Angle-domain Common-image Gathers Research Articles

Multidirectional-vector-based elastic reverse time migration and angle-domain common-image gathers with approximate wavefield decomposition of P- and S-waves

Elastic reverse time migration (E-RTM) has limitations when the migration velocities contain strong contrasts. First, the traditional scheme of P/S-wave mode separation is based on Helmholtz’s equations, which ignore the conversion between P- and S-waves at the current separation time. Thus, it contains an implicit assumption of the constant shear modulus and requires smoothing the heterogeneous model to approximately satisfy a locally constant condition. Second, the vector-based imaging condition needs to use the reflection-image normal, and it also cannot give the correct polarity of the PP image in all possible conditions. Third, the angle-domain common-image gathers (ADCIGs) calculated using the Poynting vectors (PVs) do not consider the wave interferences that happen at each reflector. Therefore, smooth models are often used for E-RTM. We relax this condition by proposing an improved data flow that involves three new contributions. The first contribution is an improved system of P/S-wave mode separation that considers the converted wave generated at the current time, and thus it does not require the constant-shear-modulus assumption. The second contribution is the new elastic imaging conditions based on multidirectional vectors; they can give the correct image polarity in all possible conditions without knowledge of the reflection-image normal. The third contribution is two methods to calculate multidirectional propagation vectors (PRVs) for RTM images and ADCIGs: One is the elastic multidirectional PV, and the other uses the sign of wavenumber-over-frequency ([Formula: see text]) ratio obtained from an amplitude-preserved approximate-propagation-angle-based wavefield decomposition to convert the particle velocities into multidirectional PRVs. The robustness of the improved data flow is determined by several 2D numerical examples. Extension of the schemes into 3D and amplitude-preserved imaging conditions is also possible.

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

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.

Vector-based excitation amplitude imaging condition for elastic RTM

In recent years, many studies have focused on elastic reverse time migration (RTM). In response to the problems associated with elastic RTM, we propose a new procedure for 2D elastic multicomponent RTM. In this new method, decomposed P- and S-wave components are obtained from the decoupled propagation of the source and receiver wavefields, which allows the expedient calculation of the Poynting vectors and the incident and reflection angles of the P- and S-waves. In addition, we deduce the vector-based excitation amplitude imaging condition. This process automatically accounts for the particle vibration directions when determining the angle-dependent signed reflection coefficients, and does not require the sign to be determined apart from the value of the reflection coefficients. This concept was further extended to the source-normalized crosscorrelation imaging condition. The reflection coefficient of the layered model test was in agreement with the Zoeppritz theory, the PP and PS wave images of the Marmousi II model were clear, and the PS wave images had higher resolution and richer details. In addition, since the calculated reflection coefficients are angle-dependent, they can be easily used for the extraction of angle-domain common-image gathers. Moreover, the imaging condition avoids the polarization reversal in PS wave images and does not require all of the source wavefield data. Consequently, the computation and storage requirements are significantly reduced, which will facilitate the use of the elastic RTM in practice.

A method of directly extracting multiwave angle-domain common-image gathers

Angle-domain common-image gathers (ADCIGs) can provide an effective way for migration velocity analysis and amplitude versus angle analysis in oil–gas seismic exploration. On the basis of multi-component Gaussian beam prestack depth migration (GB-PSDM), an alternative method of directly extracting multiwave ADCIGs is presented in this paper. We first introduce multi-component GB-PSDM, where a wavefield separation is proceeded to obtain the separated PP- and PS-wave seismic records before migration imaging for multiwave seismic data. Then, the principle of extracting PP- and PS-ADCIGs using GB-PSDM is presented. The propagation angle can be obtained using the real-value travel time of Gaussian beam in the course of GB-PSDM, which can be used to calculate the incidence and reflection angles. Two kinds of ADCIGs can be extracted for the PS-wave, one of which is P-wave incidence ADCIGs and the other one is S-wave reflection ADCIGs. In this paper, we use the incident angle to plot the ADCIGs for both PP- and PS-waves. Finally, tests of synthetic examples show that the method introduced here is accurate and effective.

