Implementation of the Marchenko Multiple Elimination algorithm

The Marchenko multiple elimination and transmission compensation schemes retrieve primary reflections in the two-way traveltime domain without model information or using adaptive subtraction. Both schemes are derived from projected Marchenko equations and similar to each other, but use different time-domain truncation operators. The Marchenko multiple elimination scheme retrieves a new dataset without internal multiple reflections. The transmission compensated Marchenko multiple elimination scheme does the same and additionally compensates for transmission losses in the primary reflections. Both schemes can be solved with an iterative algorithm based on a Neumann series. At each iteration, a convolution or correlation between the projected focusing function and the measured reflection response are performed and after each convolution or correlation, a truncation in the time domain is applied. After convergence, the resulting projected focusing function is used for retrieving the transmission compensated primary reflections and the projected Green’s function is used for the physical primary reflections. We demonstrate that internal multiples are removed by using time-windowed input data that only contain primary reflections. We evaluate both schemes in detail and develop an iterative implementation that reproduces the presented numerical examples. The software is part of our open-source suite of programs and fits into the Seismic Unix software suite of the Colorado School of Mines.

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Transmission compensated primary reflection retrieval in the data domain and consequences for imaging

Geophysics ◽

10.1190/geo2018-0340.1 ◽

2019 ◽

Vol 84 (4) ◽

pp. Q27-Q36 ◽

Cited By ~ 13

Author(s):

Lele Zhang ◽

Jan Thorbecke ◽

Kees Wapenaar ◽

Evert Slob

Keyword(s):

Thin Layer ◽

Time Domain ◽

Velocity Model ◽

Original Data ◽

Transmission Losses ◽

Multiple Reflections ◽

Data Set ◽

Numerical Examples ◽

The One ◽

The Time Domain

We have developed a scheme that retrieves primary reflections in the two-way traveltime domain by filtering the data. The data have their own filter that removes internal multiple reflections, whereas the amplitudes of the retrieved primary reflections are compensated for two-way transmission losses. Application of the filter does not require any model information. It consists of convolutions and correlations of the data with itself. A truncation in the time domain is applied after each convolution or correlation. The retrieved data set can be used as the input to construct a better velocity model than the one that would be obtained by working directly with the original data and to construct an enhanced subsurface image. Two 2D numerical examples indicate the effectiveness of the method. We have studied bandwidth limitations by analyzing the effects of a thin layer. The presence of refracted and scattered waves is a known limitation of the method, and we studied it as well. Our analysis indicates that a thin layer is treated as a more complicated reflector, and internal multiple reflections related to the thin layer are properly removed. We found that the presence of refracted and scattered waves generates artifacts in the retrieved data.

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Data-driven internal multiple elimination and its consequences for imaging: A comparison of strategies

Geophysics ◽

10.1190/geo2018-0817.1 ◽

2019 ◽

Vol 84 (5) ◽

pp. S365-S372 ◽

Cited By ~ 5

Author(s):

Lele Zhang ◽

Jan Thorbecke ◽

Kees Wapenaar ◽

Evert Slob

Keyword(s):

Inverse Scattering ◽

Computational Cost ◽

Multiple Reflection ◽

Data Driven ◽

Transmission Losses ◽

Multiple Reflections ◽

Data Set ◽

Numerical Examples ◽

Inverse Scattering Series ◽

Multiple Elimination

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.

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An internal-multiple elimination algorithm for all first-order internal multiples for a 1D earth

10.1190/segam2015-5903808.1 ◽

2015 ◽

Cited By ~ 2

Author(s):

Yanglei Zou ◽

Arthur B. Weglein

Keyword(s):

First Order ◽

Elimination Algorithm ◽

Internal Multiples ◽

Multiple Elimination

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Time-Domain Multidimensional Deconvolution: A Physically Reliable and Stable Preconditioned Implementation

Remote Sensing ◽

10.3390/rs13183683 ◽

2021 ◽

Vol 13 (18) ◽

pp. 3683

Author(s):

David Vargas ◽

Ivan Vasconcelos ◽

Matteo Ravasi ◽

Nick Luiken

Keyword(s):

