{"id":"b253df2e-94c3-4a6d-99d2-57ad00f9641d","arxiv_id":"2501.04366","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"DispFormer, a transformer pre-trained on global synthetic Rayleigh-wave dispersion data, inverts variable-length dispersion curves into shear-wave velocity profiles and beats an interpolated reference model zero-shot and a global-search baseline after few-shot fine-tuning.","lead":"DispFormer is a transformer network that maps surface wave dispersion curves to subsurface shear-wave velocity profiles, and it is built to accept curves of different lengths, missing points, and noisy measurements. Pre-trained on a global synthetic dataset, it provides zero-shot starting models and, after light fine-tuning, outperforms a particle swarm search baseline on regional tests.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Few-shot support-set selection is underspecified and may leak target labels; the claimed superiority over PSO could hinge on this selection.","rationale":"The reader's weakest assumption was that the LITHO1.0 pretraining distribution covers regional target structures, a concern the authors themselves acknowledge in Section 5.4. That concern is real but mostly affects absolute zero-shot accuracy and generalization to exotic structures; it does not directly explain the few-shot comparison with PSO, which benefits from fine-tuning adaptation. The more load-bearing issue for the paper's strongest advertised result is the few-shot evaluation protocol itself. The 'hierarchical selection process' in Section 3.2 is not defined, and the few-shot numbers in Table 2 are single runs. If the support set is selected using test labels, the comparison is biased; if it is not, the lack of repeated runs still leaves the margin over PSO unquantified. This is exactly the kind of issue that a conditional verdict should require the authors to resolve. Because the reader already issued CONDITIONAL and explicitly flagged missing repeated-run statistics and the fragility of the PSO comparison, my concern does not change the verdict; it sharpens the condition by identifying a specific, testable source of possible bias.","tokens_in":17904,"tokens_out":7296,"duration_ms":77174,"concrete_test":"Using the released code, re-run the CWD few-shot experiment with 108 labels under three support-set protocols: (1) uniformly random selection, repeated over 10 seeds; (2) selection by k-means clustering of the input dispersion curves only, with target velocities never used; (3) the original hierarchical selection. Report the mean and standard deviation of test MAE for each protocol and compare against the PSO baseline of 42.77 m/s. If random or dispersion-only selection yields MAE at or above PSO, the headline few-shot advantage is selection-dependent rather than a property of the method.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's strongest quantitative claim is the few-shot result: with 108 CWD or 180 CCD labeled samples, DispFormer achieves lower MAE than PSO (Table 2: 33.84 vs 42.77 m/s for CWD; 28.69 vs 36.87 m/s for CCD). This claim depends entirely on how the few-shot support set is chosen. Section 3.2 states only that the subset is selected via a 'hierarchical selection process' without specifying whether selection uses the target velocity profiles, the input dispersion curves, or something else. If the support set is chosen using the true velocity models from the evaluation set (for example, as k-means centroids of the test labels), the few-shot model is given information about the test distribution that a practitioner would not have, inflating the apparent gain. Section 4.3 uses random selection for the real CSRM few-shot test, which is a different protocol, so the synthetic few-shot numbers are not internally consistent with the real-data protocol. Compounding this, each few-shot configuration is reported as a single run with no seed variation or confidence interval, so it is impossible to tell whether 33.84 m/s is a stable advantage or a favorable draw. The central 'surpasses traditional global search methods' claim therefore rests on an unverified and underspecified data-selection step. This concern is separate from the acknowledged LITHO1.0 distribution limitation: even if the pretraining prior is adequate, an unfair or lucky support set could manufacture the few-shot advantage. The paper's open-source code makes this testable, but the manuscript as written does not rule out the leakage path.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript introduces DispFormer, a transformer-based neural network for inverting Rayleigh-wave phase and group dispersion curves into 1-D shear-wave velocity profiles. The network encodes each period independently with position embeddings, allowing variable-length dispersion data without resampling or padding. A depth-aware training loss dynamically aligns the output depth range with the wavelength-based sensitivity of the input data. The model is pre-trained on a global synthetic dataset built from LITHO1.0 and evaluated in zero-shot and few-shot modes on two regional synthetic datasets (CWD, CCD) and on real dispersion curves from the CSRM model. The central claims are that zero-shot DispFormer produces better initial models than the interpolated LITHO1.0 reference (Table 1), that few-shot fine-tuning with tens to hundreds of labeled samples surpasses a PSO global-search baseline (Table 2), and that the model is robust to noise and missing data (Tables 4 and 5).","tokens_in":18202,"tokens_out":4165,"duration_ms":41760,"significance":"If the results