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REVIEW 3 major objections 4 minor 56 references

Data-driven retrieval of primary plane-wave responses

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A data-domain Marchenko scheme, adapted to plane-wave sources, retrieves transmission-loss-compensated primary reflection responses directly from point-source data, enabling multiple-free reverse time migration without model information…

desk verdict Plane-wave extension of data-domain Marchenko is a genuine, if incremental, advance; the dipping-wave approximation needs quantification and the validation needs metrics before it's fully convincing. read the letter →

arxiv 1908.09554 v2 pith:EKGQV5HK submitted 2019-08-26 physics.geo-ph physics.comp-ph

Giovanni Angelo Meles , Lele Zhang , Jan Thorbecke , Kees Wapenaar , Evert Slob This is my paper · ORCID
classification physics.geo-phphysics.comp-ph
keywords seismicimagingmultipleattenuationreverse-timemigrationplane-wavesourcesMarchenkomethodsprimarysynthesisinternalmultiplesdata-drivendemultiple
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper's central claim is that the data-domain variant of the Marchenko focusing-function method, previously applied to point-source gathers, can be adapted to plane-wave sources so that primary-only reflection responses are synthesized directly from measured point-source data. The adaptation yields explicit series solutions, $V^-$ in Eq. 22 for horizontal plane waves and in Eq. 30 for dipping plane waves, whose last event at the muting-window endpoint is a transmission-loss-compensated primary reflection. Because the muting windows are surface-projected and independent of the velocity model, the same linear operator can process any linear combination of point-source gathers, including plane-wave and blended-source data, in one pass. The paper then shows numerically that standard plane-wave reverse time migration of the retrieved primaries removes internal-multiple artefacts and recovers interfaces that are hidden in the full-data images. If the claim holds, multiple-free imaging can be achieved from only a small number of plane-wave gathers, a substantial reduction in cost compared with per-shot processing.

What carries the argument

The machinery is the projected Marchenko focusing function: the up-going projected focusing function $V^-(\mathbf{x}'_0, t, \bar{T}_2)$ is defined by integrating the subsurface focusing function against the direct transmission response, so that the unknowns live entirely at the acquisition surface. It is retrieved by solving the coupled equations $V^- = \Theta R_{\mathrm{PW}} + \Theta R V^+_m$ and $V^+_m = \Theta R^\star V^-$, which combine into the Neumann series above. The load-bearing identity is that the final event of $V^-$ at the window boundary is the transmission-loss-compensated primary in the plane-wave response; this makes the method fully data-driven, with no velocity model, no picking, and no adaptive subtraction. The same linear operator $I - \Theta R \Theta R^\star$ is applied to every gather, which is why plane-wave and blended-source data can be processed simultaneously.

What would settle it

In a strongly laterally heterogeneous 2D model, compare the approximate muting-window boundary $\epsilon + \bar{T}_2 + \mathbf{p} \cdot \mathbf{x}'_H$ with the exact two-way traveltime $T_2(\mathbf{x}'_0, \mathbf{p}, z_i)$ for a known reflector; if the difference exceeds about one source-wavelet period anywhere along the receiver line, Eq. 30 will place the wrong event at the window boundary, and the retrieved gather should not match an independently computed primary-only gather.