Combining multidirectional source vector with antitruncation-artifact Fourier transform to calculate angle gathers from reverse time migration in two steps

Because receiver wavefields reconstructed from observed data are not as stable as synthetic source wavefields, the source-propagation vector and the reflector normal have often been used to calculate angle-domain common-image gathers (ADCIGs) from reverse time migration. However, the existing data flows have three main limitations: (1) Calculating the propagation direction only at the wavefields with maximum amplitudes ignores multiarrivals; using the crosscorrelation imaging condition at each time step can include the multiarrivals but will result in backscattering artifacts. (2) Neither amplitude picking nor Poynting-vector calculations are accurate for overlapping wavefields. (3) Calculating the reflector normal in space is not accurate for a structurally complicated reflection image, and calculating it in the wavenumber ([Formula: see text]) domain may give Fourier truncation artifacts. We address these three limitations in an improved data flow with two steps: During imaging, we use a multidirectional Poynting vector (MPV) to calculate the propagation vectors of the source wavefield at each time step and output intermediate source-angle-domain CIGs (SACIGs). After imaging, we use an antitruncation-artifact Fourier transform (ATFT) to convert SACIGs to ADCIGs in the [Formula: see text]-domain. To achieve the new flow, another three innovative aspects are included. In the first step, we develop an angle-tapering scheme to remove the Fourier truncation artifacts during the wave decomposition (of MPV) while preserving the amplitudes, and we use a wavefield decomposition plus angle-filter imaging condition to remove the backscattering artifacts in the SACIGs. In the second step, we compare two algorithms to remove the Fourier truncation artifacts that are caused by the plane-wave assumption. One uses an antileakage FT (ALFT) in local windows; the other uses an antitruncation-artifact FT, which relaxes the plane-wave assumption and thus can be done for the global space. The second algorithm is preferred. Numerical tests indicate that this new flow (source-side MPV plus ATFT) gives high-quality ADCIGs.

ADCIGs extraction and reflection tomography modeling for elastic wave

Based on the theory of elastic wave, we derive the migration angle formula of P- and S-wave in the Gaussian beam migration and implement the ADCIGs (angle domain common imaging gathers) extraction for Gaussian beam of PP- and PS-wave firstly. Then, we derive the reflection tomography equations for elastic wave velocity analysis. They are used for the tomography velocity modeling base on the Gaussian beam ADCIGs. Making reflection tomography and depth migration into the same velocity modeling process, this method can not only use ADCIGs of elastic wave to update the velocities, but also can apply the migration results of tomography in each iteration as quality control, until the end of whole process in velocity modeling and finally we can get the prestack depth migration results after tomography. Synthetic and field examples validate the correctness and practicability of this method.

Two algorithms to stabilize multidirectional Poynting vectors for calculating angle gathers from reverse time migration

Angle-domain common-image gathers (ADCIGs) obtained from reverse time migration are important for velocity and reflectivity inversion. Using the Poynting vector (PV) is an efficient way to calculate ADCIGs, but it suffers from inaccuracy and instability. A well-known reason is that a PV can give only one direction per grid point per time step, and thus it cannot calculate the individual directions of overlapping wavefields. This problem can be addressed by using a multidirectional PV (MPV), which decomposes the wavefields into several “approximate” directions and then calculates PVs for each decomposed wavefield. However, the MPV still suffers from another instability problem. The PV is the product of the time and space derivatives of the wavefield, and so it will be zero when the magnitude of the wavefield is at a local peak, which means that the directions are undefined. This leads to unstable points when the wavefields are close to a local magnitude peak, and it thus reduces the quality of the ADCIGs. We have developed two methods to stabilize the MPVs. The first method makes use of the property that the seismic wavelet has a short time duration, during which the propagation direction is stable. Thus, for each point in a decomposed wavefield, a time shift is used to locate the optimal PV during a short time duration, and the optimal location coincides with the local maximum magnitude of the time derivative. Therefore, there is a time shift between the wavefield and its corresponding PV. The second method combines the existing optical flow (OF) with the multidirectional scheme to produce a multidirectional OF (MOF). The MOF is iterative, and thus it has greater computational complexity. Numerical examples show that the time-shift MPV and MOF give more accurate ADCIGs than those using MPV only.

