Extended local Rytov Fourier migration method

Geophysics ◽  
1999 ◽  
Vol 64 (5) ◽  
pp. 1535-1545 ◽  
Author(s):  
Lian‐Jie Huang ◽  
Michael C. Fehler ◽  
Peter M. Roberts ◽  
Charles C. Burch
Keyword(s):  
Phase Changes ◽  
Fast Fourier Transform Algorithm ◽  
Scalar Wave ◽  
Depth Migration ◽  
Frequency Space ◽  
Rytov Approximation ◽  
Migration Method ◽  
The Stability ◽  
Wavefield Extrapolation ◽  
Lateral Variations

We develop a novel depth‐migration method termed the extended local Rytov Fourier (ELRF) migration method. It is based on the scalar wave equation and a local application of the Rytov approximation within each extrapolation interval. Wavefields are Fourier transformed back and forth between the frequency‐space and frequency‐wavenumber domains during wavefield extrapolation. The lateral slowness variations are taken into account in the frequency‐space domain. The method is efficient due to the use of a fast Fourier transform algorithm. Under the small angle approximation, the ELRF method leads to the split‐step Fourier (SSF) method that is unconditionally stable. The ELRF method and the extended local Born Fourier (ELBF) method that we previously developed can handle wider propagation angles than the SSF method and account for the phase and amplitude changes due to the lateral variations of slowness, whereas the SSF method only accounts for the phase changes. The stability of the ELRF method is controlled more easily than that of the ELBF method.

Stable depth extrapolation of seismic wavefields by a Neumann series

Geophysics ◽  
1998 ◽  
Vol 63 (6) ◽  
pp. 2063-2071 ◽  
Author(s):  
Andrzej Kostecki ◽  
Anna Półchłopek
Keyword(s):  
Low Frequency ◽  
Computation Time ◽  
Neumann Series ◽  
Complex Structures ◽  
Lateral Heterogeneity ◽  
Frequency Filter ◽  
Geological Structures ◽  
Depth Migration ◽  
Frequency Space ◽  
Lateral Variations

Several migration methods fail to work when applied to complex geological structures with strong lateral heterogeneity. The generalized migration in the frequency‐wavenumber (f-k) domain based on a convolution with a slowness- (inverse of velocity) dependent operator is capable of downward continuation of wavefield in media with strong vertical and lateral variations of velocity. Unfortunately, this method, as presented in the literature, is potentially unstable. We propose a new, stable extrapolator based on the solution of the integral Fredholm equation, which describes a one‐way wave equation in the form of a Neumann series. The resulting algorithm of depth migration is implemented in both the frequency‐wavenumber (f-k) and frequency‐space (f-x) domains and takes into account arbitrary lateral gradients of velocity, using a low‐frequency filter (in x-f domain) that is the sum of the power series. The computation time of depth migration by a Neumann series is slightly longer than for split‐step Fourier migration. The examples presented suggest that the depth migration by Neumann’s series method can be used to map complex structures with strong lateral gradients of velocity.

Seismic imaging using lateral adaptive windows

Geophysics ◽  
2010 ◽  
Vol 75 (2) ◽  
pp. S73-S79
Author(s):  
Ørjan Pedersen ◽  
Sverre Brandsberg-Dahl ◽  
Bjørn Ursin
Keyword(s):  
Seismic Data ◽  
Seismic Imaging ◽  
Synthetic Data ◽  
Real Data ◽  
Extrapolation Methods ◽  
Depth Migration ◽  
Large Velocity ◽  
Migration Method ◽  
Wavefield Extrapolation ◽  
The Impact

One-way wavefield extrapolation methods are used routinely in 3D depth migration algorithms for seismic data. Due to their efficient computer implementations, such one-way methods have become increasingly popular and a wide variety of methods have been introduced. In salt provinces, the migration algorithms must be able to handle large velocity contrasts because the velocities in salt are generally much higher than in the surrounding sediments. This can be a challenge for one-way wavefield extrapolation methods. We present a depth migration method using one-way propagators within lateral windows for handling the large velocity contrasts associated with salt-sediment interfaces. Using adaptive windowing, we can handle large perturbations locally in a similar manner as the beamlet propagator, thus limiting the impact of the errors on the global wavefield. We demonstrate the performance of our method by applying it to synthetic data from the 2D SEG/EAGE [Formula: see text] salt model and an offshore real data example.

