of polarity-reversal problem. In addition to dot-product-based imaging conditions, we analytically compare divergence- and curl-based imaging conditions and the elastic energy norm-based imaging condition with the presented imaging conditions to identify their advantages and weaknesses. Two numerical examples on a two-layer model and the SEAM 2D model are used to illustrate the effectiveness and advantages of the presented imaging conditions in suppressing low-wavenumber noise and correcting the polarity-reversal problem.

scholarly journals Time-shift imaging condition in seismic migration

Geophysics ◽  
2006 ◽  
Vol 71 (6) ◽  
pp. S209-S217 ◽  
Author(s):  
Paul Sava ◽  
Sergey Fomel
Keyword(s):  
Time Lag ◽  
Synthetic Data ◽  
Complex Salt ◽  
Time Shift ◽  
Reverse Time ◽  
Data Set ◽  
Imaging Condition ◽  
Space And Time ◽  
Wavefield Extrapolation ◽  
Zero Time

Seismic imaging based on single-scattering approximation is in the analysis of the match between the source and receiver wavefields at every image location. Wavefields at depth are functions of space and time and are reconstructed from surface data either by integral methods (Kirchhoff migration) or by differential methods (reverse-time or wavefield extrapolation migration). Different methods can be used to analyze wavefield matching, of which crosscorrelation is a popular option. Implementation of a simple imaging condition requires time crosscorrelation of source and receiver wavefields, followed by extraction of the zero time lag. A generalized imaging condition operates by crosscorrelation in both space and time, followed by image extraction at zero time lag. Images at different spatial crosscorrelation lags are indicators of imaging accuracy and are also used for image-angle decomposition. In this paper, we introduce an alternative prestack imaging condition in which we preserve multiple lags of the time crosscorrelation. Prestack images are described as functions of time shifts as opposed to space shifts between source and receiver wavefields. This imaging condition is applicable to migration by Kirchhoff, wavefield extrapolation, or reverse-time techniques. The transformation allows construction of common-image gathers presented as functions of either time shift or reflection angle at every location in space. Inaccurate migration velocity is revealed by angle-domain common-image gathers with nonflat events. Computational experiments using a synthetic data set from a complex salt model demonstrate the main features of the method.

Comparison of two viscoacoustic propagators for Q-compensated reverse time migration

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. S281-S297 ◽  
Author(s):  
Peng Guo ◽  
George A. McMechan ◽  
Huimin Guan
Keyword(s):  
Velocity Dispersion ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Layer Model ◽  
Imaging Condition ◽  
Intrinsic Attenuation ◽  
Time Migration ◽  
Standard Linear ◽  
Lossy Media ◽  
Wavefield Extrapolation

Without considering intrinsic attenuation, reverse time migration (RTM) of data from lossy media produces smeared migration images because of the [Formula: see text] effects (amplitude loss and velocity dispersion). To mitigate the [Formula: see text] effects during RTM, amplitudes need to be compensated and the propagation velocity of the compensated wavefield needs to be the same as in the attenuating wavefield. We have compared the decoupled constant [Formula: see text] (DCQ) viscoacoustic equation with the viscoacoustic equation based on the generalized standard linear solids (GSLS), for modeling and for [Formula: see text] compensation. The DCQ propagator separates amplitude loss and velocity dispersion operators; for the GSLS propagator, memory variables are used to introduce the [Formula: see text] effects. Amplitude loss and velocity dispersion are decoupled in the DCQ equation, whereas they are coupled in the GSLS equation. Viscoacoustic modeling by the two viscoacoustic propagators produces visually identical seismograms. To compensate for the [Formula: see text] effects, for the DCQ equation, we reverse the sign of the amplitude loss operator and keep the sign of the velocity dispersion operator unchanged. For the GSLS equation, the sign of the memory variables is reversed. Both approaches can compensate for the amplitude loss. Propagation velocities in the attenuating and [Formula: see text]-compensated wavefields are the same for the DCQ equation and are different for the GSLS equation. The [Formula: see text]-compensated wavefield propagates faster than the attenuating wavefield for the GSLS equation. Viscoacoustic RTM is implemented with the source normalized crosscorrelation imaging condition; the source wavefield is attenuated, and [Formula: see text] compensation is applied during receiver wavefield extrapolation. Results of [Formula: see text]-compensated migration on a three-layer model, a salt model, and the BP 2004 model using the DCQ equation are more consistent with the acoustic (nonviscous) RTM results, but they have a wider wavelet and a different [Formula: see text]-dependent amplitude behavior; there is a phase shift in the migration results when using the GSLS equation.

