A New Role for Adaptive Filters in Marchenko Equation-Based Methods for the Attenuation of Internal Multiples

Suppression of surface-related and internal multiples is an outstanding challenge in seismic data processing. The former is particularly difficult in shallow water, whereas the latter is problematic for targets buried under complex, highly scattering overburdens. We propose a two-step, amplitude- and phase-preserving, inversion-based workflow, which addresses these problems. We apply Robust Estimation of Primaries by Sparse Inversion (R-EPSI) to suppress the surface-related multiples and solve for the source wavelet. A significant advantage of the inversion approach of the R-EPSI method is that it does not rely on an adaptive subtraction step that typically limits other de-multiple methods such as SRME. The resulting Green's function is used as input to a Marchenko equation-based approach to predict the complex interference pattern of all overburden-generated internal multiples at once, without a priori subsurface information. In theory, the interbed multiples can be predicted with correct amplitude and phase and, again, no adaptive filters are required. We illustrate this workflow by applying it on an Arabian Gulf field data example. It is crucial that all pre-processing steps are performed in an amplitude preserving way to restrict any impact on the accuracy of the multiple prediction. In practice, some minor inaccuracies in the processing flow may end up as prediction errors that need to be corrected for. Hence, we decided that the use of conservative adaptive filters is necessary to obtain the best results after interbed multiple removal. The obtained results show promising suppression of both surface-related and interbed multiples.

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Marchenko imaging

Geophysics ◽

10.1190/geo2013-0302.1 ◽

2014 ◽

Vol 79 (3) ◽

pp. WA39-WA57 ◽

Cited By ~ 169

Author(s):

Kees Wapenaar ◽

Jan Thorbecke ◽

Joost van der Neut ◽

Filippo Broggini ◽

Evert Slob ◽

...

Keyword(s):

Green’S Function ◽

Inverse Scattering ◽

Green's Function ◽

Seismic Interferometry ◽

Virtual Source ◽

Target Zone ◽

Scattering Problems ◽

Inverse Scattering Problems ◽

Marchenko Equation ◽

Internal Multiples

Traditionally, the Marchenko equation forms a basis for 1D inverse scattering problems. A 3D extension of the Marchenko equation enables the retrieval of the Green’s response to a virtual source in the subsurface from reflection measurements at the earth’s surface. This constitutes an important step beyond seismic interferometry. Whereas seismic interferometry requires a receiver at the position of the virtual source, for the Marchenko scheme it suffices to have sources and receivers at the surface only. The underlying assumptions are that the medium is lossless and that an estimate of the direct arrivals of the Green’s function is available. The Green’s function retrieved with the 3D Marchenko scheme contains accurate internal multiples of the inhomogeneous subsurface. Using source-receiver reciprocity, the retrieved Green’s function can be interpreted as the response to sources at the surface, observed by a virtual receiver in the subsurface. By decomposing the 3D Marchenko equation, the response at the virtual receiver can be decomposed into a downgoing field and an upgoing field. By deconvolving the retrieved upgoing field with the downgoing field, a reflection response is obtained, with virtual sources and virtual receivers in the subsurface. This redatumed reflection response is free of spurious events related to internal multiples in the overburden. The redatumed reflection response forms the basis for obtaining an image of a target zone. An important feature is that spurious reflections in the target zone are suppressed, without the need to resolve first the reflection properties of the overburden.

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Data-driven control over short-period internal multiples in media with a horizontally layered overburden

Geophysical Journal International ◽

10.1093/gji/ggaa020 ◽

2020 ◽

Vol 221 (2) ◽

pp. 769-787 ◽

Cited By ~ 1

Author(s):

P Elison ◽

M S Dukalski ◽

K de Vos ◽

D J van Manen ◽

J O A Robertsson

Keyword(s):

Data Driven ◽

Minimum Phase ◽

Sonic Log ◽

Phase Condition ◽

Short Period ◽

Marchenko Equation ◽

Structural Image ◽

Internal Multiples ◽

The Impact ◽

Conventional Scheme

SUMMARY Short-period internal multiples, resulting from closely spaced interfaces, may interfere with their generating (bandlimited) primaries, and hence they pose a long-standing challenge in their prediction and removal. A recently proposed method based on the Marchenko equation enables removal of the entire overburden-related scattering by means of calculating an inverse transmission response. However, the method relies on time windowing and can thus be inexact in the presence of short-period internal scattering. In this work, we present a detailed analysis of the impact of band-limitation on the Marchenko method. We show the influence of an incorrect first guess, and that adding multidimensional energy conservation and a minimum phase principle may be used to correctly account for both long- and short-period internal multiple scattering. The proposed method can currently only be solved for media with a laterally invariant overburden, since a multidimensional minimum phase condition is not well understood for truly 2-D and 3-D media. We demonstrate the virtue of the proposed scheme with a complex acoustic numerical model that is based on sonic log measurements in the Middle East. The results suggest not only that the conventional scheme can be robust in this setting, but that the ‘augmented’ Marchenko method is superior, as the latter produces a structural image identical to one where the finely layered overburden is missing. This is the first demonstration of a data-driven method to account for short-period internal multiples beyond 1-D.

