{"id":"3e77ae13-cfea-44ae-afe0-7ae771bf7970","arxiv_id":"2502.05189","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"A self-supervised 3D CNN estimates primaries and a surface operator by minimizing the difference between the input wavefield and a wavefield reconstructed through the SRME equation, with no ground-truth labels.","lead":"This paper trains a neural network to remove free-surface multiples from seismic data without labeled examples, using the SRME physics equation as its only training loss. It is tested on one synthetic and one field dataset and compared visually to two standard SRME workflows.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The self-supervised loss admits the trivial solution P0 = P, A = 0 with zero reconstruction error, so the claimed primary estimation rests on unstated inductive bias; no constraint or uniqueness argument appears in the paper.","rationale":"The reader's weakest assumption identifies exactly the load-bearing issue: minimizing Eq. (3) does not uniquely or meaningfully determine the primary estimate because P0 = P, A = 0 is a zero-loss solution. I agree with the rejection as presented. The paper's self-supervised framing is attractive, but the method's success depends entirely on unstated inductive bias of the 3D CNN and its training procedure. The absence of any quantitative comparison with the benchmark SRME methods further weakens the empirical support, since visual displays cannot distinguish a genuinely de-multipled primary wavefield from a subtly transformed version of the input. My proposed test would settle whether the trivial branch is actually reached in practice, and if it is, the claim of physics-driven multiple elimination would need substantially stronger constraints and evaluation before acceptance.","tokens_in":4175,"tokens_out":3113,"duration_ms":32301,"concrete_test":"Run the synthetic salt-model experiment from an initialization chosen near the trivial branch: initialize the primary decoder to reproduce the input approximately and the surface-operator decoder near zero. After training, compute the normalized primary residual ||P0 - P|| / ||P|| and the energy of the estimated surface operator A. If this residual remains small (e.g., below 5%) and the eliminated-multiple energy is near zero, the trivial-solution branch is operative and the central claim fails. Conversely, if P0 converges to the known true primaries with a residual comparable to or better than Local LS-SRME while A is non-negligible, the concern is refuted.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that minimizing Eq. (3), the MSE between the input wavefield p and the reconstruction p_hat built through Eq. (2) as P = P0(I + AP), yields a meaningful estimate of the primary wavefield P0. This requires that the network not exploit the exact trivial solution P0 = P, A = 0, for which the reconstructed wavefield equals the input and the loss is exactly zero. In fact, for any A for which (I + AP) is invertible, one can set P0 = P(I + AP)^{-1} and obtain zero reconstruction loss, so the loss alone does not identify primaries. The paper provides no regularization, no constraint on the surface operator, no analysis of initialization or optimization trajectories, and no uniqueness argument. Because the loss is a soft reconstruction loss rather than a hard physical constraint, the network could converge to a near-trivial branch (e.g., A very small and P0 close to P) and still score well on Eq. (3). The manuscript's synthetic and field examples are only qualitative, so they do not establish that the method removes multiples rather than autoencoding the input. Without quantitative metrics and without a demonstration that the trained surface operator is non-negligible and the primary estimate differs from the input in the correct way, the central claim is unsupported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a physics-driven self-supervised deep-learning method for free-surface multiple elimination. A 3D CNN is trained to output both an estimated primary wavefield and a surface operator, using only a reconstruction loss based on the SRME forward equation P = P0(I + AP). The authors claim the method outperforms Global LS-SRME and Local LS-SRME on one synthetic and one field dataset, based on visual comparison. The central claim is that the network learns a physically meaningful primary estimate without any labeled data.","tokens_in":4500,"tokens_out":4462,"duration_ms":43850,"significance":"If the method is shown to be well-posed and validated quantitatively, the idea of embedding the SRME physics directly into a self-supervised loss is attractive and could reduce reliance on labeled or synthetic training data. The paper demonstrates a potentially useful application of physics-driven deep learning to seismic processing. However, the current manuscript does not establish that the learned factorization is physically meaningful: the loss function is degenerate, the evaluation is purely visual, and no quantitative evidence is provided. Thus the significance remains conditional on substantive