M. Dukalski

Elastodynamic Marchenko Method: Advances and Remaining Challenges

Christian Reinicke M. Dukalski Kees Wapenaar

Summary Marchenko methods aim to remove all overburden-related internal multiples. The acoustic and elastodynamic formulations observe identical equations, but different physics. The elastodynamic case highlights that the Marchenko method only handles overburden-generated reflections, i.e. forward-scattered transmitted waves (and so-called fast multiples) remain in the data. Moreover, to constrain an underdetermined problem, the Marchenko method makes two assumptions that are reasonable for acoustic, but not for elastodynamic waves. Firstly, the scheme requires an initial guess that can be realistically estimated for sufficiently-simple acoustic cases, but remains unpredictable for elastic media without detailed overburden knowledge. Secondly, the scheme assumes temporal separability of upgoing focusing and Green's functions, which holds for many acoustic media but easily fails in presence of elastic effects. The latter limitation is nearly-identical to the monotonicity requirement of the inverse scattering series, indicating that this limitation may be due to the underlying physics and not algorithm dependent. Provided that monotonicity holds, the aforementioned initial estimate can be retrieved by augmenting the Marchenko method with energy conservation and a minimum-phase condition. However, the augmentation relies on the availability of an elastic minimum-phase reconstruction method, which is currently under investigation. Finally, we discuss a geological setting where an acoustic approximation suffices.

10.3997/2214-4609.202012093

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What can Quantum Computing Mean for Geoscience?

M. Dukalski

Summary In the recent years quantum technologies have matured enough that modern quantum computers outperform their classical counterparts at some very special computational tasks. It is however not entirely clear what kind of practical problems can be solved using present or future quantum computers. Here we will try to give a first attempt at answering this question with focus on optimization problems in geoscience.

10.3997/2214-4609.202012090

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Robust estimation of primaries by sparse inversion and Marchenko equation-based workflow for multiple suppression in the case of a shallow water layer and a complex overburden: A 2D case study in the Arabian Gulf

Geophysics (2020)

Myrna Staring M. Dukalski Mikhail Belonosov Rolf Baardman Jewoo Yoo

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 have developed a two-step, amplitude- and phase-preserving, inversion-based workflow that addresses these problems. We apply robust estimation of primaries by sparse inversion (R-EPSI) to solve simultaneously for the surface-related primaries Green’s function and 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 demultiple methods such as surface-related multiple elimination. The resulting Green’s function is used as the input to a Marchenko equation-based approach to predict the complex interference pattern of all overburden-generated internal multiples at once. In this approach, no a priori information about the subsurface is needed. 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 preprocessing 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 for which corrections will be needed. Hence, we conclude that the use of conservative adaptive filters were necessary to obtain the best results after interbed multiple removal. The obtained results indicate promising suppression of surface-related and interbed multiples.

Multiple

Overburden

10.1190/geo2020-0204.1

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Citations (18)

Acoustic Plane-Wave Marchenko Multiple Elimination Applied on Complex Marine Data

83rd EAGE Annual Conference & Exhibition (2022)

Giovanni Angelo Meles Christian Reinicke M. Dukalski Kees Wapenaar

Summary Marchenko redatuming retrieves Green's functions inside an unknown medium, by solving a set of coupled Marchenko equations, which are derived from an under-determined system of equation and two temporal truncations. To constrain the problem, two assumptions are made, which hold reasonably well for acoustic, but not for elastodynamic waves. First, an early part of the inverse transmission field is needed which can be estimated for sufficiently-simple acoustic cases, but remains hard to predict for elastic media without detailed overburden knowledge. Secondly, the scheme assumes temporal separability of up-going focusing and Green's functions, which holds for many acoustic media but easily fails in presence of elastic effects. The impact of the failure to meet these assumptions is a somewhat controllable problem in 1.5D media. Independently, in acoustic media one can use a time-only focusing to retrieve focusing functions which collapse to a single plane wave below the overburden. We apply this approach to elastic data from a very complex almost 1.5D medium. The numerical example shows that the plane-wave approach can also be combined with mitigation of failure to satisfy the aforementioned assumptions and the result could lead to a high-fidelity internal multiple-free image.

10.3997/2214-4609.202210143

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Effective Media Theory Consistent Multiple Elimination with the Marchenko Equation Based Methods

Christian Reinicke M. Dukalski

Summary Deposition processes result in an almost length-scale-independent layering, which gives rise to many (usually weak) internal multiples. In frequently (and strongly) scattering media these multiples can have a (very) strong collective effect and result is a complex interference pattern (one that is typically characterized by specific frequencies) rather than stand-alone events. This is contradictory to event-based internal multiple estimation (IME) strategies (e.g. the Jakubowicz IME). In these cases such approaches do not adhere to the true nature of the multiples. In contrast, Marchenko-equation-based multiple elimination methods promise to remove all orders of internal multiples, and hence should account for the aforementioned collective spectral effect. The ultimate step of the Marchenko method is the deconvolution step, which we approximate by a so-called double de-reverberation, which allows to explicitly identify the generation mechanism and the collective spectral effects of the (later removed) multiples. To illustrate the expected and realistic impact of internal multiples, we apply this methodology to a complex synthetic model based on a well-log from the Middle East. The result near-to-perfectly describes the collective effect of the true multiples and is consistent with the effective media theories.