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Extended reading notes

Core claim

The core discovery is that surface-projected Marchenko focusing functions, when integrated over the acquisition surface, satisfy the same kind of coupled equations as the point-source case, with the plane-wave response replacing the point-source response in the source term. For a horizontal plane-wave source, the projected focusing function $V^-$ obeys $(I - \Theta R \Theta R^\star) V^- = \Theta R_{\mathrm{PW}}$, where $R$ is the convolution operator built from the measured point-source reflection response, $R^\star$ is its time-reversed version, $\Theta$ the muting window with endpoint $\bar{T}_2$, and $R_{\mathrm{PW}}$ the horizontal plane-wave reflection response. The series solution $V^- = \Theta R_{\mathrm{PW}} + \sum_{M=1}^{\infty} (\Theta R \Theta R^\star)^M \Theta R_{\mathrm{PW}}$ has, as its last event, a transmission-loss-compensated primary; stacking the results for all $\bar{T}_2$ reconstructs the primary-only plane-wave gather. The same construction works for dipping plane waves after shifting the window by $\mathbf{p} \cdot \mathbf{x}'_H$, with the upper boundary approximated as parallel to the lower one so that no subsurface information is required. Numerical tests on 2D models with thin layers, diffractors, and dipping interfaces show that migrating the retrieved gathers yields images largely free of internal-multiple artefacts, with dipping interfaces recovered when several angle gathers are stacked.

Load-bearing premise

The load-bearing premise is that, for dipping plane waves, the time interval used to isolate the primary can be chosen as a straight band of constant thickness across the receiver line, with the top boundary just a shifted copy of the bottom boundary; if true two-way traveltimes to reflectors bend away from that straight band in complex media, the retrieved primary is no longer guaranteed to be a primary.

Editorial extensions

If this is right

  • A single demultipled horizontal plane-wave gather migrated once can yield a multiple-free image for gently dipping structures, as demonstrated in the first numerical test.
  • Dipping-plane-wave retrieval extends illumination: stacking 11 retrieved gathers with angles between -25 and 25 degrees resolves dipping interfaces that are barely visible with horizontal illumination alone.
  • Because the operator is linear and gather-independent, blended-source data with different source spectra can be demultipled in one pass, matching the sum of individual point-source results to within 0.1 percent in the numerical test.
  • The retrieved primary gathers feed standard plane-wave reverse time migration without any modification, so the method slots directly into existing imaging workflows.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The parallel-muting-window approximation for dipping plane waves is the point most worth testing; comparing Eq. 30 retrievals against independently computed primaries in strongly laterally heterogeneous media would quantify where the straight-window assumption breaks.
  • Because the same operator is applied to every plane-wave angle, the marginal cost of adding an extra angle gather is essentially one application of the series; this makes large stacks of angle gathers computationally attractive, though the paper only demonstrates a stack of 11 gathers.
  • The same surface-projected focusing logic could extend to other areal source geometries, such as curved wavefronts or focused beams, as long as the source delays can be folded into the muting-window definition; the paper restricts itself to plane waves.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper extends data-domain Marchenko primary-synthesis methods from point-source gathers to plane-wave source responses. It defines plane-wave projected focusing functions V^- and V_m^+ and derives series solutions (Eqs. 22 and 30) that, when evaluated for all constant two-way-time windows and storing results at the window end time, yield estimates of transmission-loss-compensated primary plane-wave reflections. The method is tested on two synthetic 2D acoustic models. For a gently dipping model, horizontal plane-wave data produce a multiple-free migrated image. For a more complex model with thin layers, diffractors and dipping layers, horizontal and dipping plane-wave gathers are processed and stacked, yielding a cleaner image than migrating the full data. The paper claims the algorithm is fully data-driven, requires no picking, and needs only a small number of plane-wave gathers for imaging.

Significance. If the claims hold, the method is a useful extension of data-domain Marchenko methods: it offers a computationally cheaper alternative to point-source primary synthesis for plane-wave migration, and it is fully data-driven in the sense that no model information enters the multiple-elimination step. The paper builds on published theory (Zhang et al. 2019b; Meles et al. 2018) rather than introducing free parameters fitted to data, and the numerical examples are performed with independent finite-difference modeling. The main novelty, the dipping-plane-wave extension, rests on an approximation that is not quantified, and the validation is entirely visual. The core horizontal-plane-wave derivation appears sound, but the load-bearing approximation in Section 3.3 and the absence of quantitative convergence and error analysis mean the paper is not yet at the standard for publication without revision.

