Comprehending and analyzing the leading order and higher order imaging closed forms derived from inverse scattering series

2007 ◽  
Author(s):  
Jingfeng Zhang ◽  
Fang Liu ◽  
Kristopher Innanen ◽  
Arthur B. Weglein
Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. Q27-Q40 ◽  
Author(s):  
Katrin Löer ◽  
Andrew Curtis ◽  
Giovanni Angelo Meles

We have evaluated an explicit relationship between the representations of internal multiples by source-receiver interferometry and an inverse-scattering series. This provides a new insight into the interaction of different terms in each of these internal multiple prediction equations and explains why amplitudes of estimated multiples are typically incorrect. A downside of the existing representations is that their computational cost is extremely high, which can be a precluding factor especially in 3D applications. Using our insight from source-receiver interferometry, we have developed an alternative, computationally more efficient way to predict internal multiples. The new formula is based on crosscorrelation and convolution: two operations that are computationally cheap and routinely used in interferometric methods. We have compared the results of the standard and the alternative formulas qualitatively in terms of the constructed wavefields and quantitatively in terms of the computational cost using examples from a synthetic data set.


Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. V255-V269 ◽  
Author(s):  
Jian Sun ◽  
Kristopher A. Innanen

Internal multiple prediction and removal is a critical component of seismic data processing prior to imaging, inversion, and quantitative interpretation. Inverse scattering series methods predict multiples without identification of generators, and without requiring a velocity model. Land environments present several challenges to the inverse scattering series prediction process. This is particularly true for algorithm versions that explicitly account for elastic conversions and incorporate multicomponent data. The theory for elastic reference medium inverse scattering series internal multiple prediction was introduced several decades ago, but no numerical analysis or practical discussion of how to prepare data for it currently exists. We have focused our efforts on addressing this gap. We extend the theory from 2D to 3D, analyze the properties of the input data required by the existing algorithm, and, motivated by earlier research results, reformulate the algorithm in the plane-wave domain. The success of the prediction process relies on the ordering of events in either pseudodepth or vertical traveltime being the same as the ordering of reflecting interfaces in true depth. In elastic-multicomponent cases, it is difficult to ensure that this holds true because the events to be combined may have undergone multiple conversions as they were created. Several variants of the elastic-multicomponent prediction algorithm are introduced and examined for their tendency to violate ordering requirements (and create artifacts). A plane-wave domain prediction, based on elastic data that have been prepared (1) using variable, “best-fit” velocities as reference velocities, and (2) with an analytically determined vertical traveltime stretching formula, is identified as being optimal in the sense of generating artifact-free predictions with relatively small values of the search parameter [Formula: see text], while remaining fully data driven. These analyses are confirmed with simulated data from a layered model; these are the first numerical examples of elastic-multicomponent inverse scattering series internal multiple prediction.


Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. S365-S372 ◽  
Author(s):  
Lele Zhang ◽  
Jan Thorbecke ◽  
Kees Wapenaar ◽  
Evert Slob

We have compared three data-driven internal multiple reflection elimination schemes derived from the Marchenko equations and inverse scattering series (ISS). The two schemes derived from Marchenko equations are similar but use different truncation operators. The first scheme creates a new data set without internal multiple reflections. The second scheme does the same and compensates for transmission losses in the primary reflections. The scheme derived from ISS is equal to the result after the first iteration of the first Marchenko-based scheme. It can attenuate internal multiple reflections with residuals. We evaluate the success of these schemes with 2D numerical examples. It is shown that Marchenko-based data-driven schemes are relatively more robust for internal multiple reflection elimination at a higher computational cost.


2003 ◽  
Vol 19 (6) ◽  
pp. R27-R83 ◽  
Author(s):  
Arthur B Weglein ◽  
Fernanda V Araújo ◽  
Paulo M Carvalho ◽  
Robert H Stolt ◽  
Kenneth H Matson ◽  
...  

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