hold, DispFormer would be a useful contribution to surface-wave inversion: it addresses a real practical limitation (variable-length, gappy dispersion curves), introduces a physically motivated depth-alignment heuristic, and demonstrates a pre-training/fine-tuning workflow for geophysical inversion. The manuscript also releases code and data, which supports reproducibility and comparison. The synthetic few-shot comparison against PSO is a meaningful benchmark, and the paper's honest discussion of LITHO1.0 coverage limitations (Section 5.4) is a strength. However, the load-bearing few-shot and real-data claims rest on an underspecified support-set selection procedure and on a validation protocol that is partly circular. These issues need to be resolved before the claims of superiority over conventional methods and of robust real-world generalization can be fully accepted.","major_comments":[{"comment":"The few-shot support-set selection is described only as a 'hierarchical selection process' with no algorithmic detail. The central claim that few-shot DispFormer 'surpasses traditional global search methods' depends on this selection. If the subset is chosen using the target velocity profiles (for example, by clustering the true models in the evaluation set), then the experiment leaks information about the test distribution and the comparison with PSO in Table 2 is not a fair assessment of a deployable method. Please specify the exact selection procedure, state explicitly what information it uses (input dispersion curves only, or also target models), and report results over multiple random selections or seeds with means and standard deviations. As written, each configuration is a single run, so the margin in Table 2 (e.g., 33.84 vs 42.77 m/s for CWD) cannot be distinguished from sampling luck.","section":"Section 3.2 and Table 2"},{"comment":"The real-data few-shot evaluation is partly circular: the fine-tuning labels are synthetic dispersion curves generated from the CSRM reference model via CPS, and the reported MAE is computed against that same reference model. Consequently, the improvement seen in Figure 9 after fine-tuning partly reflects fitting the network to the reference model's velocity profiles, not necessarily better inversion of the observed real dispersion data. The data-residual analysis in Figure 10 is a more independent criterion, but the main quantitative claim in the text is based on MAE to the reference model. Please add an explicit statement of this limitation and supplement the evaluation with metrics that do not use the reference model that generated the labels, such as residuals on a hold-out portion of observed dispersion curves or comparisons against an independent regional model.","section":"Section 3.3 and Figure 9"},{"comment":"The zero-shot baseline is the interpolated LITHO1.0 model, which is also the source distribution for pre-training. The abstract and conclusion state that zero-shot DispFormer 'outperforms the interpolated reference model used as the pretraining target'; this is supported by Table 1, but it is a relatively weak form of validation. It shows that the network extracts additional information from the regional dispersion curves beyond a spatially smoothed global model, but it does not establish absolute accuracy or generalizability to geological settings far from LITHO1.0. The paper partially acknowledges this in Section 5.4, but the abstract and conclusion would benefit from wording that does not imply stronger generalization than the experiment actually demonstrates.","section":"Section 4.1 and Table 1"}],"minor_comments":[{"comment":"The empirical scaling factors C1=1/3, C2=1/2, and C3=1.1 are presented without a sensitivity analysis. Since the depth-alignment strategy is a claimed contribution and Table 3 quantifies its benefit, a short sensitivity study (e.g., varying each constant by ±20%) would help establish robustness and guide users for other period ranges.","section":"Section 3.1, Eqs. (6) and (7)"},{"comment":"The PSO baseline is described only as having a search range of ±0.6 km/s around the true model and an iteration limit of 2000. Please report the swarm size, inertia and cognitive/social parameters, convergence criterion, and the number of independent PSO runs. This matters for reproducibility and for interpreting the runtime comparison (159 hours for the full CWD dataset).","section":"Section 4.2"},{"comment":"It is unclear whether noise and missing data were added only to the test curves or also to the few-shot fine-tuning data. This distinction affects the interpretation of robustness results. Please clarify the experimental protocol.","section":"Sections 5.2, Tables 4 and 5"},{"comment":"The uncertainty experiment perturbs observed data with Gaussian white noise at 10% standard deviation, but the text does not specify whether this is 10% of each period's value or 10% of the global data standard deviation. Also, the reported uncertainty in panel (c) should be defined precisely (standard deviation over the 1000 realizations for each depth layer).","section":"Section 5.3"},{"comment":"There are several minor typographical and language issues: 'Interped LITHO1.0' in Table 1, 'When partial labeled data available' in the abstract, and 'accesses' for 'assesses' in Section 4.1. A careful proofreading pass would improve readability.