revisions.","major_comments":[{"comment":"The loss in Eq. (3) admits trivial zero-error solutions. Setting the estimated surface operator a_hat = 0 and the estimated primary p0_hat = p yields p_hat = p and J = 0. More generally, for any A for which (I + AP) is invertible, choosing P0 = P(I + AP)^{-1} exactly reconstructs P. The manuscript provides no constraint, regularization, or analysis of initialization or training dynamics to exclude these non-physical branches. Since the central claim is that the network estimates primaries, the authors must either add a constraint that breaks this degeneracy or empirically demonstrate that the trained network avoids it, for example by reporting the estimated A and showing that the estimated primaries differ from the input in the expected way. As written, Eq. (3) enforces only consistency with Eq. (2), which is an identity for infinitely many (P0, A) pairs, so the loss alone does not identify a physically meaningful primary.","section":"The Proposed Physics-Driven Learning Method (Eq. (3))"},{"comment":"The claim that the proposed method outperforms Global LS-SRME and Local LS-SRME is based solely on visual comparison of one synthetic and one field example. No quantitative metrics are reported: for the synthetic data, where true primaries are known, one could compute SNR or residual multiple energy; for the field data, one could compare the predicted multiples with a reference prediction or measure energy in a multiple-only window. Quantitative evaluation is especially important given the trivial-solution issue above: a model that simply outputs the input as primaries would show no 'primary leakage' in a visual comparison while failing to remove multiples. The authors should provide numeric measures of estimation accuracy and, for the field data, a demonstration that the learned surface operator is non-trivial and that the eliminated multiples have plausible physical characteristics.","section":"Synthetic Data Examples and Field Data Example"},{"comment":"The manuscript does not report the estimated surface operator a_hat or its properties (e.g., its length, amplitude spectrum, or spatial variation). The surface operator is a key physical output of the network; without showing it, the reader cannot assess whether the learned A corresponds to a physically reasonable free-surface operator or is an arbitrary filter that happens to satisfy the reconstruction. Reporting the learned A, at least for the synthetic case where the true source wavelet and reflectivity are known, would substantially strengthen the claim that the network has learned physics rather than an autoencoding factorization.","section":"Proposed Method / Experiments"}],"minor_comments":[{"comment":"There is a typo: 'framewrok' should be 'framework'.","section":"SRME Theory"},{"comment":"The caption states 'estimated primaries from Global LS-SRME, Local LS-SRME, and the proposed method, respectively' but then refers to '(c) to (f)'; only (c), (d), and (e) are present. Please correct the caption.","section":"Synthetic Data Examples, Figure 2 caption"},{"comment":"The summation limits in Eq. (3) are typeset in a garbled way and should be written using standard notation, e.g., J = (1/(n_s n_r n_t)) sum_{i,j,k} |p(i,j,k) - p_hat(i,j,k)|^2.","section":"Eq. (3)"},{"comment":"Please provide the training hyperparameters (optimizer, learning rate, batch size, initialization scheme, number of layers, filter sizes, and data normalization) to enable reproducibility. The current description gives only the filter-count progression.","section":"Proposed Method"},{"comment":"It would be helpful to specify how the field data were preprocessed (e.g., deghosting, designature, regularization) and how the SRME benchmarks were configured (window lengths, filter lengths) so that the comparison is reproducible.","section":"Field Data Example"},{"comment":"There is a typo: 'gnerateing' should be 'generating'.","section":"Discussions"}],"recommendation":"major_revision","confidential_remarks":"The manuscript reads like an extended abstract rather than a full journal paper. The most serious issue is the degenerate loss function: without additional constraints or a demonstration that the optimization avoids trivial solutions, the method's output is not established to be physically meaningful. The authors should be asked to address this head-on. I recommend requiring quantitative comparisons, a display of the learned surface operator, and a discussion of the identifiability of the factorization. If the authors can provide evidence that their trained networks consistently avoid the trivial branch and that the results are quantitatively accurate, the paper could become a valuable contribution."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's the short version. The idea is genuinely new: instead of supervised DL for multiple elimination, they embed the SRME equation P = P0(I + AP) directly into the loss, and train a 3D CNN to output both the primaries P0 and the surface operator A. No labels, no synthetic-to-field domain shift. I have not seen that exact formulation before. The authors show it on a synthetic salt model and a 2D marine field dataset, with Global and Local LS-SRME as benchmarks. The visual results look plausible, and the paper is honestly written about its per-dataset nature and computational cost.