Target-oriented velocity analysis using Marchenko-redatumed data

Imaging a target zone and analyzing its corresponding velocities using seismic surface data can be challenging, in particular if the target zone is located below a highly scattering overburden. Marchenko redatuming enables the redatuming of the surface reflection response to an arbitrary new datum level below such an overburden. The obtained reflection response is free of internal multiples originating in the overburden, and thus, such data can be the starting point for target-oriented analyses. We develop the first application of Marchenko-redatumed data for target-oriented velocity analysis. Marchenko-redatumed data are used as the input for a conventional migration method to create angle-domain common-image gathers. Using incorrect velocities for redatuming or migration leads to residual moveout of reflections in such angle gathers. Thus, semblance analysis of the angle gathers allows us to correct an erroneous velocity profile. By combining events occurring at different depths in the angle gathers, we can correctly determine and separate the error inherent in the overburden of the velocity model used for redatuming and in the target zone used for migration. We tested the approach of velocity analysis with Marchenko-redatumed data in the simple case of a horizontally layered model and obtained the correct velocity model updates using interval velocity corrections. We then extended our approach and successfully applied a ray-based tomographic inversion to angle gathers created with Marchenko-redatumed data for a medium having lateral heterogeneity (dipping layers) and proved the advantages of velocity analysis using Marchenko-redatumed data compared with surface data.

High resolution diffraction imaging for reliable interpretation of fracture systems

Small-scale subsurface features, such as natural fractures, act as scattering sources for seismic waves propagating through the subsurface. The wavefield generated by those source points is identified as diffraction energy. The amplitude of this type of energy is much smaller than the recorded events reflected from actual interfaces between different geological layers. Moreover, diffraction energy is normally suppressed by conventional processing and standard imaging algorithms, where summations and averaging processes are applied. The common objective in such processing workflows is to focus on the high specular amplitudes in order to enhance the continuity of seismic reflection events for improving the structural mapping of the subsurface. Our goal is to complement the traditional seismic interpretation workflow by integrating information relative to diffraction energy as another seismic attribute to be interpreted. The technique applied in this paper is based on a depth imaging algorithm that maps and bins the recorded surface information into multi-dimensional, local angle domain (LAD) common image gathers. The advantage of this system is its unique ability to decompose the wavefield into reflection and diffraction energy directly at the image locations. This paper provides a brief overview of the technology and illustrates its benefits when applied to the Eagle Ford and Barnett shale reservoirs, where seismic data can be of moderate quality, leading to accurate, high-resolution, and highcertainty seismic interpretation for risk-managed field development.

Angle-domain common-image gathers from anisotropic Gaussian beam migration and its application to anisotropy-induced imaging errors analysis

An approach for extracting angle-domain common-image gathers (ADCIGs) from anisotropic Gaussian beam prestack depth migration (GB-PSDM) is presented in this paper. The propagation angle is calculated in the process of migration using the real-value traveltime information of Gaussian beam. Based on the above, we further investigate the effects of anisotropy on GB-PSDM, where the corresponding ADCIGs are extracted to assess the quality of migration images. The test results of the VTI syncline model and the TTI thrust sheet model show that anisotropic parameters ε, δ, and tilt angle 𝜃, have a great influence on the accuracy of the migrated image in anisotropic media, and ignoring any one of them will cause obvious imaging errors. The anisotropic GB-PSDM with the true anisotropic parameters can obtain more accurate seismic images of subsurface structures in anisotropic media.

