Multidirectional slowness vector for computing angle gathers from reverse time migration

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. S55-S68 ◽  
Author(s):  
Chen Tang ◽  
George A. McMechan
Keyword(s):  
Fourier Transforms ◽  
Grid Point ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Slowness Vector ◽  
Migration Velocity Analysis ◽  
Wavefield Decomposition ◽  
Complex Valued

Angle gathers are important for true-amplitude migration, migration velocity analysis, and angle-dependent inversion. Among existing methods, calculating the [Formula: see text] direction vector is efficient, but it can give only one direction per grid point and fails to give multiple directions for overlapping wavefields associated with multipaths and reflections. The slowness vectors (SVs) in [Formula: see text] and [Formula: see text] can be connected by Fourier transforms (FTs); the forward FT from [Formula: see text] to [Formula: see text] decomposes the wavefields into different vector components, and the inverse FT sums these components into a unique direction. Therefore, the SV has multiple directions in [Formula: see text], but it has only one direction in [Formula: see text]. Based on this relation, we have separated the computation of propagation direction into two steps: First, we used the forward FT, [Formula: see text] binning, and several inverse FTs to separate the wavefields into vector subsets with different approximate propagation angles, which contained much less wave overlapping; then, we computed [Formula: see text] SVs for each separated wavefield, and the set of these single-direction SVs constituted a multidirectional SV (MSV). In this process, the FTs between [Formula: see text] and [Formula: see text] domains required a large input/output (I/O) time. We prove the conjugate relation between the decomposition results using positive- and negative-frequency wavefields, and we use complex-valued modeling to obtain the positive-frequency wavefields. Thus, we did wavefield decomposition in [Formula: see text] instead of [Formula: see text], and avoided the huge I/O caused by the FT between the [Formula: see text] and [Formula: see text] domains. Our tests demonstrated that the MSV can give multiple directions for overlapping wavefields and improve the quality of angle gathers.

Least-squares inversion-based elastic reverse time migration with PP- and PS-angle-domain common-imaging gathers

Geophysics ◽  
2021 ◽  
Vol 86 (1) ◽  
pp. S29-S44
Author(s):  
Bingluo Gu ◽  
Jianping Huang ◽  
Jianguang Han ◽  
Zhiming Ren ◽  
Zhenchun Li
Keyword(s):  
Adjoint Operator ◽  
Optimization Method ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Migration Velocity Analysis ◽  
Velocity Information ◽  
The Difference ◽  
Amplitude Variation With Angle

Elastic angle-domain common-imaging gathers (ADCIGs) extracted from elastic reverse time migration (ERTM) play a pivotal part in elastic migration velocity analysis, elastic amplitude variation with angle, and attribute interpretation. In practice, however, elastic ADCIGs often suffer from unbalanced amplitude behavior, poor resolution, and low-wavenumber artifacts because of insufficient velocity information, limited recording aperture, uneven illumination, and other inaccuracies of the migration operator. We have developed a new method to improve the quality of elastic ADCIGs extracted from ERTM by posing ERTM imaging as an inverse problem whose misfit function measures the difference between simulated and observed data. The misfit function can be minimized by updating elastic offset-domain common-imaging gathers (ODCIGs) using an optimization method. Based on the transformation between ADCIGs and ODCIGs, the forward operator generates multicomponent seismic data from elastic ODCIGs by applying a scattering condition, and the adjoint operator generates elastic ODCIGs from ERTM using a subsurface space-shift imaging condition. Compared with elastic ODCIGs extracted from ERTM, our method effectively improves the focusing of elastic ODCIGs to produce elastic ADCIGs with higher resolution, fewer artifacts, and improved amplitude coherency across different reflection angles. Several synthetic examples were used to validate the effectiveness of the method.

The dynamically correct Poynting vector formulation for acoustic media with application in calculating multidirectional propagation vectors to produce angle gathers from reverse time migration

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. S365-S374 ◽  
Author(s):  
Chen Tang ◽  
George A. McMechan
Keyword(s):  
Computational Complexity ◽  
Poynting Vector ◽  
Fourier Transforms ◽  
Time Integration ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Slowness Vector ◽  
Acoustic Media ◽  
Energy Flux Density

