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Abma, R., and J. Claerbout, 1995, Lateral prediction for noise attenuation by
t-x and F-X techniques: Geophysics, 60, 1887-1896.
-
-
Bednar, J. B., 1998, Least squares dip and coherency attributes: 68th Ann.
Internat. Mtg, Soc. of Expl. Geophys., 653-655.
-
-
Brown, M., and R. Clapp, 2000, T-X domain, pattern-based ground-roll
removal, in 70th Annual Internat. Mtg., Soc. Expl. Geophys., Expanded
Abstracts: Soc. Expl. Geophys., 2103-2106.
-
-
Burg, J. P., 1975, Maximum entropy spectral analysis: PhD thesis, Stanford
University.
-
-
Canales, L. L., 1984, Random noise reduction: 54th Ann. Internat. Mtg, Soc. of
Expl. Geophys., Session:S10.1.
-
-
Claerbout, J., 1998, Multidimensional recursive filters via a helix:
Geophysics, 63, 1532-1541.
-
-
----, 1999, Geophysical estimation by example: Environmental soundin gs
image enhancement: Stanford Exploration Project.
-
-
Claerbout, J., and M. Brown, 1999, Two-dimensional textures and
prediction-error filters: 61st Mtg., Eur. Assn. Geosci. Eng., Session:1009.
-
-
Claerbout, J. F., 1992, Earth Soundings Analysis: Processing Versus
Inversion: Blackwell Scientific Publications.
-
-
----, 1994, Applications of two- and three-dimensional filtering: 64th Ann.
Internat. Mtg, Soc. of Expl. Geophys., 1572-1575.
-
-
Clapp, R. G., 2001, Geologically constrained migration velocity analysis: PhD
thesis, Stanford University.
-
-
Clapp, R. G., B. L. Biondi, S. B. Fomel, and J. F. Claerbout, 1998,
Regularizing velocity estimation using geologic dip information: 68th Ann.
Internat. Mtg, Soc. of Expl. Geophys., 1851-1854.
-
-
Crawley, S., 2000, Seismic trace interpolation with nonstationary
prediction-error filters: PhD thesis, Stanford University.
-
-
Crawley, S., J. Claerbout, and R. Clapp, 1999, Interpolation with smoothly
nonstationary prediction-error filters: 69th Ann. Internat. Mtg, Soc. of
Expl. Geophys., 1154-1157.
-
-
Fomel, S., 2001, Three-dimensional seismic data regularization: PhD thesis,
Stanford University.
-
-
Fomel, S., and J. F. Claerbout, 2002, Multidimensional recursive filter
preconditioning in geophysical estimation problems: Geophysics, accepted for
publication.
-
-
Freeman, W. T., and E. H. Adelson, 1991, The design and use of steerable
filters: IEEE Trans. on Pattern Analysis and Machine Intelligence, 1,
891-906.
-
-
Guitton, A., M. Brown, J. Rickett, and R. Clapp, 2001, Multiple attenuation
using a t-x pattern-based subtraction method: 71st Ann. Internat. Mtg, Soc.
of Expl. Geophys., 1305-1308.
-
-
Gulunay, N., 1986, Fx decon and complex Wiener prediction filter: 56th Ann.
Internat. Mtg., Soc. of Expl. Geophys., Session:POS2.10.
-
-
Harlan, W. S., J. F. Claerbout, and F. Rocca, 1984, Signal/noise separation
and velocity estimation: Geophysics, 49, 1869-1880.
-
-
Kim, S., and W. W. Symes, 1998, Smooth detectors of linear phase: Inverse
Problems, 14, 101-112.
-
-
Neidell, N. S., and M. T. Taner, 1971, Semblance and other coherency measures
for multichannel data: Geophysics, 36, 482-497.
-
-
Nichols, D., 1990, Estimation of missing data by least squares, in
SEP-65: Stanford Exploration Project, 271-294.
-
-
Schwab, M., 1998, Enhancement of discontinuities in seismic 3-D images using
a Java estimation library: PhD thesis, Stanford University.
-
-
Schwab, M., J. Claerbout, and C. Holden, 1996, Revealing geological
discontinuities by plane reflector suppression, in 66th Annual
Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts: Society Of
Exploration Geophysicists, 302-305.
-
-
Simoncelli, E. P., and H. Farid, 1996, Steerable wedge filters for local
orientation analysis: IEEE Trans. on Image Processing, 5, 1377-1382.
-
-
Soubaras, R., 1995, Prestack random and impulsive noise attenuation by F-X
projection filtering: 65th Ann. Internat. Mtg, Soc. of Expl. Geophys.,
711-714.
-
-
Spitz, S., 1991, Seismic trace interpolation in the F-X domain:
Geophysics, 56, 785-794.
-
-
----, 1999, Pattern recognition, spatial predictability, and subtraction of
multiple events: The Leading Edge, 18, 55-58.
-
-
Symes, W. W., 1994, The plane wave detection problem: Inverse Problems, 10, 1361-1391.
-
-
Symes, W. W., and J. J. Carazzone, 1991, Velocity inversion by differential
semblance optimization: Geophysics, 56, 654-663.
-
-
Yilmaz, O., and D. Cumro, 1983, Worldwide assortment of field seismic records,
released by Western Geophysical Company of America: Houston.
-
Appendix
A
Determining filter coefficients by Taylor expansion
This appendix details the derivation of equations (9)
and (10). The main idea to match the frequency responses
of the approximate plane-wave filters to the response of the exact
phase-shift operator at low frequencies.
The Taylor series expansion of the phase-shift operator
around the zero frequency
takes the form
 |
(24) |
The Taylor expansion of the six-point implicit finite-difference operator
takes the form
Matching the corresponding terms of expansions (A-1)
and (A-2), we arrive at the system of nonlinear equations
System (A-3-A-5) does not uniquely constrain the
filter coefficients
,
, and
because
equation (A-4) simply follows from (A-3) andb
ecause all the coefficients can be multiplied simultaneously by an
arbitrary constant without affecting the ratios in
equation (A-2). I chose an additional constraint in the
form
 |
(29) |
which ensures that the filter
does not alter the zero
frequency component. System (A-3-A-5) with the
additional constraint (A-6) resolves uniquely to
the coefficients of filter (9) in the main text:
The
filter of equation (10) is constructed in a
completely analogous way, using longer Taylor expansions to constrain
the additional coefficients. Generalization to longer filters is
straightforward.
The technique of this appendix aims at matching the filter responses
at low frequencies. One might construct different filter families by
employing other criteria for filter design (least squares fit,
equiripple, etc.)
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2014-03-29