Phase shift plus residual frequency‐space finite‐difference migration: A better migration tool in complex structural areas

1990 ◽  
Author(s):  
Shih‐Yeng Kuo ◽  
Charles F. Barron
Keyword(s):  
Phase Shift ◽  
Finite Difference ◽  
Frequency Space ◽  
Complex Structural

scholarly journals Compensating finite‐difference errors in 3-D migration and modeling

Geophysics ◽  
1991 ◽  
Vol 56 (10) ◽  
pp. 1650-1660 ◽  
Author(s):  
Zhiming Li
Keyword(s):  
Wave Equation ◽  
Phase Shift ◽  
Finite Difference ◽  
Interpolation Method ◽  
Splitting Method ◽  
Three Dimensional ◽  
Lateral Velocity ◽  
Frequency Space ◽  
Difference Grid ◽  
Imaging Results

One‐pass three‐dimensional (3-D) depth migration potentially offers more accurate imaging results than does conventional two‐pass 3-D migration for variable velocity media. Conventional one‐pass 3-D migration, using the method of finite‐difference inline and crossline splitting, however, creates large errors in the image of complex structures. These errors are due to paraxial wave‐equation approximation of the one‐way wave equation, inline‐crossline splitting, and finite‐difference grid dispersion. To compensate for these errors, and still preserve the efficiency of the conventional finite‐difference splitting method, a phase‐correction operator is derived by minimizing the difference between the ideal 3-D migration (or modeling) and the actual, conventional 3-D migration (or modeling). For frequency‐space 3-D finite‐difference migration and modeling, the compensation operator is implemented using either the phase‐shift, or phase‐shift‐plus‐interpolation method, depending on the extent of lateral velocity variations. The compensation operator increases the accuracy of handling steep dips, suppresses the inline and crossline splitting error, and reduces finite‐difference grid dispersions.

scholarly journals Verification of seiching processes in a large and deep lake (Trichonis, Greece)

2000 ◽  
Vol 1 (1) ◽  
pp. 79 ◽  
Author(s):  
I. ZACHARIAS
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Phase Shift ◽  
Finite Difference ◽  
Phase Difference ◽  
Experimental Verification ◽  
Computational Analysis ◽  
Power Spectral Analysis ◽  
Deep Lake ◽  
Power Spectral

A computational analysis of the periods and structure of surface seiches of Lake Trichonis in Greece and its experimental verification from three simultaneous water gauge recordings, mounted along the shores in Myrtia, Panetolio and Trichonio is given. The first five theoretical modes are calculated with a finite difference code of tidal equations, which yield the eigenperiodes, co-range and co-tidal lines that are graphically displayed and discussed in detail.Experimental verifications are from recordings taken during spring. Visual observations of the record permit identification of the five lowest order modes, including inter station phase shift. Power spectral analysis of two time series and interstation phase difference and coherence spectra allow the identification of the same five modes. Agreement between the theoretically predicted and the experimentally determined periods was excellent for most of the calculated modes.

Fourier finite‐difference migration

Geophysics ◽  
1994 ◽  
Vol 59 (12) ◽  
pp. 1882-1893 ◽  
Author(s):  
Dietrich Ristow ◽  
Thomas Rühl
Keyword(s):  
Phase Shift ◽  
Finite Difference ◽  
Difference Operator ◽  
Shift Operator ◽  
Velocity Model ◽  
Downward Continuation ◽  
The Other ◽  
Finite Difference Schemes ◽  
Other Hand ◽  
Arbitrary Velocity

Many existing migration schemes cannot simultaneously handle the two most important problems of migration: imaging of steep dips and imaging in media with arbitrary velocity variations in all directions. For example, phase‐shift (ω, k) migration is accurate for nearly all dips but it is limited to very simple velocity functions. On the other hand, finite‐difference schemes based on one‐way wave equations consider arbitrary velocity functions but they attenuate steeply dipping events. We propose a new hybrid migration method, named “Fourier finite‐difference migration,” wherein the downward‐continuation operator is split into two downward‐continuation operators: one operator is a phase‐shift operator for a chosen constant background velocity, and the other operator is an optimized finite‐difference operator for the varying component of the velocity function. If there is no variation of velocity, then only a phase‐shift operator will be applied automatically. On the other hand, if there is a strong variation of velocity, then the phase‐shift component is suppressed and the optimized finite‐difference operator will be fully applied. The cascaded application of phase‐shift and finite‐difference operators shows a better maximum dip‐angle behavior than the split‐step Fourier migration operator. Depending on the macro velocity model, the Fourier finite‐difference migration even shows an improved performance compared to conventional finite‐difference migration with one downward‐continuation step. Finite‐difference migration with two downward‐continuation steps is required to reach the same migration performance, but this is achieved with about 20 percent higher computation costs. The new cascaded operator of the Fourier finite‐difference migration can be applied to arbitrary velocity functions and allows an accurate migration of steeply dipping reflectors in a complex macro velocity model. The dip limitation of the cascaded operator depends on the variation of the velocity field and, hence, is velocity‐adaptive.

2-D elastic wave modeling with frequency-space 25-point finite-difference operators

2009 ◽  
Vol 6 (3) ◽  
pp. 259-266 ◽  
Author(s):  
Jianping Liao ◽  
Huazhong Wang ◽  
Zaitian Ma
Keyword(s):  
Finite Difference ◽  
Elastic Wave ◽  
Difference Operators ◽  
Wave Modeling ◽  
Frequency Space
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