Eliminating artifacts in migration of surface-related multiples: An application to marine data

Migration of multiples can use surface-related multiples to provide extra illumination of the subsurface; however, the migrated images usually contain many migration artifacts. We have developed an efficient workflow to eliminate the artifacts in migration of surface-related multiples and applied it to marine data. Our workflow was based on the criterion that true seismic events in angle-domain common-image gathers (ADCIGs) should be flat. The ADCIGs were obtained via the one-way wave-equation migration and then processed by high-resolution parabolic Radon transform to separate the artifacts. Using the adjoint Radon transform, the filtered ADCIGs can be stacked to get the final image with a high signal-to-noise ratio. We also discovered that the ADCIGs can be extracted from Fourier finite-difference migration more efficiently than by reverse time migration. In the application to marine data, most noise generated by the crosscorrelation of undesired seismic events was suppressed. This shows that the final images can be a valuable complement to conventional migration using primaries only.

Reverse time migration angle gathers using Poynting vectors

Angle-domain common-image gathers provide much useful data about the subsurface, such as seismic velocities and amplitude-versus-angle (AVA) information, and they can be manipulated to provide high-quality stacked images. However, the computation of angle gathers for reverse time migration (RTM), the most physically accurate migration algorithm, has proven to be costly in terms of computer time and memory usage. We have developed an algorithm for computing RTM angle gathers in a relatively efficient manner. Our method is based on the construction of the directions of propagation of the source and receiver wavefields, given by the direction of energy flux, known as the Poynting vector. The computation is carried out in the space-time domain, avoiding the need to transform the wavefield to, for example, frequency-wavenumber space, as is needed for methods based on wavefront projection. Given accurate Poynting vectors for source and receiver wavefields, one may compute the local reflection angle and azimuth, as well as the reflector dip and azimuth. An important advantage of our method is that it is based on local direction information at the reflection point, and thus it avoids the loss of resolution and smearing that can occur with some other techniques. A simple implementation of the Poynting-vector method can lead to noisy gathers, with leakage between angle bins, caused by unstable division of the local wavefields. We have developed an efficient technique to mitigate this noise and evaluated examples illustrating the aforementioned smearing issues of the subsurface-offset-based gathers and the improvements in the Poynting-vector gathers arising from our algorithm enhancement. Finally, the use of angle gathers for AVA analysis requires that (relative) amplitudes as a function of angle be correct. To this end, we derive weight functions for computing gathers with the correct AVA behavior. We determine the correctness of these weights by testing them with synthetic data.

Scalar and vector imaging based on wave mode decoupling for elastic reverse time migration in isotropic and transversely isotropic media

Recording P- and S-wave modes acquires more information related to rock properties of the earth’s interior. Elastic migration, as a part of multicomponent seismic data processing, potentially offers a great improvement over conventional acoustic migration to create a spatial image of some medium properties. In the framework of elastic reverse time migration, we have developed new scalar and vector imaging conditions assisted by efficient polarization-based mode decoupling to avoid crosstalk among the different wave modes for isotropic and transversely isotropic media. For the scalar imaging, we corrected polarity reversal of zero-lag PS images using the local angular attributes on the fly of angle-domain imaging. For the vector imaging, we naturally used the polarization information in the decoupled single-mode vector fields to automatically avoid the polarity reversal and to estimate the local angular attributes for angle-domain imaging. Examples of increasing complexity in 2D and 3D cases found that the proposed approaches can be used to obtain a physically interpretable image and angle-domain common-image gather at an acceptable computational cost. Decoupling and imaging the 3D S-waves involves some complexity, which has not been addressed in the literature. For this reason, we also attempted at illustrating the physical contents of the two separated S-wave modes and their contribution to seismic full-wave imaging.

