Multiple attenuation on wide azimuth towed streamer data with a model‐based two‐way wave‐equation approach

2008 ◽  
Author(s):  
Zhiyong Jiang
Keyword(s):  
Wave Equation ◽  
Equation Approach ◽  
Model Based ◽  
Multiple Attenuation ◽  
Streamer Data

An optimization of the inverse scattering multiple attenuation method for OBS and VC data

Geophysics ◽  
2002 ◽  
Vol 67 (4) ◽  
pp. 1293-1303 ◽  
Author(s):  
Luc T. Ikelle ◽  
Lasse Amundsen ◽  
Seung Yoo
Keyword(s):  
Free Surface ◽  
Data Storage ◽  
Inverse Scattering ◽  
Water Depth ◽  
Seismic Data ◽  
Computation Time ◽  
Ocean Bottom ◽  
Multiple Attenuation ◽  
Obs Data ◽  
Streamer Data

The inverse scattering multiple attenuation (ISMA) algorithm for ocean‐bottom seismic (OBS) data can be formulated in the form of a series expansion for each of the four components of OBS data. Besides the actual data, which constitute the first term of the series, each of the other terms is computed as a multidimensional convolution of OBS data with streamer data, and aims at removing one specific order of multiples. If the streamer data do not contain free‐surface multiples, we found that the computation of only the second term of the series is needed to predict and remove all orders of multiples, whatever the water depth. As the computation of the various terms of the series is the most expensive part of ISMA, this result can produce significant savings in computation time, even in data storage, as we no longer need to store the various terms of the series. For example, if the streamer data contained free‐surface multiples, OBS seismic data of 6‐s duration, corresponding to a geological model of the subsurface with 250‐m water depth, require the computation of five terms of the series for each of the four components of OBS data. With the new implementation, in which the streamer data do not contain free‐surface multiples, we need the computation of only one term of the series for each component of the OBS data. The saving in CPU time for this particular case is at least fourfold. The estimation of the inverse source signature, which is an essential part of ISMA, also benefits from the reduction of the number of terms needed for the demultiple to two because it becomes a linear inverse problem instead of a nonlinear one. Assuming that the removal of multiple events produces a significant reduction in the energy of the data, the optimization of this problem leads to a stable, noniterative analytic solution. We have also adapted these results to the implementation of ISMA for vertical‐cable (VC) data. This implementation is similar to that for OBS data. The key difference is that the basic model in VC imaging assumes that data consist of receiver ghosts of primaries instead of the primaries themselves. We have used the following property to achieve this goal. The combination of VC data with surface seismic data, which do not contain free‐surface multiples, allows us to predict free‐surface multiples and receiver ghosts as well as the receiver ghosts of primary reflections. However, if the direct wave arrivals are removed from the VC data, this combination will not predict the receiver ghosts of primary reflections. The difference between these two predictions produces data containing only receiver ghosts of primaries.

3D multiple attenuation of OBC converted‐wave data using wave‐equation multiple modeling

2010 ◽  
Author(s):  
Andrew Dawson ◽  
Joffrey Brunellière ◽  
Peter Allan ◽  
Mark Ibram
Keyword(s):  
Wave Equation ◽  
Converted Wave ◽  
Wave Data ◽  
Multiple Attenuation

A current algebra model based on a wave equation

1969 ◽  
Vol 63 (2) ◽  
pp. 598-608
Author(s):  
B. Hamprecht
Keyword(s):  
Wave Equation ◽  
Current Algebra ◽  
Model Based ◽  
A Current ◽  
Algebra Model

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

2001 ◽  
Vol 25 (11) ◽  
pp. 717-726 ◽  
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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