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

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. S69-S77 ◽  
Author(s):  
Xiongwen Wang ◽  
Jianliang Qian ◽  
Huazhong Wang
Keyword(s):  
Plane Wave ◽  
Model Building ◽  
Computational Cost ◽  
Decomposition Algorithm ◽  
Reverse Time ◽  
Imaging Condition ◽  
Plane Wave Decomposition ◽  
Time Migration ◽  
Imaging Result ◽  
Wave Decomposition

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.

Comparison of methods for extracting ADCIGs from RTM

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. S89-S103 ◽  
Author(s):  
Hu Jin ◽  
George A. McMechan ◽  
Huimin Guan
Keyword(s):  
Plane Wave ◽  
Low Noise ◽  
Direction Vector ◽  
Reverse Time ◽  
Imaging Condition ◽  
Plane Wave Decomposition ◽  
Time Migration ◽  
Local Plane ◽  
Local Shift ◽  
Wave Decomposition

Methods for extracting angle-domain common-image gathers (ADCIGs) during 2D reverse-time migration fall into three main categories; direction-vector-based methods, local-plane-wave decomposition methods, and local-shift imaging condition methods. The direction-vector-based methods, which use either amplitude gradients or phase gradients, cannot handle overlapping events because of an assumption of one propagation direction per imaging point per imaging time; however, the ADCIGs from the direction-vector-based methods have the highest angle resolution. A new direction-vector-based method using instantaneous phase gradients in space and time gives the same propagation directions and ADCIGs as those obtained by the Poynting vector or polarization vector based methods, where amplitudes are large. Angles calculated by the phase gradients have larger uncertainties at smaller amplitudes, but they do not significantly degrade the ADCIGs because they contribute only small amplitudes. The local-plane-wave decomposition and local-shift imaging condition methods, implemented either by a Fourier transform or by a slant stack transform, can handle overlapping events, and produce very similar angle gathers. ADCIGs from both methods depend on the local window size in which the transforms are done. In small local windows, both methods produce ADCIGs with low noise, but also with low angle resolution; in large windows, they have high angle resolution, but contain smeared artifacts.

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

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. S359-S376 ◽  
Author(s):  
Chen Tang ◽  
George A. McMechan
Keyword(s):  
Fourier Transform ◽  
Plane Wave ◽  
Poynting Vector ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Step ◽  
Imaging Condition ◽  
Time Migration ◽  
Reflection Image ◽  
Wave Decomposition

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.

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

Geophysics ◽  
2016 ◽  
Vol 81 (1) ◽  
pp. S1-S9 ◽  
Author(s):  
Jiangtao Hu ◽  
Huazhong Wang ◽  
Xiongwen Wang
Keyword(s):  
Plane Wave ◽  
Time Domain ◽  
Computational Cost ◽  
Imaging Method ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Imaging Condition ◽  
Time Migration ◽  
Local Plane ◽  
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.

Surface-offset gathers from elastic reverse time migration and velocity analysis

Geophysics ◽  
2020 ◽  
Vol 85 (1) ◽  
pp. S47-S64
Author(s):  
Yang Zhao ◽  
Tao Liu ◽  
Xueyi Jia ◽  
Hongwei Liu ◽  
Zhiguang Xue ◽  
...  
Keyword(s):  
Velocity Ratio ◽  
Computational Cost ◽  
Cost Effective ◽  
Velocity Estimation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
The Common ◽  
Wave Decomposition

Angle-domain common-image gathers (ADCIGs) from elastic reverse time migration (ERTM) are valuable tools for seismic elastic velocity estimation. Traditional ADCIGs are based on the concept of common-offset domains, but common-shot domain implementations are often favored for computational cost considerations. Surface-offset gathers (SOGs) built from common-offset migration may serve as an alternative to the common-shot ADCIGs. We have developed a theoretical kinematic framework between these two domains, and we determined that the common SOG gives an alternative measurement of kinematic correctness in the presence of incorrect velocity. Specifically, we exploit analytical expressions for the image misposition between these two domains, with respect to the traveltime perturbation caused by velocity errors. Four formulations of the PP and PS residual moveout functions are derived and provide insightful information of the velocity error, angle, and PS velocity ratio contained in ERTM gathers. The analytical solutions are validated with homogeneous examples with a series of varied parameters. We found that the SOGs may perform in the way of simplicity and linearity as an alternative to the common-shot migration. To make a full comparison with ADCIGs, we have developed a cost-effective workflow of ERTM SOGs. A fast vector P- and S-wave decomposition can be obtained via spatial gradients at selected time steps. A selected ERTM imaging condition is then modified in which the migration is done by offset groups between each source and receiver pair for each P- and S-wave decomposition. Two synthetic (marine and land) examples are used to demonstrate the feasibility of our methods.