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Accounting for free-surface multiples in Marchenko imaging

Geophysics ◽

10.1190/geo2015-0646.1 ◽

2017 ◽

Vol 82 (1) ◽

pp. R19-R30 ◽

Cited By ~ 26

Author(s):

Satyan Singh ◽

Roel Snieder ◽

Joost van der Neut ◽

Jan Thorbecke ◽

Evert Slob ◽

...

Keyword(s):

Free Surface ◽

Green’S Function ◽

Green's Function ◽

Small Scale ◽

Scattering Problems ◽

Area Of Interest ◽

The Earth ◽

Marchenko Equation ◽

Virtual Point ◽

Internal Multiples

Imagine placing a receiver at any location in the earth and recording the response at that location to sources on the surface. In such a world, we could place receivers around our reservoir to better image the reservoir and understand its properties. Realistically, this is not a feasible approach for understanding the subsurface. We have developed an alternative and realizable approach to obtain the response of a buried virtual receiver for sources at the surface. Our method is capable of retrieving the Green’s function for a virtual point in the subsurface to the acquisition surface. In our case, a physical receiver is not required at the subsurface point; instead, we require the reflection measurements for sources and receivers at the surface of the earth and a macromodel of the velocity (no small-scale details of the model are necessary). We can interpret the retrieved Green’s function as the response to sources at the surface for a virtual receiver in the subsurface. We obtain this Green’s function by solving the Marchenko equation, an integral equation pertinent to inverse scattering problems. Our derivation of the Marchenko equation for the Green’s function retrieval takes into account the free-surface reflections present in the reflection response (previous work considered a response without free-surface multiples). We decompose the Marchenko equation into up- and downgoing fields and solve for these fields iteratively. The retrieved Green’s function not only includes primaries and internal multiples as do previous methods, but it also includes free-surface multiples. We use these up- and downgoing fields to obtain a 2D image of our area of interest, in this case, below a synclinal structure.

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Internal multiple elimination: Can we trust an acoustic approximation?

Geophysics ◽

10.1190/geo2020-0850.1 ◽

2021 ◽

pp. 1-44

Author(s):

Christian Reinicke ◽

Marcin Dukalski ◽

Kees Wapenaar

Keyword(s):

Field Data ◽

A Priori ◽

Elastic Field ◽

Substantial Impact ◽

Marchenko Equation ◽

Acoustic Media ◽

Particle Velocities ◽

Internal Multiples ◽

Multiple Elimination ◽

Acoustic Approximation

Correct handling of strong elastic, internal, multiples remains a challenge for seismic imaging. Methods aimed at eliminating them are currently limited by monotonicity violations, a lack of a-priori knowledge about mode conversions, or unavailability of multi-component sources and receivers for not only particle velocities but also the traction vector. Most of these challenges vanish in acoustic media such that Marchenko-equation-based methods are able in theory to remove multiples exactly (within a certain wavenumber-frequency band). In practice, however, when applied to (elastic) field data, mode conversions are unaccounted for. Aiming to support a recently published marine field data study, we build a representative synthetic model. For this setting, we demonstrate that mode conversions can have a substantial impact on the recovered multiple-free reflection response. Nevertheless, the images are significantly improved by acoustic multiple elimination. Moreover, after migration the imprint of elastic effects is considerably weaker and unlikely to alter the seismic interpretation.