scholarly journals Depth Migration Based on Two-Way Wave Equation to Image OBS Multiples: A Case Study in the South Shetland Margin (Antarctica)

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Sha Song ◽  
Jiachun You ◽  
Qing Cao ◽  
Bin Chen ◽  
Xiaomeng Cao
Keyword(s):  
Wave Equation ◽  
Extrapolation Method ◽  
Seismic Exploration ◽  
Ocean Bottom Seismometer ◽  
The South ◽  
Time Migration ◽  
Multiple Imaging ◽  
Imaging Results ◽  
Obs Data ◽  
Wavefield Extrapolation

With the development of marine seismic exploration, the ocean bottom seismometer (OBS) as a new seismic acquisition technology has been widely concerned. Although multiple waves are frequently viewed as noises, they may carry a wealth of subsurface information and produce a broader illumination than primary waves. To perform multiple wave imaging, we propose to utilize a two-way wave equation depth wavefield extrapolation method which is rarely used in this field. A simple dipping model is imaged by using primary and multiple waves, which proves the superiority of multiple waves in imaging over the primary waves and lays a foundation for practical application. Moreover, the comparison of multiple imaging results by reverse time migration and those by our proposed method demonstrates that our proposed method requires less storage space. In this study, we apply this migration method to actual OBS data collected in the South Shetland margin (Antarctica), where gas hydrates have been well documented. Firstly, the wavefield separation method is adopted to process the OBS data, so as to produce reliable primary and multiples waves; secondly, the ray-tracing method is used to derive the velocity field; and finally, the depth wavefield extrapolation method based on the two-way wave equation is applied to image primary and multiple waves. Migration results show that multiple waves provide a broader illumination and a clearer sediment structure than primary waves, especially for the highly shallow reflections.

Imaging conditions for prestack reverse-time migration

Geophysics ◽  
2008 ◽  
Vol 73 (3) ◽  
pp. S81-S89 ◽  
Author(s):  
Sandip Chattopadhyay ◽  
George A. McMechan
Keyword(s):  
Amplitude Ratio ◽  
Reflection Coefficients ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Imaging Condition ◽  
Angle Dependence ◽  
Time Migration ◽  
Dependence Scale ◽  
Correct Angle ◽  
Imaging Conditions

Numerical implementations of six imaging conditions for prestack reverse-time migration show widely differing ability to provide accurate, angle-dependent estimates of reflection coefficients. Evaluation is in the context of a simple, one-interface acoustic model. Only reflection coefficients estimated by normalization of a crosscorrelation image by source illumination or by receiver-/source-wavefield amplitude ratio have the correct angle dependence, scale factor, and sign and the required (dimensionless) units; thus, these are the preferred imaging-condition algorithms. To obtain accurate image amplitudes, source- and receiver-wavefield extrapolations must be able to accurately reconstruct their respective wavefields at the target reflector.

scholarly journals Depth-Extrapolation-Based True-Amplitude Full-Wave-Equation Migration from Topography

2021 ◽  
Vol 11 (7) ◽  
pp. 3010
Author(s):  
Hao Liu ◽  
Xuewei Liu
Keyword(s):  
Wave Equation ◽  
Partial Derivative ◽  
Model Experiment ◽  
Surface Velocity ◽  
Seismic Exploration ◽  
Initial Condition ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Full Wave ◽  
Time Migration

The lack of an initial condition is one of the major challenges in full-wave-equation depth extrapolation. This initial condition is the vertical partial derivative of the surface wavefield and cannot be provided by the conventional seismic acquisition system. The traditional solution is to use the wavefield value of the surface to calculate the vertical partial derivative by assuming that the surface velocity is constant. However, for seismic exploration on land, the surface velocity is often not uniform. To solve this problem, we propose a new method for calculating the vertical partial derivative from the surface wavefield without making any assumptions about the surface conditions. Based on the calculated derivative, we implemented a depth-extrapolation-based full-wave-equation migration from topography using the direct downward continuation. We tested the imaging performance of our proposed method with several experiments. The results of the Marmousi model experiment show that our proposed method is superior to the conventional reverse time migration (RTM) algorithm in terms of imaging accuracy and amplitude-preserving performance at medium and deep depths. In the Canadian Foothills model experiment, we proved that our method can still accurately image complex structures and maintain amplitude under topographic scenario.

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