Multicomponent prestack depth migration by scalar wavefield extrapolation

Geophysics ◽  
2002 ◽  
Vol 67 (6) ◽  
pp. 1886-1894 ◽  
Author(s):  
Anning Hou ◽  
Kurt J. Marfurt
Keyword(s):  
Wave Equation ◽  
Single Shot ◽  
Complex Structures ◽  
Scalar Wave ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Polarization Filtering ◽  
Polarity Reversals ◽  
Wavefield Extrapolation ◽  
Propagation Velocities

We present a new multicomponent prestack depth migration methodology based on successive application of conventional scalar wave equation migration. We do not separate the data into PP‐ and PS‐waves; rather, we migrate each x‐, y‐, and z‐component of the data using both P and S propagation velocities, followed by polarization filtering in the depth domain. By generating intermediate images in the depth domain, we can account for polarity reversals of the PS reflection for all dips. Since the polarization angles are calculated from the data, it is straightforward to accommodate anisotropic effects (quasi‐P and quasi‐S) into multicomponent migration. The multicomponent migration results in our synthetic examples demonstrate that even for a single shot gather, we can obtain clean PP‐ and PS‐wave images over complex structures and resolve the problem of PS‐wave polarity reversals.

The design of stable, sparse wavefield extrapolators using projections onto convex sets

Geophysics ◽  
2013 ◽  
Vol 78 (1) ◽  
pp. T11-T20 ◽  
Author(s):  
Wail A. Mousa
Keyword(s):  
Convex Sets ◽  
Design Method ◽  
Depth Migration ◽  
Frequency Space ◽  
Small Complex ◽  
Sparse Operators ◽  
Zero Offset ◽  
Wavefield Extrapolation ◽  
Complex Valued ◽  
Migration Technique

We present the results of poststack explicit depth migration of the well-known 2D SEG/EAGE salt model zero-offset seismic data using sparse wavefield extrapolators. The extrapolators are designed to be sparse by forcing some of the very small complex-valued coefficients’ magnitude values to be zero. The proposed extrapolators design method combines the previously reported modified projections onto convex sets (MPOCS) for designing explicit depth frequency-space ([Formula: see text]) wavefield extrapolation operators with hard-thresholding of the small extrapolators coefficients’ magnitude. The real and imaginary parts of the MPOCS operators, with small magnitudes, are replaced by zeros during the MPOCS algorithm iterations. The migrated result of the SEG/EAGE salt model data, using such sparse designed operators, shows comparable migrated results using the nonsparse version of the MPOCS extrapolation operators as well as the image obtained using the well-known phase-shift plus interpolation (PSPI) migration technique. Overall, the sparse operators result in poststack imaging computational savings (in terms of used flops) of about 28% when compared to poststack imaging of the same data using the nonsparse MPOCS designed operators, and of more than 87.77% saved flops using the PSPI technique.

Stability versus accuracy for an explicit wavefield extrapolation operator

Geophysics ◽  
1993 ◽  
Vol 58 (2) ◽  
pp. 277-283 ◽  
Author(s):  
Atul Nautiyal ◽  
Samuel H. Gray ◽  
N. D. Whitmore ◽  
John D. Garing
Keyword(s):  
Fourier Transform ◽  
Unconditional Stability ◽  
Space Domain ◽  
Stability Properties ◽  
Depth Migration ◽  
Frequency Space ◽  
Wavefield Extrapolation ◽  
Extrapolation Operator ◽  
Accuracy And Stability

Wavefield extrapolation by recursive (depth‐by‐ depth) application of a convolutional operator in the frequency‐space domain, commonly used for depth migration in a laterally‐varying earth, has interesting accuracy and stability properties. We analyze these properties by investigating the operator and its spatial Fourier transform. In particular, we show that the instability caused by spatially truncating the operator can be remedied unconditionally by applying an appropriately chosen spatial taper. However, unconditional stability is gained only at the expense of accuracy. We also identify frequencies and depth extrapolation step sizes for which the problems of accuracy or stability are the most pronounced.

