{"id":"51c45cc7-6b3a-445a-a33c-47b1aed5b814","arxiv_id":"1908.09554","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"The authors extend data-domain Marchenko primary retrieval from point sources to horizontal and dipping plane-wave sources, enabling fully data-driven demultiple of plane-wave seismic data and multiple-free reverse time migration.","lead":"This paper derives a way to remove internal multiples from seismic recordings when the source is a plane wave, producing 'primary-only' plane-wave data for cleaner subsurface images. It extends a known data-driven demultiple method from point sources to horizontal and dipping plane-wave sources, which makes multiple-free imaging cheaper because fewer gathers need to be migrated.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Dipping plane-wave retrieval rests on an untested linear-moveout assumption for the muting window: T2(x',p,zi)-p·x' is taken constant, which is generally not exact in laterally heterogeneous media; the paper never quantifies this.","rationale":"The derivation of Eqs. 22 and 30 is internally consistent when the window operator uses the true, model-dependent T2. The paper's model-independent version, however, replaces T2 by a linear function of the receiver coordinate. That replacement is an assumption about the kinematics of plane-wave primaries, not a consequence of the Marchenko equations. The same issue exists in muted form for horizontal plane waves (p=0) in laterally varying media; the dipping case makes it explicit because the assumed moveout slope is nonzero. The numerical experiments show plausible images, but they do not isolate the error introduced by the window approximation: no comparison with true primaries is shown, and residual artifacts are attributed without analysis to 'thin layers, diffractors and dipping layers'. A direct comparison would settle whether the approximation holds on the very model used to demonstrate the method. This concern does not refute the central construction; the horizontal-plane-wave and point-source results appear sound, and the paper is transparent about the approximation. It does mean the strongest claim—fully data-driven retrieval for dipping plane waves in complex media—is not yet established. The reader's CONDITIONAL verdict is appropriate.","tokens_in":13062,"tokens_out":19399,"duration_ms":208100,"concrete_test":"Compute a reference primary-only plane-wave gather for the Fig. 5 model (e.g., by finite-difference modeling with multiple-generating contrasts removed, or by Born/primary-only modeling) for the same p values used in the paper (-25° to 25°). Apply Eq. 30 with the approximate parallel window and compare the retrieved gather to this reference: report normalized L2 misfit and maximum time shift of the primary event as a function of p. If, for the 15° gather, the retrieved event is shifted or smeared by more than one dominant period of the 20 Hz Ricker wavelet (≈50 ms), or the L2 misfit exceeds ~10%, the parallel-window approximation is quantitatively inadequate for this model.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is in Section 3.3, where the model-dependent muting boundary T2(x'_0,p,z_i) is replaced by the parallel, model-independent boundary \\bar{T}_2 + p·x'_H. The text says only 'in analogy to the previous cases' that the upper boundary can be taken parallel to the lower one. This assumes that for every primary event the two-way plane-wave traveltime has the exact linear moveout T2 = \\bar{T}_2 + p·x'_H (constant intercept). For a 1D medium this is true, but for the laterally varying and dipping models used in Section 4 it is generally false: T2(x',p,z_i) - p·x'_H varies across the receiver aperture. When it varies, Eq. 30 with the approximate window samples V^- at times that do not coincide with the primary event, so the value stored at t = \\bar{T}_2 + p·x'_H is not the transmission-compensated primary; the event is mispositioned or smeared. The paper provides no error bound or sensitivity analysis, and the validation is qualitative (Figs. 6-7). Because this approximation is the only mechanism that makes the dipping-plane-wave algorithm model-independent, the central claim is conditionally supported at best.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":13332,"tokens_out":3390,"duration_ms":33215,"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":[{"comment":"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.","section":"Section 3.3, Eq. (30)"},{"comment":"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.","section":"Section 4, 'first 20 terms' (Eqs. 22/30)"},{"comment":"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.","section":"Section 4, Figs. 3-7"}],"minor_comments":[{"comment":"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.","section":"Section 4, paragraph 2"},{"comment":"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.","section":"Eqs. (26)-(30)"},{"comment":"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.","section":"Discussion, Eq. (31) and following paragraph"},{"comment":"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.","section":"Abstract and Introduction"}],"recommendation":"major_revision","confidential_remarks":"The paper relies heavily on the authors' own prior work (Zhang et al. 2019b; Meles et al. 2018), but this is not a novelty concern per se. The main uncertainty is whether the dipping-plane-wave window approximation can be made rigorous or at least quantitatively bounded; if it cannot, the dipping-plane-wave contribution may need to be presented as heuristic with a clear statement of its limited domain of validity. The horizontal-plane-wave part alone is a solid incremental contribution, but the paper's stated scope includes dipping plane waves, so the revision should address the approximation head-on."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Root: the paper delivers a real extension of the data-domain Marchenko primary retrieval (Zhang et al. 2019b) to horizontal and dipping plane-wave sources. The central observation that the muting window is independent of the particular gather is genuinely useful: it means blended-source and plane-wave data can be processed with the same linear operator, which is a nice practical simplification. The derivation is clean and the synthetic examples are visually convincing: internal multiples are suppressed and primaries recovered in both the gentle and the complex models.