\n\nBut the central argument has a hole. Equation (3) is only a reconstruction loss between the input and P0(I + AP). If the network sets A = 0 and P0 = P, the loss is exactly zero. More generally, for any A with invertible (I + AP), P0 = P(I + AP)^{-1} gives zero loss. So the loss alone cannot identify the primaries; it defines an infinite family of factorizations. The paper provides no constraint on A, no regularization, no uniqueness argument, no analysis of initialization or optimization trajectory. The success depends on the unstated inductive bias of the CNN. That may be real, but the paper does not demonstrate it. And all results are qualitative. There is no quantitative metric showing the output differs from the input in a physically correct way, or that the estimated A is non-negligible. Without that, \"outperforms SRME\" is not established.\n\nI am not calling the method a failure. The qualitative examples show more than pure autoencoding if you look at the figures, and the idea is worth pursuing. But the current manuscript lacks the analysis that would make the claim credible. As a submission it needs major revision: add a constraint or penalty that breaks the trivial solution (e.g., penalize ||A|| or enforce an energy criterion on multiples), report the norm of A and the difference between P0 and P, add quantitative comparisons like multiple residual energy or signal-to-noise, and ideally release code and data.\n\nMy recommendation: send it to peer review rather than desk reject. The novelty is sufficient, and the flaw is identifiable and fixable. A good referee can push the authors to close the gap. I would want to see the revision before citing it myself.","headline":"Novel self-supervised SRME formulation with a genuine trivial-solution flaw; the idea deserves a serious referee but the current evidence does not support the central claim.","tokens_in":4999,"tokens_out":2274,"would_cite":false,"duration_ms":21381,"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 neural network can learn to remove free-surface multiples from seismic data without labeled examples, using only a physics-based reconstruction loss.","keywords":["free-surface multiple elimination","primary estimation","self-supervised deep learning","physics-driven loss","SRME","seismic wavefield reconstruction","3D convolutional neural network"],"falsifier":"On synthetic data with known true primaries, train the network from several random initializations and compare each estimated primary wavefield with the true one; if any low-loss solution yields $\\hat{P}_0$ far from the true primaries or $\\hat{A} \\approx 0$, then the reconstruction loss alone does not identify the primaries.","tokens_in":3977,"feed_emoji":"🌊","tokens_out":5962,"duration_ms":53509,"temperature":0.7,"pith_summary":"This paper proposes a self-supervised deep-learning method for free-surface multiple elimination in seismic data. The core idea is to train a 3D convolutional network to output an estimated primary wavefield $\\hat{P}_0$ and a surface operator $\\hat{A}$ such that, when recombined through the physical SRME equation $\\hat{P} = \\hat{P}_0(I + \\hat{A}P)$, they reproduce the measured full wavefield $P$. The network is trained by minimizing the mean-square error between $P$ and $\\hat{P}$, so it never needs ground-truth primaries as labels. If the claim holds, free-surface multiple attenuation no longer requires labeled training data or carefully tuned adaptive subtraction; a single physics-based loss drives the separation, and the paper reports more complete primary estimation and less multiple energy leakage than global and local least-squares SRME benchmarks on synthetic and field data, at a higher computational cost.","feed_headline":"Neural network removes seismic multiples without labels","feed_subtitle":"Training a 3D CNN on the SRME physics equation yields primary estimates that rival adaptive subtraction on synthetic and field data.","key_machinery":"The load-bearing object is the factorized wavefield relation $P = P_0(I + AP)$ (Equation 2), restated from SRME, together with the reconstruction loss (Equation 3). Here $P$ is the measured full wavefield, $P_0$ is the primary-only wavefield, and $A$ is the surface operator $A = I R S^{-1}$, combining surface reflectivity $R$ and source wavelet $S$. The network maps $P$ to $(\\hat{P}_0, \\hat{a})$; plugging those into the relation reconstructs $\\hat{P}$, and the loss compares it to $P$. This turns multiple elimination into a self-supervised factorization problem: no labeled primaries are needed, because the physical equation acts as the training supervisor.","core_discovery":"The paper's central claim is that the free-surface multiple-free wavefield can be parameterized directly by a deep network trained only on the full wavefield, provided the