The Poynting vector (PV) has been widely used to calculate propagation vectors of a pressure field (PF) in acoustic media. The most widely used acoustic PV formula is the negative of a product of the time and space derivatives. These two derivatives result in a phase shift between the PF and its PV; particularly, for a PF at a local magnitude peak, the PV modulus is zero and thus the propagation direction there is undefined. This “zero-modulus” issue is not consistent with the physical definition of the PV, which is the directional energy flux density of a PF because this definition indicates that the variation of the PV modulus should be consistent with the PF magnitude. This PV is only considered as kinematically correct and defined as K-PV. We derive the dynamically correct PV (D-PV) formula for acoustic media, which is the negative of the product of the reciprocal of the density, the PF itself, and a factor that is obtained by applying a time integration and a space derivative to the PF. There are two derivations. One uses the slowness vector, and the other is by simplifying the elastic PV. This D-PV does not suffer from the zero-modulus problem, and we also use it to update the multidirectional PV (MPV), which produces a D-MPV. Two strategies are provided to reduce the computational complexity of the time integration in the D-PV formula. Because the MPV already involves Fourier transforms between the time and frequency domains (which facilitates implementation of the time integration), its updated version causes only a very minor increase in the computational complexity of the original one. Numerical examples indicate that the D-PV provides more reliable propagation vectors than the K-PV, and the D-MPV provides more accurate angle-domain common-image gathers from reverse time migration of acoustic media than the K-MPV.

Least-squares reverse time migration using analytic-signal-based wavefield decomposition

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. S149-S157 ◽  
Author(s):  
Young Seo Kim ◽  
Ali Almomin ◽  
Woodon Jeong ◽  
Constantine Tsingas
Keyword(s):  
Least Squares ◽  
Fourier Transforms ◽  
Early Stage ◽  
Vertical Direction ◽  
Analytic Signal ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Inversion Process ◽  
Time Migration ◽  
Wavefield Decomposition

An intrinsic problem during migration and imaging of seismic wavefields using the two-way wave equation is the crosstalk interference between the up/down propagation of the corresponding source and receiver wavefields. To mitigate this crosstalk, the downgoing source and upgoing receiver wavefield imaging condition (IC) is adopted at an early stage of the inversion process, improving convergence and obtaining cleaner reflection images. A wavefield decomposition methodology can also be incorporated into a least-squares reverse time migration (LSRTM) algorithm. The separation of wavefields based on the propagation direction in the early iterations of LSRTM is to reduce interference noise during the inversion process given that the IC considers only primary reflections. Wavefields decomposed with respect to the vertical direction can be easily obtained by Fourier transforms on the time and vertical axes; however, they usually require significantly higher computational effort especially for 3D applications. Vertical wavefield decomposition by a complex-valued analytic signal is an alternative method implemented by the Hilbert transform, which can be conducted by 1D Fourier transform only on the vertical axis. An LSRTM algorithm adopting this decomposition method has a disadvantage in that it requires two additional wave modelings at each iteration. However, by adapting the deprimary IC into LSRTM, only one more modeling is additionally required in the backward wavefield propagation as compared with conventional LSRTM. Our LSRTM using wavefield decomposition has the ability to produce broader band reflectivity images than conventional LSRTM. This is demonstrated with numerical examples using synthetic and real data resulting artifact-free migration results and broadband reflectivity images.

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.

Plane-wave least-squares reverse time migration with a preconditioned stochastic conjugate gradient method

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. S33-S46 ◽  
Author(s):  
Chuang Li ◽  
Jianping Huang ◽  
Zhenchun Li ◽  
Rongrong Wang
Keyword(s):  
Plane Wave ◽  
Least Squares ◽  
Conjugate Gradient ◽  
Sampling Method ◽  
Singular Spectrum Analysis ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Numerical Tests ◽  
Time Migration

This study derives a preconditioned stochastic conjugate gradient (CG) method that combines stochastic optimization with singular spectrum analysis (SSA) denoising to improve the efficiency and image quality of plane-wave least-squares reverse time migration (PLSRTM). This method reduces the computational costs of PLSRTM by applying a controlled group-sampling method to a sufficiently large number of plane-wave sections and accelerates the convergence using a hybrid of stochastic descent (SD) iteration and CG iteration. However, the group sampling also produces aliasing artifacts in the migration results. We use SSA denoising as a preconditioner to remove the artifacts. Moreover, we implement the preconditioning on the take-off angle-domain common-image gathers (CIGs) for better results. We conduct numerical tests using the Marmousi model and Sigsbee2A salt model and compare the results of this method with those of the SD method and the CG method. The results demonstrate that our method efficiently eliminates the artifacts and produces high-quality images and CIGs.

scholarly journals Local Explosion Detection and Infrasound Localization by Reverse Time Migration Using 3-D Finite-Difference Wave Propagation

2021 ◽  
Vol 9 ◽  
Author(s):  
David Fee ◽  
Liam Toney ◽  
Keehoon Kim ◽  
Richard W. Sanderson ◽  
Alexandra M. Iezzi ◽  
...  
Keyword(s):  
Numerical Modeling ◽  
Finite Difference ◽  
Grid Point ◽  
Reverse Time ◽  
Computationally Efficient ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Straight Line ◽  
Active Vent ◽  
Time Reversal Mirror