\n\nThe soft spots are real but manageable. The most important is the dipping plane-wave window approximation in Section 3.3. The paper replaces the model-dependent upper muting boundary T2(x',p,z_i) with a parallel, model-independent boundary \\bar{T}_2 + p·x'_H, and the stress-test concern is right: T2 - p·x'_H is only constant for a 1D medium or a perfectly linear moveout. For the laterally varying and dipping models in Section 4, it is not exact, and the paper provides no error estimate or sensitivity analysis. The synthetic results suggest it holds well enough for these examples, but that is not a general guarantee. This needs to be quantified, or at least explicitly bounded, before the dipping-plane-wave claim can be taken as fully established. Secondly, the series truncation at 20 terms is unexamined; a convergence test would be a page of work and would remove a nagging question. Third, validation is entirely qualitative — no SNR or amplitude error metrics, no comparison to a known primary response. And the computational advantage is claimed but not measured. None of these flaws are fatal; they are the difference between a conference-level demonstration and a solid journal paper.\n\nThe citation pattern is appropriate: the paper builds on Zhang et al. (2019b) and Meles et al. (2018) and credits them clearly. The blend of self-citation is justified because the earlier results are published and the new contribution is a genuine extension.\n\nWho is this for? Seismic imaging researchers working on multiple attenuation or Marchenko methods will want to read it. It is a solid within-subfield contribution, not a breakthrough. I would send it to peer review; the core idea is sound and the synthetic evidence is promising. I would ask the authors to address the dipping-wave approximation, add convergence checks, and at least one quantitative comparison before acceptance.","headline":"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.","tokens_in":13855,"tokens_out":3422,"would_cite":true,"duration_ms":33201,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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…","keywords":["seismic imaging","multiple attenuation","reverse-time migration","plane-wave sources","Marchenko methods","primary synthesis","internal multiples","data-driven demultiple"],"falsifier":"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.","tokens_in":12855,"feed_emoji":"🌊","tokens_out":13806,"duration_ms":110689,"temperature":0.7,"pith_summary":"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.","feed_headline":"Plane-wave seismic images cleaned of multiples, no model needed","feed_subtitle":"Turns point-source data into multiple-free plane-wave gathers, cutting migration cost and internal-multiple artefacts.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the point-source data-domain primary-retrieval method and the identity that the last event of the projected focusing function is a transmission-loss-compensated primary.","marker":"Zhang et al. (2019b)"},{"why":"Introduced data-domain Marchenko / adaptive overburden elimination, the projected-focusing idea that Eqs. 9-14 build on.","marker":"van der Neut and Wapenaar (2016)"},{"why":"Adapted Marchenko redatuming to plane-wave sources, the template for the plane-wave extension presented here.","marker":"Meles et al. (2018)"},{"why":"Makes the dependence of the projected focusing functions on the two-way traveltime parameter explicit, supporting the constant-window scanning used in implementation.","marker":"Zhang and Slob (2020a)"},{"why":"Defines the focusing functions, truncated medium, and one-sided illumination assumptions underlying the borrowed Marchenko formalism.","marker":"Wapenaar et al. (2014)"},{"why":"Provides the practice of evaluating the scheme for constant two-way traveltime values and storing results at that time to reconstruct the full primary response.","marker":"Zhang and Staring (2018)"},{"why":"Underpins the convergence of the Neumann-series solution of the projected-focusing equation.","marker":"Fokkema and van den Berg (1993)"}],"fun_headline_variants":["Plane-wave primaries from data alone, no model","Data-driven plane-wave gathers strip internal multiples","No-model plane-wave seismic: primaries only","Multiple-free plane-wave imaging without a model"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Plane-wave primaries from data alone, no model","Data-driven plane-wave gathers strip internal multiples","No-model plane-wave seismic: primaries only","Multiple-free plane-wave imaging without a model"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000632,"raw_usage":{"total_tokens":2955,"prompt_tokens":1021,"completion_tokens":1934,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":637,"completion_tokens_details":{"reasoning_tokens":1875}},"tokens_in":637,"tokens_out":1934,"duration_ms":13479,"temperature":1.0,"reasoning_tokens":1875,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T11:07:16.123259+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"and Wapenaar, K","cited_arxiv_id":null,"evidence_quote":"Introduced data-domain Marchenko / adaptive overburden elimination, the projected-focusing idea that Eqs. 9-14 build on."},{"cited_title":"A., Wapenaar, K., and Thorbecke, J","cited_arxiv_id":null,"evidence_quote":"Adapted Marchenko redatuming to plane-wave sources, the template for the plane-wave extension presented here."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the focusing functions, truncated medium, and one-sided illumination assumptions underlying the borrowed Marchenko formalism."},{"cited_title":"and Staring, M","cited_arxiv_id":null,"evidence_quote":"Provides the practice of evaluating the scheme for constant two-way traveltime values and storing results at that time to reconstruct the full primary response."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Underpins the convergence of the Neumann-series solution of the projected-focusing equation."}],"review_version":1}