On plane‐wave decomposition: Alias removal

Geophysics ◽  
1989 ◽  
Vol 54 (10) ◽  
pp. 1339-1343 ◽  
Author(s):  
S. C. Singh ◽  
G. F. West ◽  
C. H. Chapman
Keyword(s):  
Plane Wave ◽  
Seismic Data ◽  
P Wave ◽  
S Wave ◽  
Plane Wave Decomposition ◽  
Time Migration ◽  
Time Distance ◽  
P Domain ◽  
Wave Decomposition ◽  
Rapid Modeling

The delay‐time (τ‐p) parameterization, which is also known as the plane‐wave decomposition (PWD) of seismic data, has several advantages over the more traditional time‐distance (t‐x) representation (Schultz and Claerbout, 1978). Plane‐wave seismograms in the (τ, p) domain can be used for obtaining subsurface elastic properties (P‐wave and S‐wave velocities and density as functions of depth) from inversion of the observed oblique‐incidence seismic data (e.g., Yagle and Levy, 1985; Carazzone, 1986; Carrion, 1986; Singh et al., 1989). Treitel et al. (1982) performed time migration of plane‐wave seismograms. Diebold and Stoffa (1981) used plane‐wave seismograms to derive a velocity‐depth function. Decomposing seismic data also allows more rapid modeling, since it is faster to compute synthetic seismograms in the (τ, p) than in the (t, x) domain. Unfortunately, the transformation of seismic data from the (t, x) to the (τ, p) domain may produce artifacts, such as those caused by discrete sampling, of the data in space.

Plane‐wave decomposition of seismograms

Geophysics ◽  
1982 ◽  
Vol 47 (10) ◽  
pp. 1375-1401 ◽  
Author(s):  
Sven Treitel ◽  
P. R. Gutowski ◽  
D. E. Wagner
Keyword(s):  
Plane Wave ◽  
Three Dimensional ◽  
Radial Symmetry ◽  
Angle Of Incidence ◽  
Plane Wave Decomposition ◽  
Time Migration ◽  
Predictive Deconvolution ◽  
Seismic Recording ◽  
Wave Decomposition ◽  
Slant Stacking

A point‐source seismic recording can be decomposed into a set of plane‐wave seismograms for arbitrary angles of incidence. Such plane‐wave seismograms possess an inherently simple structure that make them amenable to existing inversion methods such as predictive deconvolution. Implementation of plane‐wave decomposition (PWD) takes place in the frequency‐wavenumber domain under the assumption of radial symmetry. This version of PWD is equivalent to slant stacking if allowance is made for the customary use of linear recording arrays on the surface of a three‐dimensional medium. An imaging principle embodying both kinematic as well as dynamic characteristics allows us to perform time migration of the plane‐wave seismograms. The imaging procedure is implementable as a two‐dimensional filter whose independent variables are traveltime and angle of incidence.

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.

scholarly journals Common-image gathers using the excitation amplitude imaging condition

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. S261-S269 ◽  
Author(s):  
Mahesh Kalita ◽  
Tariq Alkhalifah
Keyword(s):  
Computational Cost ◽  
Velocity Model ◽  
Excitation Amplitude ◽  
Time Lags ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Imaging Condition ◽  
Disk Storage ◽  
Time Migration ◽  
Migration Velocity Analysis

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.

Reflectivity blurring in subsurface extended image gathers

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. S521-S532
Author(s):  
Colin J. Thomson ◽  
Robin P. Fletcher ◽  
Philip W. Kitchenside ◽  
James Hobro
Keyword(s):  
Plane Wave ◽  
Reservoir Characterization ◽  
Wave Reflection ◽  
Computational Cost ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Reflection Coefficients ◽  
Reverse Time ◽  
Reflection Function ◽  
Time Migration

We explain how a reverse time migration (RTM) subsurface extended-image gather (EIG) relates to the reflection function for a finite-contrast interface via a blurring function. For a plane interface between locally homogeneous media, the reflection function contains the plane-wave reflection coefficients, and so we determine how the EIG relates to amplitude versus angle. The EIG and reflection function are multidimensional; hence, the blurring function in their linear relationship is higher dimensional. We explain how it may be computed and show that it describes spatial blurring and blurring over angle of the plane-wave reflection coefficients. We determine explicitly how a slant stack of the EIG at one slowness depends on the plane-wave coefficients at nearby slownesses. This angle blurring stems from the spatial nonstationarity of the blurring function, so it should be the most significant where the illumination changes most rapidly in space. To evaluate the theory, we use finite-difference modeling in the Sigsbee 2a model to generate synthetic survey data, RTM EIGs, blurring functions, and modeled gathers for a deep reflector. Two example image points are chosen. One has good illumination, with blurring over the angle less than 5°. The other point is just under the salt body, with poorer illumination and angle blurring of almost 10°. The description and examples are for two dimensions, but the extension to three dimensions is conceptually straightforward, as is an interface that dips relative to the EIG datum level. The computational cost of blurring functions implies their targeted use for the foreseeable future, for example, in reservoir characterization. The extension to elasticity and more-complicated scatterers is also foreseeable, and we emphasize the separation of the overburden and survey-geometry blurring effects from target properties.

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