Inverse Problem ◽

Time Domain ◽

Body Wave ◽

Complex Salt ◽

Iterative Solvers ◽

Physical Constraints ◽

Damping Parameter ◽

Band Limited ◽

The Time Domain ◽

Multiple Elimination

Multidimensional deconvolution constitutes an essential operation in a variety of geophysical scenarios at different scales ranging from reservoir to crustal, as it appears in applications such as surface multiple elimination, target-oriented redatuming, and interferometric body-wave retrieval just to name a few. Depending on the use case, active, microseismic, or teleseismic signals are used to reconstruct the broadband response that would have been recorded between two observation points as if one were a virtual source. Reconstructing such a response relies on the the solution of an ill-conditioned linear inverse problem sensitive to noise and artifacts due to incomplete acquisition, limited sources, and band-limited data. Typically, this inversion is performed in the Fourier domain where the inverse problem is solved per frequency via direct or iterative solvers. While this inversion is in theory meant to remove spurious events from cross-correlation gathers and to correct amplitudes, difficulties arise in the estimation of optimal regularization parameters, which are worsened by the fact they must be estimated at each frequency independently. Here we show the benefits of formulating the problem in the time domain and introduce a number of physical constraints that naturally drive the inversion towards a reduced set of stable, meaningful solutions. By exploiting reciprocity, time causality, and frequency-wavenumber locality a set of preconditioners are included at minimal additional cost as a way to alleviate the dependency on an optimal damping parameter to stabilize the inversion. With an interferometric redatuming example, we demonstrate how our time domain implementation successfully reconstructs the overburden-free reflection response beneath a complex salt body from noise-contaminated up- and down-going transmission responses at the target level.

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A fast algorithm for multiple elimination and transmission compensation in primary reflections

Geophysical Journal International ◽

10.1093/gji/ggaa005 ◽

2020 ◽

Vol 221 (1) ◽

pp. 371-377 ◽

Cited By ~ 5

Author(s):

Lele Zhang ◽

Evert Slob

Keyword(s):

Computational Cost ◽

Initial Estimate ◽

Transmission Losses ◽

Multiple Reflections ◽

Excellent Performance ◽

Numerical Examples ◽

Acoustic Reflection ◽

Time Value ◽

Order Of Magnitude ◽

Multiple Elimination

SUMMARY The transmission compensated primary reflections can be obtained from the single-sided acoustic reflection response in the two-way traveltime domain. This is achieved by eliminating free-surface and internal multiple reflections and compensating for transmission losses in primary reflections without model information. The substantial computational cost of the proposed scheme can be reduced by an order of magnitude with a fast implementation version. This is achieved by using the previously computed filter functions as initial estimate for every new truncation time value. We evaluate the success of the scheme with simple and complex 2-D numerical examples. We find that the scheme has excellent performance in most cases, except for the case where strong reflectors are present. In such case, the current scheme suffers from lack of convergence.

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Archimedean Spiral Antenna Calibration Procedures to Increase the Downrange Resolution of a SFCW Radar

International Journal of Antennas and Propagation ◽

10.1155/2008/378285 ◽

2008 ◽

Vol 2008 ◽

pp. 1-7 ◽

Cited By ~ 7

Author(s):

Ioan Nicolaescu ◽

Piet van Genderen

Keyword(s):

Time Domain ◽

Continuous Wave ◽

Phase Variation ◽

Antenna System ◽

Spiral Antenna ◽

Multiple Reflections ◽

Archimedean Spiral ◽

Wave Radar ◽

Time Domain Response ◽

The Time Domain

This paper deals with the calibration procedures of an Archimedean spiral antenna used for a stepped frequency continuous wave radar (SFCW), which works from 400 MHz to 4845 MHz. Two procedures are investigated, one based on an error-term flow graph for the frequency signal and the second based on a reference metallic plate located at a certain distance from the ground in order to identify the phase dispersion given by the antenna. In the second case, the received signal is passed in time domain by applying an ifft, the multiple reflections are removed and the phase variation due to the time propagation is subtracted. After phase correction, the time domain response as well as the side lobes level is decreased. The antenna system made up of two Archimedean spirals is employed by SFCW radar that operates with a frequency step of 35 MHz.

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THEORETICAL SEISMOGRAMS WITH FREQUENCY AND DEPTH DEPENDENT ABSORPTION

Geophysics ◽

10.1190/1.1439098 ◽

1962 ◽

Vol 27 (6) ◽

pp. 766-785 ◽

Cited By ~ 37

Author(s):

A. W. Trorey

Keyword(s):

Absorption Coefficient ◽

Time Domain ◽

Network Theory ◽

Digital Computer ◽

Arrival Time ◽

Synthetic Seismograms ◽

Multiple Reflections ◽

Frequency Spectra ◽

Dependent Absorption ◽

The Time Domain

In the computation of conventional theoretical (or “synthetic”) seismograms, the effects of the variation of frequency‐dependent absorption with depth are presently ignored. Such absorption can produce significant differences in both the relative amplitudes and frequency spectra of primary and multiple reflections having the same arrival time. This paper describes a feasible way, using a digital computer of the IBM 7090 class, for computing theoretical seismograms which properly take into account the variation of absorption with both frequency and depth, it being assumed that the absorption coefficient varies linearly with frequency. It is pointed out that attempts to solve the problem using Fourier analysis in the frequency domain would lead to significant aliasing errors. Consequently a method borrowed from the field of network theory utilizing deconvolution is devised whereby solutions are obtained directly in the time domain. Both “primary” and “primary‐plus‐all‐multiple” traces are computed, the former including the “peg‐leg” multiples described by Anstey (1960) and Webster (1960). These calculations demonstrate that absorption can reduce the multiple content of theoretical seismograms.

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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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