Parallel Butterworth and Chebyshev dip filters with applications to 3-D seismic migration

Geophysics ◽  
1999 ◽  
Vol 64 (5) ◽  
pp. 1573-1578 ◽  
Author(s):  
Hongbo Zhou ◽  
George A. McMechan
Keyword(s):  
Transfer Function ◽  
Phase Compensation ◽  
Space Domain ◽  
Seismic Migration ◽  
Butterworth Filter ◽  
Depth Migration ◽  
Frequency Space ◽  
Chebyshev Filters ◽  
The Cost ◽  
Chebyshev Filter

Dip filtering is a necessary part of accurate frequency‐space domain migration, so design and application of reliable and efficient filters are of practical as well as theoretical importance. Frequency‐space domain dip filters are implemented using Butterworth and Chebyshev algorithms. By transforming the product terms of the filter transfer function into summations, a cascaded (serial) Butterworth or Chebyshev dip filter can be made parallel, which improves computational efficiency. For a given order of filter, the cost of the Butterworth and Chebyshev filters is the same. However, the Chebyshev filter has a sharper transition zone than that of a Butterworth filter with the same order, which makes it more effective for phase compensation than a Butterworth filter, but at the expense of some wavenumber‐dependent amplitude ripples. Both implementations have been incorporated into 3-D one‐way frequency‐space depth migration for evanescent energy removal and for phase compensation of splitting errors; a single filter achieves both goals.

Post-stack depth migration in the frequency–space domain

1986 ◽  
Vol 23 (6) ◽  
pp. 839-848 ◽  
Author(s):  
Panos G. Kelamis ◽  
Einar Kjartansson ◽  
E George Marlin
Keyword(s):  
Synthetic Data ◽  
Real Data ◽  
Wave Number ◽  
Lateral Velocity ◽  
Space Domain ◽  
Frequency Wave ◽  
Depth Migration ◽  
Frequency Space ◽  
Time Space ◽  
Z Domain

The 45 °monochromatic one-way wave equation, along with the thin-lens term, is used, and a depth-migration algorithm is developed in the frequency–space (ω, x) domain. Using this approach, an unmigrated stack section is directly transformed into a depth-migrated section taking into account both vertical and lateral velocity variations. In practice, the algorithm can accommodate steep events with dips of the order of 60–65°. The use of the frequency–space domain offers several advantages over the conventional time–space and frequency–wave-number domains. Time derivatives are evaluated exactly by a simple multiplication, while the use of the space (x, z) domain facilitates the handling of lateral velocity inhomogeneities. The performance of the depth-migration algorithm is tested with synthetic data from complicated models and real data from the Foothills area of western Canada.

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.

scholarly journals Coupling matrix synthesis of general chebyshev filters

2020 ◽  
Vol 309 ◽  
pp. 01011
Author(s):  
Lihua Qi ◽  
Dongqiu Xing ◽  
Rui Wang ◽  
Xinshe Qi ◽  
Jing Zhao
Keyword(s):  
Global Minimum ◽  
Microwave Filters ◽  
Hybrid Optimization ◽  
Final Solution ◽  
Matrix Synthesis ◽  
Excellent Performance ◽  
Coupling Matrix ◽  
Hybrid Optimization Algorithms ◽  
Chebyshev Filters ◽  
The Cost

A single optimization algorithm based on SolvOpt that synthesizes coupling matrices for cross-coupled microwave filters is presented. The rules for setting initial values of SolvOpt are proposed to find global minimum of the cost function. SolvOpt method provides faster convergence and higher accuracy to find the final solution compared with hybrid optimization algorithms. Application examples illustrate the excellent performance and the validity of this method.

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.

An overview of depth imaging in exploration geophysics

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCA5-WCA17 ◽  
Author(s):  
John Etgen ◽  
Samuel H. Gray ◽  
Yu Zhang
Keyword(s):  
Structural Description ◽  
Practical Application ◽  
Depth Imaging ◽  
Seismic Migration ◽  
Depth Migration ◽  
The Past ◽  
The Earth ◽  
Seismic Images ◽  
Migration Technique ◽  
Made In

Prestack depth migration is the most glamorous step of seismic processing because it transforms mere data into an image, and that image is considered to be an accurate structural description of the earth. Thus, our expectations of its accuracy, robustness, and reliability are high. Amazingly, seismic migration usually delivers. The past few decades have seen migration move from its heuristic roots to mathematically sound techniques that, using relatively few assumptions, render accurate pictures of the interior of the earth. Interestingly, the earth and the subjects we want to image inside it are varied enough that, so far, no single migration technique has dominated practical application. All techniques continually improve and borrow from each other, so one technique may never dominate. Despite the progress in structural imaging, we have not reached the point where seismic images provide quantitatively accurate descriptions of rocks and fluids. Nor have we attained the goal of using migration as part of a purely computational process to determine subsurface velocity. In areas where images have the highest quality, we might be nearing those goals, collectively called inversion. Where data are more challenging, the goals seem elusive. We describe the progress made in depth migration to the present and the most significant barriers to attaining its inversion goals in the future. We also conjecture on progress likely to be made in the years ahead and on challenges that migration might not be able to meet.

Analytic synthetic seismograms for depth migration testing

Geophysics ◽  
1991 ◽  
Vol 56 (5) ◽  
pp. 697-700
Author(s):  
Samuel H. Gray ◽  
Chester A. Jacewitz ◽  
Michael E. Epton
Keyword(s):  
Velocity Field ◽  
Acoustic Velocity ◽  
Synthetic Seismograms ◽  
Lateral Velocity ◽  
Seismic Migration ◽  
Depth Migration ◽  
Circular Arcs ◽  
Velocity Variations ◽  
Migration Testing ◽  
Speed And Accuracy

By using the fact that raypaths in a linear acoustic velocity field are circular arcs, we analytically generate a number of distinct nontrivial synthetic seismograms. The seismograms yield accurate traveltimes from reflection events, but they do not give reflection amplitudes. The seismograms are useful for testing seismic migration programs for both speed and accuracy, in settings where lateral velocity variations can be arbitrarily high and dipping reflectors arbitrarily steep. Two specific examples are presented as illustrations.

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