major comments (3)
  1. [Section 3.3, Eq. (30)] The claim that the upper muting boundary can be replaced by the model-independent expression epsilon + \bar{T}_2 + p·x'_H is not justified. For a laterally heterogeneous or dipping medium, T_2(x'_0,p,z_i) - p·x'_H varies with x'_0, so the upper boundary of the muting window is not exactly parallel to the lower boundary epsilon + p·x'_H. Storing results at t = \bar{T}_2 + p·x'_H then does not necessarily sample the primary event. The paper asserts this approximation "in analogy to the previous cases" without proof, error bound, or sensitivity analysis. Since this approximation is the only mechanism that makes the dipping-plane-wave algorithm model-independent, the central claim of Section 3.3 is not established. Please either prove the approximation under stated conditions, quantify its error for the models in Section 4, or restrict the dipping-plane-wave claims to media where it holds.
  2. [Section 4, 'first 20 terms' (Eqs. 22/30)] The numerical examples compute only the first 20 terms of the Neumann series, with no convergence test. The series representation is the basis for retrieving primaries, and a reader cannot tell whether 20 terms are sufficient for the models shown. Please show a convergence plot (e.g., energy of successive partial sums, or difference between 10, 20, and 30 terms) for at least one representative gather. Without this, the examples do not demonstrate that the truncated series produces the claimed primaries.
  3. [Section 4, Figs. 3-7] The validation is qualitative. The paper claims transmission-loss compensation and primary retrieval, but no quantitative metric is given: there is no comparison against a directly modeled primary-only response, no amplitude or traveltime error measurement, and no signal-to-noise ratio for the demultipled gathers. Because the method is intended to produce true-amplitude primaries suitable for migration, a quantitative check (e.g., normalized L2 error against a synthetic primary-only dataset, or a measure of multiple suppression in the migrated image) is needed to support the strength of the claims.
minor comments (4)
  1. [Section 4, paragraph 2] The text refers to "the estimated primaries in Fig. 6(d)" when discussing the horizontal plane-wave case, but Fig. 6(d) corresponds to the -15 degree dipping plane wave; the horizontal-plane-wave primaries are shown in Fig. 6(e). Please correct the figure reference.
  2. [Eqs. (26)-(30)] The lower muting boundary is written as \epsilon + p·x'_H, but p·x'_H can be negative, while the physical time interval should start at a nonnegative small value for the retrieved events to be causal. A brief clarification of the allowed range of p and of the resulting lower boundary would help.
  3. [Discussion, Eq. (31) and following paragraph] The statement that "the window operators discussed here are the same for each input data" is accurate for horizontal plane waves but not for dipping plane waves, where the operator depends on p through the p·x'_H term. The sentence should be qualified to avoid over-generalization.
  4. [Abstract and Introduction] The abstract says the scheme "operates on plane-wave datasets," but the input is the full point-source reflection response; the output is a plane-wave primary response. This distinction is clear in the body but could be emphasized in the abstract to avoid misleading readers.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the plane-wave primary retrieval is a data-driven extension of a published, externally validated point-source method, with no fitted parameters and no output redefined as input.

full rationale

The central retrieval equations (Eqs. 22 and 30) are genuine extensions of the point-source data-domain Marchenko algorithm. They are not tautological: V- is defined as an integral of the point-source projected focusing function, and the plane-wave primary is then obtained by solving a Neumann series with data-driven muting windows. The property that the last event of v- is a transmission-loss-compensated primary is imported from Zhang et al. (2019b), a published, peer-reviewed derivation with explicit assumptions (acoustic medium, one-sided illumination, co-located sources and receivers) that do not include the plane-wave output itself; this is independent support rather than circular self-citation. The numerical tests use independently constructed synthetic velocity/density models and finite-difference data; no parameter is fitted to the retrieved primary gathers, and migration results are compared with known reflectors. The dipping-plane-wave step in Section 3.3 approximates the upper muting boundary as parallel to the lower boundary, which is an untested accuracy assumption in laterally heterogeneous media, but it is a correctness risk, not a circular reduction. The paper's reliance on the authors' own prior work is load-bearing but does not reduce the central claim to a self-citation: the priors are concrete, reproducible derivations, and the plane-wave extension adds new structure. No step equates the prediction with an input by definition, and no fitted parameter is renamed as a prediction. Therefore the paper is not circular.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The method introduces no new free parameters or invented physical entities. The projected focusing functions V- and V+m are mathematical constructs inherited from prior Marchenko work. The load-bearing assumptions are the standard Marchenko acquisition and medium assumptions, the convergence of the Neumann series, the identification of the last event of V- as a primary, and the ad hoc model-independent muting window for dipping plane waves.