10.3997/2214-4609.202010907

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The Role of Minimum Phase in Internal Multiple Removal

M. Dukalski

Summary Given true-amplitude pre-processed data, Marchenko equation based methods could remove all overburden-borne internal multiples without the adaptive subtraction. The method hinges on calculating an inverse transmission response, however in many practical cases to find a solution, one is required to provide a part of it on input. This requirement can be lifted by invoking minimum phase - a mathematical property familiar to many geophysicists, yet normally not associated with a de-multiple workflow. Here we discuss the state of the art, challenges and road ahead for minimum phase enriched internal de-multiple. In particular we focus on the differences in minimum phase reconstruction between single input single output (1.5-D single mode) vs multiple input multiple output systems (everything else).

Minimum phase

Subtraction

Multiple

10.3997/2214-4609.202012091

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Citations (4)

Propagator and transfer matrices, Marchenko focusing functions and their mutual relations

arXiv (Cornell University) (2023)

Kees Wapenaar M. Dukalski Christian Reinicke Roel Snieder

Many seismic imaging methods use wave field extrapolation operators to redatum sources and receivers from the surface into the subsurface. We discuss wave field extrapolation operators that account for internal multiple reflections, in particular propagator matrices, transfer matrices and Marchenko focusing functions. A propagator matrix is a square matrix that `propagates' a wave-field vector from one depth level to another. It accounts for primaries and multiples and holds for propagating and evanescent waves. A Marchenko focusing function is a wave field that focuses at a designated point in space at zero time. Marchenko focusing functions are useful for retrieving the wave field inside a heterogeneous medium from the reflection response at its surface. By expressing these focusing functions in terms of the propagator matrix, the usual approximations (such as ignoring evanescent waves) are avoided. While a propagator matrix acts on the full wave-field vector, a transfer matrix (according to the definition employed in this paper)`transfers' a decomposed wave-field vector (containing downgoing and upgoing waves) from one depth level to another. It can be expressed in terms of decomposed Marchenko focusing functions. We present propagator matrices, transfer matrices and Marchenko focusing functions in a consistent way and discuss their mutual relations. In the main text we consider the acoustic situation and in the appendices we discuss other wave phenomena. Understanding these mutual connections may lead to new developments of Marchenko theory and its applications in wave field focusing, Green's function retrieval and imaging.

Propagator

Transfer matrix

Matrix (chemical analysis)

10.48550/arxiv.2302.11858

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Marchenko Multiple Elimination Using Conventional Vs Advanced 3-D To 2-D Conversion on Marine Data

83rd EAGE Annual Conference & Exhibition (2022)

M. Dukalski Christian Reinicke

Summary Amplitude fidelity is critical for data-driven and wave equation-based methods. In particular, the more advanced methods are often (first) applied on (2-D) sail lines, due to a sparse cross-line sampling, high computational cost or both. Hence, the acquired seismic data needs to be correctly converted from 3-D to 2-D. This is particularly true for the Marchenko method, as it is the only method capable of suppressing internal multiple without the need for adaptive subtraction, but at the cost of the need for a correct global and time- and frequency-dependent scaling. We study the consequences of the conventional ("sqrt-t" and "sqrt-omega") and advanced 3-D to 2-D conversion on a controlled synthetic dataset. We show that, the impact is particularly significant for the marine setting, where most Marchenko field data applications are expected to be carried out due to high pre-processing requirements. We show that for a simple enough model, the Marchenko method combined with the conventional conversion could under-estimates multiples, whereas the advanced conversion does well. This has important implication for existing and future field data applications.

Multiple

Subtraction

High fidelity

10.3997/2214-4609.202210182

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Citations (2)

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

Geophysical Journal International (2020)

Patrick Elison M. Dukalski K. de Vos D.J. van Manen Johan O. A. Robertsson

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.

Multiple

Overburden

Bandlimiting

10.1093/gji/ggaa020

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Citations (31)

Propagator and transfer matrices, Marchenko focusing functions and their mutual relations

Geophysical Journal International (2023)

Kees Wapenaar M. Dukalski Christian Reinicke Roel Snieder

Many seismic imaging methods use wave field extrapolation operators to redatum sources and receivers from the surface into the subsurface. We discuss wave field extrapolation operators that account for internal multiple reflections, in particular propagator matrices, transfer matrices and Marchenko focusing functions. A propagator matrix is a square matrix that `propagates' a wave-field vector from one depth level to another. It accounts for primaries and multiples and holds for propagating and evanescent waves. A Marchenko focusing function is a wave field that focuses at a designated point in space at zero time. Marchenko focusing functions are useful for retrieving the wave field inside a heterogeneous medium from the reflection response at its surface. By expressing these focusing functions in terms of the propagator matrix, the usual approximations (such as ignoring evanescent waves) are avoided. While a propagator matrix acts on the full wave-field vector, a transfer matrix (according to the definition employed in this paper)`transfers' a decomposed wave-field vector (containing downgoing and upgoing waves) from one depth level to another. It can be expressed in terms of decomposed Marchenko focusing functions. We present propagator matrices, transfer matrices and Marchenko focusing functions in a consistent way and discuss their mutual relations. In the main text we consider the acoustic situation and in the appendices we discuss other wave phenomena. Understanding these mutual connections may lead to new developments of Marchenko theory and its applications in wave field focusing, Green's function retrieval and imaging.

Propagator

Inverse theory

10.1093/gji/ggad309

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Citations (3)

Papers

Citation

H-Index

i-10 index

Papers

Citation

H-Index

i-10 index