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Adaptive overburden elimination with the multidimensional Marchenko equation

Geophysics ◽

10.1190/geo2016-0024.1 ◽

2016 ◽

Vol 81 (5) ◽

pp. T265-T284 ◽

Cited By ~ 48

Author(s):

Joost van der Neut ◽

Kees Wapenaar

Keyword(s):

Field Data ◽

Synthetic Data ◽

Velocity Model ◽

Thin Layers ◽

Multiple Reflections ◽

Data Set ◽

Marchenko Equation ◽

Recorded Data ◽

Internal Multiples ◽

Multiple Elimination

Iterative substitution of the multidimensional Marchenko equation has been introduced recently to integrate internal multiple reflections in the seismic imaging process. In so-called Marchenko imaging, a macro velocity model of the subsurface is required to meet this objective. The model is used to back-propagate the data during the first iteration and to truncate integrals in time during all successive iterations. In case of an erroneous model, the image will be blurred (akin to conventional imaging) and artifacts may arise from inaccurate integral truncations. However, the scheme is still successful in removing artifacts from internal multiple reflections. Inspired by these observations, we rewrote the Marchenko equation, such that it can be applied early in a processing flow, without the need of a macro velocity model. Instead, we have required an estimate of the two-way traveltime surface of a selected horizon in the subsurface. We have introduced an approximation, such that adaptive subtraction can be applied. As a solution, we obtained a new data set, in which all interactions (primaries and multiples) with the part of the medium above the picked horizon had been eliminated. Unlike various other internal multiple elimination algorithms, the method can be applied at any specified target horizon, without having to resolve for internal multiples from shallower horizons. We successfully applied the method on synthetic data, where limitations were reported due to thin layers, diffraction-like discontinuities, and a finite acquisition aperture. A field data test was also performed, in which the kinematics of the predicted updates were demonstrated to match with internal multiples in the recorded data, but it appeared difficult to subtract them.

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THE SERIES SOLUTION OF THE GEL'FAND–LEVITAN–MARCHENKO EQUATION

Acta Mathematica Scientia ◽

10.1016/s0252-9602(18)30484-3 ◽

1987 ◽

Vol 7 (1) ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Bangqing Xu ◽

Changgui Shao

Keyword(s):

Series Solution ◽

Marchenko Equation

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Adaptive Filters with Codified Error LMS Algorithm

Telecommunications and Radio Engineering ◽

10.1615/telecomradeng.v65.i6.60 ◽

2006 ◽

Vol 65 (6) ◽

pp. 567-579 ◽

Cited By ~ 6

Author(s):

Jose Velazquez-Lopez ◽

Juan Carlos Sanchez-Garcia ◽

Hector Manuel Perez-Meana

Keyword(s):

Adaptive Filters ◽

Lms Algorithm

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A Variable Step-Size for Sparse Nonlinear Adaptive Filters

2020 28th European Signal Processing Conference (EUSIPCO) ◽

10.23919/eusipco47968.2020.9287864 ◽

2021 ◽

Author(s):

Alberto Carini ◽

Markus V. S. Lima ◽

Hamed Yazdanpanah ◽

Simone Orcioni ◽

Stefania Cecchi

Keyword(s):

Adaptive Filters ◽

Variable Step Size ◽

Step Size ◽

Variable Step

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Realization of Enhanced LMS Filter Using Carry Skip Adder And Quantum Dot Cellular Automation In VLSI For Removing Impulse Noises In Medical Image

Current Signal Transduction Therapy ◽

10.2174/1574362414666190703151222 ◽

2019 ◽

Vol 14 ◽

Author(s):

K.R. Shankarkumar ◽

Gokul Kumar

Keyword(s):

Adaptive Filtering ◽

Adaptive Filters ◽

Pass Band ◽

Least Mean Square ◽

Low Pass ◽

Parallel Prefix ◽

Loop Feedback ◽

Band Pass ◽

The Difference ◽

Prefix Adder

: Filtering is an important step in the field of image processing to suppress the required parts or to remove any artifacts present in it. There are different types of filters like low pass, high pass, Band pass, IIR, FIR and adaptive filtering etc.., in these filters adaptive filters is an important filter because it is used to remove the noisy signal and images. Least Mean Square filter is a type of an adaptive filtering which is used to remove the noises present in the medical images. The working of LMS is based on the minimization of the difference between the error images using a closed loop feedback. Therefore presented technique called as Q-CSKA. Here the CSKA performs its operation in stages which is based on the nucleus stage. In the traditional CSKA the nucleus stage is depend on the parallel prefix adder in this work it is replaced by the QCA adder. The QCA adder utilizes the less area compared to PPA and it can be realized in Nanometer range also. For multiplexers, And OR Invert, OR and Invert logic is used to reduce the area and delay. Due to these advantages of the QCA, AOI-OAI logic the proposed method outperformed the LMS implementation in area, power, and accuracy and delay, this based five type image noise of medical pictures related to the best technique is out comes. It helps to medicinal practitioner to resolve the symptoms of patient with ease.

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