assumptions (4)
  • domain assumption The medium is acoustic and the acquisition surface is reflection-free, with one-sided illumination from co-located point sources and receivers.
    Inherited from standard Marchenko theory (Wapenaar et al. 2014; Zhang et al. 2019b) and assumed in the numerical setup (Section 4).
  • standard math The Neumann series (I - Theta R Theta R*)^-1 converges under standard convergence conditions.
    Invoked in Eqs. 13-14 and 21-22, citing Fokkema and van den Berg (1993); convergence is not demonstrated for the examples, only a 20-term truncation is used.
  • domain assumption The last event of V- at t = T2 is a transmission loss compensated primary reflection in the plane-wave response.
    This is the central identification inherited from Zhang et al. (2019b) and extended to plane waves in Eqs. 19-22; it is not independently proven here.
  • ad hoc to paper For dipping plane-waves, the upper boundary of the muting window can be approximated as model-independent: T2(x'_0,p,z_i)+eps = eps + T2_bar + p.x'_H.
    Stated in Section 3.3 and illustrated in Fig. 1; this approximation is load-bearing for the dipping extension and its accuracy for complex models is not quantified.

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Cite this review

Pith. "Pith review of Data-driven retrieval of primary plane-wave responses." pith.science (2026). https://pith.science/paper/EKGQV5HK

@misc{pith2026190809554,
  author       = {Pith},
  title        = {Pith review of: Data-driven retrieval of primary plane-wave responses},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EKGQV5HK}},
  note         = {Machine review of arXiv:1908.09554}
}
read the original abstract

Seismic images provided by reverse time migration can be contaminated by artefacts associated with the migration of multiples. Multiples can corrupt seismic images, producing both false positives, i.e. by focusing energy at unphysical interfaces, and false negatives, i.e. by destructively interfering with primaries. Multiple prediction / primary synthesis methods are usually designed to operate on point source gathers, and can therefore be computationally demanding when large problems are considered. A computationally attractive scheme that operates on plane-wave datasets is derived by adapting a data-driven point source gathers method, based on convolutions and cross-correlations of the reflection response with itself, to include plane-wave concepts. As a result, the presented algorithm allows fully data-driven synthesis of primary reflections associated with plane-wave source responses. Once primary plane-wave responses are estimated, they are used for multiple-free imaging via plane-wave reverse time migration. Numerical tests of increasing complexity demonstrate the potential of the proposed algorithm to produce multiple-free images from only a small number of plane-wave datasets.

Figures

Figures reproduced from arXiv: 1908.09554 by the authors.

Figure 1
Figure 1. The shaded green areas show the support of representative muting operators for [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. (a) Velocity and (b) density models used in the first numerical experiment. [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. (a) Full dataset associated with a plane-wave source fired at the surface of the model. [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: (a) Standard plane-wave reverse time migration of the dataset in Fig. 3(a). Red [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: (a) Velocity and (b) density models used in the second numerical experiment. [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: (a-c): reflection responses associated with plane wave sources at [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]
Figure 7
Figure 7. Figure 7: (a) Standard plane-wave reverse time migration of the dataset in Fig. 6(a). Red [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]
Figure 8
Figure 8. Figure 8: (a) Full dataset associated with 5 point sources with different spectrum content [PITH_FULL_IMAGE:figures/full_fig_p016_8.png]

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.