Common-image gathers using the excitation amplitude imaging condition

Common-image gathers (CIGs) are extensively used in migration velocity analysis. Any defocused events in the subsurface offset domain or equivalently nonflat events in angle-domain CIGs are accounted for revising the migration velocities. However, CIGs from wave-equation methods such as reverse time migration are often expensive to compute, especially in 3D. Using the excitation amplitude imaging condition that simplifies the forward-propagated source wavefield, we have managed to extract extended images for space and time lags in conjunction with prestack reverse time migration. The extended images tend to be cleaner, and the memory cost/disk storage is extensively reduced because we do not need to store the source wavefield. In addition, by avoiding the crosscorrelation calculation, we reduce the computational cost. These features are demonstrated on a linear [Formula: see text] model, a two-layer velocity model, and the Marmousi model.

Polarized wavefield magnitudes with optical flow for elastic angle-domain common-image gathers

We have developed a polarized wavefield magnitude (PWM) approach to determine the polarity of an elastic vector wavefield magnitude, for elastic prestack reverse time migration imaging and common-image gather generation. Explicit decomposition of the coupled elastic wavefield into separate P-waves and converted S-waves is performed by using decoupled elastodynamic wavefield propagation. Stable source and receiver wavefield propagation angles are determined by an optical flow method for elastic media. The sign ambiguity in the propagation directions for incident P- and reflected P- and S-wavefield vector magnitudes is resolved by establishing a relation between the propagation and particle velocity vectors. From the computed propagation angles, PP- and PS-wavefields are imaged using source-normalized crosscorrelation followed by sorting into common-image gathers. Modeling of amplitude variations with angle (AVA) from single-shot migrations and from elastic angle-domain common-image gathers demonstrates that the amplitude fidelity is maintained. Mode-converted PS reflectivities also give an independent set of accurate AVA information. Numerical results for the elastic Marmousi2 model confirm PWM as a physically valid and robust method for elastic wavefield imaging in arbitrarily complicated media.

P‐ and S‐wave angle‐domain common‐image gathers (ADCIGs) based on elastic‐wave reverse‐time migration

AbstractElastic‐wave reverse‐time migration is an important imaging strategy because of its ability to image complex geologic structures and to efficiently extract elastic‐wave angle‐domain common‐image gathers (ADCIGs), which is an important task for amplitude‐versus‐angle (AVA) analysis and migration velocity analysis (MVA) in multicomponent exploration. Based on the characteristics of Poynting vectors in an elastic medium, we derive the wavefield‐separation imaging conditions for elastic reverse‐time migration (RTM) and establish the method of calculating the incident angle of source P‐wavefield using the propagation angle of source P‐wavefield and local dip angle of the reflector. Accurate ADCIGs can then be extracted based on the estimated incident angles with small computational cost. Two numerical examples show that the proposed method for extracting elastic‐wave ADCIGs can provide clear and accurate image and image gathers for elastic‐wave imaging tasks and therefore can provide reliable amplitude information for AVA and MVA. Copyright © 2016 John Wiley & Sons, Ltd.

Efficient angle-domain common-image gathers using Cauchy-condition-based polarization vectors

Because angle-domain common-image gathers (ADCIGs) from reverse time migration (RTM) are capable of obtaining the correct illumination of a subsurface geologic structure, they provide more reliable information for velocity model building, amplitude-variation versus angle analysis, and attribute interpretation. The approaches for generating ADCIGs mainly consist of two types: (1) indirect approaches that convert extended image gathers into ADCIGs and (2) direct approaches that first obtain propagating angles of wavefronts and then map the imaging result to the angle domain. In practice, however, generation of ADCIGs usually incurs high computational cost, poor resolution, and other drawbacks. To generate efficient ADCIGs using RTM methods, we have introduced a novel approach to obtain polarization vectors — directions of particle motion — from the Cauchy wavefield (CWF) and an efficient localized plane-wave decomposition algorithm to implement the angle-domain imaging condition. The CWF is a wavefield constructed from the Cauchy condition of the wave equation at any given time, and it only contains negative frequencies of the original wavefield so that the polarization vector is obtained from the local CWF in the wavenumber domain. With polarization vectors at our disposal, we have further developed an efficient localized plane-wave decomposition algorithm to implement the angle-domain imaging condition. Numerical examples have indicated that the new approach is able to handle complex wave phenomenon and has advantages in illuminating subsurface structure.