Gaussian beam migration of common-shot records

Geophysics ◽  
2005 ◽  
Vol 70 (4) ◽  
pp. S71-S77 ◽  
Author(s):  
Samuel H. Gray
Keyword(s):  
Gaussian Beam ◽  
Seismic Velocity ◽  
Data Sets ◽  
Model Data ◽  
Near Surface ◽  
Depth Migration ◽  
Migration Method ◽  
Gaussian Beam Migration ◽  
Wavefield Extrapolation ◽  
Natural Way

Gaussian beam migration is a depth migration method whose accuracy rivals that of migration by wavefield extrapolation — so-called “wave-equation migration” — and whose efficiency rivals that of Kirchhoff migration. This migration method can image complicated geologic structures, including very steep dips, in areas where the seismic velocity varies rapidly. However, applications of prestack Gaussian beam migration either have been limited to common-offset common-azimuth data volumes, and thus are inflexible, or suffer from multiarrival inaccuracies in a common-shot implementation. In order to optimize both the flexibility and accuracy of Gaussian beam migration, I present a common-shot implementation that handles multipathing in a natural way. This allows the migration of data sets that can include a variety of azimuths, and it allows a simplified treatment of near-surface issues. Application of this method to model data typical of Canadian Foothills structures and to model data that includes a complicated salt body demonstrates the accuracy and versatility of the migration.

Gaussian beam migration

Geophysics ◽  
1990 ◽  
Vol 55 (11) ◽  
pp. 1416-1428 ◽  
Author(s):  
N. Ross Hill
Keyword(s):  
Gaussian Beam ◽  
Wave Field ◽  
Seismic Source ◽  
Velocity Model ◽  
Downward Continuation ◽  
Gaussian Beams ◽  
Seismic Velocities ◽  
Migration Method ◽  
Gaussian Beam Migration ◽  
Lateral Variations

Just as synthetic seismic data can be created by expressing the wave field radiating from a seismic source as a set of Gaussian beams, recorded data can be downward continued by expressing the recorded wave field as a set of Gaussian beams emerging at the earth’s surface. In both cases, the Gaussian beam description of the seismic‐wave propagation can be advantageous when there are lateral variations in the seismic velocities. Gaussian‐beam downward continuation enables wave‐equation calculation of seismic propagation, while it retains the interpretive raypath description of this propagation. This paper describes a zero‐offset depth migration method that employs Gaussian beam downward continuation of the recorded wave field. The Gaussian‐beam migration method has advantages for imaging complex structures. Like finite‐difference migration, it is especially compatible with lateral variations in velocity, but Gaussian beam migration can image steeply dipping reflectors and will not produce unwanted reflections from structure in the velocity model. Unlike other raypath methods, Gaussian beam migration has guaranteed regular behavior at caustics and shadows. In addition, the method determines the beam spacing that ensures efficient, accurate calculations. The images produced by Gaussian beam migration are usually stable with respect to changes in beam parameters.

A Plane Wave Depth Migration Method for Pre-Stack Seismic Data

2003 ◽  
Vol 46 (6) ◽  
pp. 1176-1185 ◽  
Author(s):  
Shengchang CHEN ◽  
Jingzhong CAO ◽  
Zaitian MA
Keyword(s):  
Plane Wave ◽  
Seismic Data ◽  
Depth Migration ◽  
Migration Method

Refraction wavefield migration

Geophysics ◽  
2020 ◽  
Vol 85 (6) ◽  
pp. Q27-Q37
Author(s):  
Yang Shen ◽  
Jie Zhang
Keyword(s):  
Signal To Noise Ratio ◽  
Surface Velocity ◽  
Data Set ◽  
Near Surface ◽  
Depth Migration ◽  
Reflection Data ◽  
Imaging Tool ◽  
Imaging Results ◽  
Migration Method ◽  
Single Method

Refraction methods are often applied to model and image near-surface velocity structures. However, near-surface imaging is very challenging, and no single method can resolve all of the land seismic problems across the world. In addition, deep interfaces are difficult to image from land reflection data due to the associated low signal-to-noise ratio. Following previous research, we have developed a refraction wavefield migration method for imaging shallow and deep interfaces via interferometry. Our method includes two steps: converting refractions into virtual reflection gathers and then applying a prestack depth migration method to produce interface images from the virtual reflection gathers. With a regular recording offset of approximately 3 km, this approach produces an image of a shallow interface within the top 1 km. If the recording offset is very long, the refractions may follow a deep path, and the result may reveal a deep interface. We determine several factors that affect the imaging results using synthetics. We also apply the novel method to one data set with regular recording offsets and another with far offsets; both cases produce sharp images, which are further verified by conventional reflection imaging. This method can be applied as a promising imaging tool when handling practical cases involving data with excessively weak or missing reflections but available refractions.

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