loss function encodes the physics of surface-related multiple generation. In this framework, one encoder and two decoders estimate the primaries $\\hat{P}_0$ and a one-dimensional, spatially invariant surface operator $\\hat{a}$. These outputs are fed through Equation (2), $P = P_0(I + AP)$, to form a reconstructed full wavefield, and the MSE between reconstruction and input is the entire training signal. The authors argue that the governing equation alone supplies enough constraint for the network to learn a useful separation, and they demonstrate on synthetic and field examples that the resulting primaries show better multiple suppression and primary preservation than the two SRME-based benchmarks, while acknowledging a higher computational burden.","pith_inferences":["The minimization of Equation (3) admits a trivial exact solution $\\hat{P}_0 = P$ and $\\hat{A} = 0$; the paper does not analyze why training avoids it, so reproducibility across initializations and architectures is a critical untested condition.","A quantitative comparison on synthetic data, where true primaries are known, would sharpen the claim of outperforming SRME, which the paper supports mainly through visual inspection of seismic sections.","Because the reconstruction loss checks consistency rather than physical uniqueness, the network could converge to different factorizations that all fit the data; adding sparsity or a multiple-prediction term could stabilize the solution.","The same self-supervised structure could be adapted to 3D acquisition and to tasks like deghosting or deblending, but scaling and compute remain open."],"forward_implications":["Free-surface multiple elimination becomes a label-free inverse problem, and the same physics-loss recipe can be applied to other wavefield-separation tasks with known governing equations.","The SRME benchmarks require adaptive subtraction with parameter tuning, while the proposed network avoids that tuning step at the price of per-dataset retraining on a GPU.","If the factorization is reliable, the estimated surface operator $\\hat{a}$ may itself be a usable byproduct, encoding information about surface reflectivity and the source wavelet.","Extending from one dataset per training run to multi-dataset or cross-gather training is the stated next step; success there would make the method practical for large surveys."],"supporting_citations":[{"why":"Establishes the SRME relation $P = P_0 + P_0 A P$ that the paper's governing equation is built on.","marker":"Verschuur et al. (1992)"},{"why":"Provides the salt-model synthetic data and the marine field data used in both tests, along with the closed-loop SRME context.","marker":"Lopez Angarita (2016)"},{"why":"Introduces EPSI, an inversion-based primary estimation method whose forward model is the same wavefield factorization the network uses.","marker":"Van Groenestijn and Verschuur (2009)"},{"why":"Documents supervised-learning and domain-shift limitations that motivate the self-supervised, physics-driven strategy.","marker":"Hou and Messud (2021)"},{"why":"Presents a closed-loop SRME variant, showing how the same equation supports iterative primary estimation.","marker":"Wang et al. (2017)"}],"fun_headline_variants":["Deep learning removes seismic multiples with no labels","Physics-driven network eliminates multiples without ground truth","Neural net uses physics to suppress multiples, no labels","Self-supervised DL beats SRME in multiple elimination","Physics loss trains network to separate primaries, no labels"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"Everything rests on the assumption that minimizing the reconstruction error in Equation (3) leads the network to a physically meaningful factorization rather than the trivial one where the estimated primaries equal the input and the surface operator is zero; the paper does not constrain, regularize, or analyze this degeneracy.","fun_headline_variants_meta":{"raw":{"variants":["Deep learning removes seismic multiples with no labels","Physics-driven network eliminates multiples without ground truth","Neural net uses physics to suppress multiples, no labels","Self-supervised DL beats SRME in multiple elimination","Physics loss trains network to separate primaries, no labels"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000163,"raw_usage":{"total_tokens":1225,"prompt_tokens":909,"completion_tokens":316,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":525,"completion_tokens_details":{"reasoning_tokens":242}},"tokens_in":525,"tokens_out":316,"duration_ms":3427,"temperature":1.0,"reasoning_tokens":242,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T14:11:49.422250+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"On synthetic data with known true primaries, train the network from several random initializations and compare each estimated primary wavefield with the true one; if any low-loss solution yields $\\hat{P}_0$ far from the true primaries or $\\hat{A} \\approx 0$, then the reconstruction loss alone does not identify the primaries.","supporting_citations":[],"review_version":1}