Angle gathers from reverse time migration using analytic wavefield propagation and decomposition in the time domain

Angle-domain common imaging gathers (ADCIGs) are important input data for migration velocity analysis and amplitude variation with angle analysis. Compared with Kirchhoff migration and one-way wave equation migration, reverse time migration (RTM) is the most accurate imaging method in complex areas, such as the subsalt area. We have developed a method to generate ADCIGs from RTM using analytic wavefield propagation and decomposition. To estimate the wave-propagation direction and angle by spatial Fourier transform during the time domain wave extrapolation, we have developed an analytic wavefield extrapolation method. Then, we decomposed the extrapolated source and receiver wavefields into their local angle components (i.e., local plane-wave components) and applied the angle-domain imaging condition to form ADCIGs. Because the angle-domain imaging condition is a convolution imaging condition about the source and receiver propagation angles, it is costly. To increase the efficiency of the angle-domain imaging condition, we have developed a local plane-wave decomposition method using matching pursuit. Numerical examples of synthetic and real data found that this method could generate high-quality ADCIGs. And these examples also found that the computational cost of this approach was related to the complexity of the source and receiver wavefields.

Vector-based elastic reverse time migration

Prestack elastic reverse time migration (RTM) of multicomponent seismic data requires separating PP and PS reflections before, or as part of, applying the image condition, and using image conditions that preserve the angle and amplitude information. Both of these requirements are best achieved when all operations are on vectors. We have created a new 2D migration context for isotropic, elastic RTM, which included decomposition of the elastic source and receiver wavefields into P- and S-wave vectors by decoupled elastodynamic extrapolation, which retained the same stress and particle velocity components as the input data. Then, the propagation directions of the incident and reflected P- and S-waves were calculated directly from the stress and particle velocity definitions of the P- and S-wave Poynting vectors. An excitation-amplitude image condition that scaled the receiver wavelet by the source vector magnitude produced angle-dependent images of PP and PS reflection coefficients with the correct polarities, polarization, and amplitudes. It thus simplified the process of obtaining PP and PS angle-domain common-image gathers (ADCIGs); it was less effort to generate ADCIGs from vector data than from scalar data. We found that the resulting prestack elastic images were nearly identical to the corresponding source-normalized crosscorrelation images and had improved resolution because the wavelet broadening that resulted from the crosscorrelation was not present.

Removing smearing-effect artifacts in angle-domain common-image gathers from reverse time migration

Local plane-wave decomposition (LPWD) and local shift imaging condition (LSIC) methods for extracting angle-domain common-image gathers (ADCIGs) from prestack reverse time migration are based on the local plane-wave assumption, and both suffer from a trade-off in choosing the local window size. Small windows produce clean ADCIGs, but with low angle resolution, whereas large windows produce noisy ADCIGs, which include smearing-effect artifacts, but with high angle resolution. The cause of the smearing-effect artifacts in LPWD is the crosscorrelation of plane waves obtained by decomposition of the source and receiver wavefronts, at points that do not lie on the source wavefront excitation time trajectory. The cause of the smearing-effect artifacts in LSIC is the decomposition of curved events of offset-domain common-image gathers (ODCIGs) at incorrect depth points at zero offset. These artifacts can occur even if the migration velocity model is correct. Two methods were proposed to remove the artifacts. In the LPWD method, the smearing-effect artifacts were removed by decomposing and crosscorrelating the resulting source and receiver plane waves only at image points and excitation (image) times. In the LSIC method, the artifacts were removed by decomposing curved events in ODCIGs into planar events only at zero-offset target image points. Numerical tests with synthetic data revealed the success of the proposed methods.