Suppression of water‐layer multiples — from deconvolution to wave‐equation approach

In many areas offshore, the conventional seismic record has the appearance of a series of sine waves or simple odd harmonic combinations of sine waves, with a fundamental wave length four times the water depth. Burg, et al., in a ray theory treatment, ascribe this oscillatory phenomenon to guided energy traveling in the water layer. A solution of the pressure wave equation for a point source in the water layer has been obtained. It allows one to examine not only the frequency dependence with the depth, but also the transient amplitude response with depth and time. It is concluded that in most actual situations, the phenomenon cannot be wholly explained by the assumed mechanism, because the theory indicates too rapid a decay of the energy.

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Deep‐water peg legs and multiples: Emulation and suppression

Geophysics ◽

10.1190/1.1442070 ◽

1986 ◽

Vol 51 (12) ◽

pp. 2177-2184 ◽

Cited By ~ 45

Author(s):

J. R. Berryhill ◽

Y. C. Kim

Keyword(s):

Wave Equation ◽

Seismic Data ◽

Water Layer ◽

Original Data ◽

Equation Method ◽

Multiple Reflections ◽

Step Method ◽

Arrival Times ◽

Sea Floor ◽

Water Bottom

This paper discusses a two‐step method for predicting and attenuating multiple and peg‐leg reflections in unstacked seismic data. In the first step, an (observed) seismic record is extrapolated through a round‐trip traversal of the water layer, thus creating an accurate prediction of all possible multiples. In the second step, the record containing the predicted multiples is compared with and subtracted from the original. The wave‐equation method employed to predict the multiples takes accurate account of sea‐floor topography and so requires a precise water‐bottom profile as part of the input. Information about the subsurface below the sea floor is not required. The arrival times of multiple reflections are reproduced precisely, although the amplitudes are not accurate, and the sea floor is treated as a perfect reflector. The comparison step detects the similarities between the computed multiples and the original data, and estimates a transfer function to equalize the amplitudes and account for any change in waveform caused by the sea‐floor reflector. This two‐step wave‐equation method is effective even for dipping sea floors and dipping subsurface reflectors. It does not depend upon any assumed periodicity in the data or upon any difference in stacking velocity between primaries and multiples. Thus it is complementary to the less specialized methods of multiple suppression.

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The wave equation approach for solving inverse eigenvalue problems of a multi-connected region in R3 with Robin conditions

Applied Mathematics and Computation ◽

10.1016/s0096-3003(02)00807-x ◽

2004 ◽

Vol 147 (3) ◽

pp. 721-739 ◽

Cited By ~ 1

Author(s):

E.M.E. Zayed

Keyword(s):

Wave Equation ◽

Eigenvalue Problems ◽

Connected Region ◽

Equation Approach ◽

Inverse Eigenvalue Problems ◽

Inverse Eigenvalue

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The wave equation approach to an inverse eigenvalue problem for an arbitrary multiply connected drum inℝ2with Robin boundary conditions

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171201005300 ◽

2001 ◽

Vol 25 (11) ◽

pp. 717-726 ◽

Cited By ~ 8

Author(s):

E. M. E. Zayed ◽

I. H. Abdel-Halim

Keyword(s):

Wave Equation ◽

Boundary Conditions ◽

Inverse Eigenvalue Problem ◽

Robin Boundary Conditions ◽

Two Dimensional ◽

Equation Approach ◽

Multiply Connected ◽

Inverse Eigenvalue ◽

Negative Laplacian ◽

Robin Boundary

The spectral functionμˆ(t)=∑j=1∞exp(−itμj1/2), where{μj}j=1∞are the eigenvalues of the two-dimensional negative Laplacian, is studied for small|t|for a variety of domains, where−∞<t<∞andi=−1. The dependencies ofμˆ(t)on the connectivity of a domain and the Robin boundary conditions are analyzed. Particular attention is given to an arbitrary multiply-connected drum inℝ2together with Robin boundary conditions on its boundaries.

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