Infrasound data are routinely used to detect and locate volcanic and other explosions, using both arrays and single sensor networks. However, at local distances (<15 km) topography often complicates acoustic propagation, resulting in inaccurate acoustic travel times leading to biased source locations when assuming straight-line propagation. Here we present a new method, termed Reverse Time Migration-Finite-Difference Time Domain (RTM-FDTD), that integrates numerical modeling into the standard RTM back-projection process. Travel time information is computed across the entire potential source grid via FDTD modeling to incorporate the effects of topography. The waveforms are then back-projected and stacked at each grid point, with the stack maximum corresponding to the likely source. We apply our method to three volcanoes with different network configurations, source-receiver distances, and topography. At Yasur Volcano, Vanuatu, RTM-FDTD locates explosions within ∼20 m of the source and differentiates between multiple vents. RTM-FDTD produces a more accurate location for the two Yasur subcraters than standard RTM and doubles the number of detected events. At Sakurajima Volcano, Japan, RTM-FDTD locates the source within 50 m of the active vent despite notable topographic blocking. The RTM-FDTD location is similar to that from the Time Reversal Mirror method, but is more computationally efficient. Lastly, at Shishaldin Volcano, Alaska, RTM and RTM-FDTD both produce realistic source locations (<50 m) for ground-coupled airwaves recorded on a four-station seismic network. We show that RTM is an effective method to detect and locate infrasonic sources across a variety of scenarios, and by integrating numerical modeling, RTM-FDTD produces more accurate source locations and increases the detection capability.

Reverse time migration of phase encoded all-order multiples

Geophysics ◽  
2021 ◽  
pp. 1-42
Author(s):  
Yike Liu ◽  
Yanbao Zhang ◽  
Yingcai Zheng
Keyword(s):  
Virtual Source ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Phase Encoding ◽  
Seismic Migration ◽  
Computational Costs ◽  
Time Migration ◽  
Source Data ◽  
Decomposition Strategies

Multiples follow long paths and carry more information on the subsurface than primary reflections, making them particularly useful for imaging. However, seismic migration using multiples can generate crosstalk artifacts in the resulting images because multiples of different orders interfere with each others, and crosstalk artifacts greatly degrade the quality of an image. We propose to form a supergather by applying phase-encoding functions to image multiples and stacking several encoded controlled-order multiples. The multiples are separated into different orders using multiple decomposition strategies. The method is referred to as the phase-encoded migration of all-order multiples (PEM). The new migration can be performed by applying only two finite-difference solutions to the wave equation. The solutions include backward-extrapolating the blended virtual receiver data and forward-propagating the summed virtual source data. The proposed approach can significantly attenuate crosstalk artifacts and also significantly reduce computational costs. Numerical examples demonstrate that the PEM can remove relatively strong crosstalk artifacts generated by multiples and is a promising approach for imaging subsurface targets.

Angle-domain common-image gathers from plane-wave least-squares reverse time migration

Geophysics ◽  
2021 ◽  
pp. 1-60
Author(s):  
Chuang Li ◽  
Zhaoqi Gao ◽  
Jinghuai Gao ◽  
Feipeng Li ◽  
Tao Yang
Keyword(s):  
Inverse Problem ◽  
Plane Wave ◽  
Least Squares ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Migration Velocity Analysis ◽  
Amplitude Versus

Angle-domain common-image gathers (ADCIGs) that can be used for migration velocity analysis and amplitude versus angle analysis are important for seismic exploration. However, because of limited acquisition geometry and seismic frequency band, the ADCIGs extracted by reverse time migration (RTM) suffer from illumination gaps, migration artifacts, and low resolution. We have developed a reflection angle-domain pseudo-extended plane-wave least-squares RTM method for obtaining high-quality ADCIGs. We build the mapping relations between the ADCIGs and the plane-wave sections using an angle-domain pseudo-extended Born modeling operator and an adjoint operator, based on which we formulate the extraction of ADCIGs as an inverse problem. The inverse problem is iteratively solved by a preconditioned stochastic conjugate gradient method, allowing for reduction in computational cost by migrating only a subset instead of the whole dataset and improving image quality thanks to preconditioners. Numerical tests on synthetic and field data verify that the proposed method can compensate for illumination gaps, suppress migration artifacts, and improve resolution of the ADCIGs and the stacked images. Therefore, compared with RTM, the proposed method provides a more reliable input for migration velocity analysis and amplitude versus angle analysis. Moreover, it also provides much better stacked images for seismic interpretation.

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