A field data example of Marchenko multiple elimination

Zhang, Lele; Slob, Evert

doi:10.1190/geo2019-0327.1

Cited by 34 publications

(9 citation statements)

References 31 publications

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“…Inversion of the Marchenko equation has proven to be an effective tool for the retrieval of Green's functions in an unknown acoustic medium from single-sided reflection data [1,2]. For an introduction to this subject, the numerical implementation of the Marchenko equation, field data applications and recent developments, see [3][4][5][6][7][8][9][10][11], respectively. An equivalent (Marchenko) equation has also been derived for wave propagation in elastic media [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Marchenko Green’s Function Retrieval in Layered Elastic Media from Two-Sided Reflection and Transmission Data

et al. 2022

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By solving a Marchenko equation, Green’s functions at an arbitrary (inner) depth level inside an unknown elastic layered medium can be retrieved from single-sided reflection data, which are collected at the top of the medium. To date, it has only been possible to obtain an exact solution if the medium obeyed stringent monotonicity conditions and if all forward-scattered (non-converted and converted) transmissions between the acquisition level and the inner depth level were known a priori. We introduce an alternative Marchenko equation by revising the window operators that are applied in its derivation. We also introduce an auxiliary equation for transmission data, which are collected at the bottom of the medium, and a coupled equation, which is based on both reflection and transmission data. We show that the joint system of the Marchenko equation, the auxiliary equation and the coupled equation can be succesfully inverted when broadband reflection and transmission data are available. This results in a novel methodology for elastodynamic Green’s function retrieval from two-sided data. Apart from these data, our approach requires P- and S-wave transmission times between the inner depth level and the top of the medium, as well as two angle-dependent amplitude scaling factors, which can be estimated from the data by enforcing energy conservation.

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Section: Introductionmentioning

confidence: 99%

Marchenko Green’s Function Retrieval in Layered Elastic Media from Two-Sided Reflection and Transmission Data

et al. 2022

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“…Zhang and Staring (2018) found that this information is not necessary, and the truncation time can be chosen independent of offset. Their work filters out primary reflections from acoustic data without using any model information and was successfully applied to field data (Zhang and Slob, 2020a). The scheme was adapted to remove free‐surface and internal multiples simultaneously (Zhang and Slob, 2019).…”

Section: Introductionmentioning

confidence: 99%

Unified elimination of 1D acoustic multiple reflection

Slob

Zhang

2021

Geophysical Prospecting

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Migration, velocity and amplitude analysis are the employed processing steps to find the desired subsurface information from seismic reflection data. The presence of freesurface and internal multiples can mask the primary reflections for which many processing methods are built. The ability to separate primary from multiple reflections is desirable. Connecting Marchenko theory with classical one-dimensional inversion methods allows to understand the process of multiple reflection elimination as a datafiltering process. The filter is a fundamental wave field, defined as a pressure and particle velocity that satisfy the wave equation. The fundamental wave field does not depend on the presence or absence of free-surface multiples in the data. The backbone of the filtering process is that the fundamental wave field is computed from the measured pressure and particle velocity without additional information. Two different multiples-free datasets are obtained: either directly from the fundamental wave field or by applying the fundamental wave field to the data. In addition, the known schemes for Marchenko multiple elimination follow from the main equation. Numerical examples show that source and receiver ghosts, free-surface and internal multiples can be removed simultaneously using a conjugate gradient scheme. The advantage of the main equation is that the source wavelet does not need to be known and no preprocessing is required. The fact that the reflection coefficients can be obtained is an interesting feature that could lead to improved amplitude analysis and inversion than would be possible with other processing methods.

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“…The MME scheme retrieves the primaries from the reflection data, while the T-MME retrieves the transmission compensated primaries from the upgoing filter function. The MME scheme has been tested on numerical and field data (Zhang and Slob, 2020a). The examples in show that all orders of internal multiple reflections are successfully eliminated by both schemes.…”

Section: Introductionmentioning

confidence: 99%

Implementation of the Marchenko multiple elimination algorithm

et al. 2021

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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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A field data example of Marchenko multiple elimination

Cited by 34 publications

References 31 publications

Marchenko Green’s Function Retrieval in Layered Elastic Media from Two-Sided Reflection and Transmission Data

Marchenko Green’s Function Retrieval in Layered Elastic Media from Two-Sided Reflection and Transmission Data

Unified elimination of 1D acoustic multiple reflection

Implementation of the Marchenko multiple elimination algorithm

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