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is well within the scope of JGR: Machine Learning and Computation and has the benefit of released code and data. The main scientific concern is methodological: the few-shot support-set selection and the circular real-data validation must be clarified or re-analyzed before the claims of superiority over traditional methods can be accepted. I recommend major revision and would be willing to review a revised version. The paper's own limitation statement in Section 5.4 is honest, but the abstract and conclusion currently overstate the strength of the zero-shot and real-data evidence."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. First, DispFormer is real engineering: a transformer that encodes each period independently, handles arbitrary length, and ships with code, data, and a credible depth-aware loss. Second, the headline few-shot result (Table 2: 108 samples beat PSO) is plausible but not yet proven, because the paper never says how the fine-tuning subset was chosen, and every number is a single run with no error bar.\n\nWhat is genuinely new: this is the first transformer-based dispersion-curve inversion I know of that explicitly targets variable-length input, and the per-period encoding plus positional embedding is a clean solution to a practical pain point. The depth-aware loss is also a real contribution; Table 3 is a controlled comparison showing it helps. The robustness tests against noise and missing data are useful, and the open-source release makes the whole thing reproducible. The paper is honest about its limits, especially in Section 5.4, where it admits LITHO1.0 does not represent very complex shallow velocity contrasts.\n\nNow the soft spots, in proportion. The zero-shot claim is weak: beating the interpolated LITHO1.0 model is a low bar, and the authors themselves frame zero-shot as an initial-model generator, which is fair. The larger issue is the few-shot comparison. The stress-test note is right that Section 3.2's \"hierarchical selection process\" is underspecified. If selection uses the true velocity profiles (e.g., k-means on test labels), the 108-sample result is unfair. Even if it uses only dispersion curves, the lack of seed variation means 33.84 vs 42.77 m/s could be one lucky draw. The real-data fine-tuning also has an element of circularity: labels are synthesized from the CSRM reference model, and MAE is measured against that same model. That said, the code is public, so all of this is checkable, and none of it makes the architecture worthless.\n\nNet: this paper deserves a serious referee, not a desk reject, but the referee should demand (1) a precise description of the support-set selection, (2) repeated runs with seeds and confidence intervals, and (3) a real-data evaluation that separates label generation from the test target. If those hold up, DispFormer is a useful tool for practitioners who need initial models or fast inversion with gappy data. I would not cite it yet for the few-shot superiority claim, but I would keep it on the table for the architecture.","headline":"A genuinely useful transformer for variable-length dispersion inversion, but the few-shot claim of beating PSO is under-supported until the support-set selection and run-to-run variability are pinned down.","tokens_in":18749,"tokens_out":2082,"would_cite":false,"duration_ms":22523,"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":"DispFormer claims a transformer can invert surface-wave dispersion curves with zero labels and beat its interpolated reference model.","keywords":["shear-wave velocity inversion","surface wave dispersion","transformer","pretraining","zero-shot learning","few-shot learning","depth sensitivity","Rayleigh waves"],"falsifier":"Run the identical zero-shot and few-shot protocol on a regional dataset whose velocity profiles contain sharp shallow contrasts or strong vertical heterogeneity, such as a sedimentary basin or a dense-array near-surface site, and compare MAE against the interpolated LITHO1.0 baseline; if zero-shot error rises to or above baseline, the generalization claim fails for that structure class. Alternatively, rerun the few-shot comparison against a multi-CPU parallelized particle swarm optimization with the same search range and iteration budget, and check whether the accuracy advantage survives.","tokens_in":17683,"feed_emoji":"🌊","tokens_out":4548,"duration_ms":40517,"temperature":0.7,"pith_summary":"This paper introduces DispFormer, a transformer network that maps Rayleigh-wave phase and group dispersion curves directly to one-dimensional shear-wave velocity ($v_s$) profiles. Its central claim is that a model pretrained on global synthetic data can, with no regional labels, produce inversion profiles with lower mean absolute error than the interpolated LITHO1.0 model conventionally used as an initial guess; on the tested regions the reported zero-shot error is roughly 73 m/s versus 234 m/s. With a small number of labeled samples for fine-tuning, the same model outperforms a particle swarm optimization baseline, for example 33.84 m/s versus 42.77 m/s on the Central and Western US dataset with 108 samples. The paper argues that processing each period independently removes the fixed-length input constraint that limits earlier deep-learning inversions, and that a dynamic depth-alignment term supplies the physical constraint that makes transfer work. A sympathetic reader would care because the method promises a deployable initial-model generator and a data-efficient alternative to expensive global search in surface-wave tomography.","feed_headline":"Zero-shot transformer inverts seismic curves without labels","feed_subtitle":"Pretrained on synthetic data, it beats interpolated models and, fine-tuned, beats global search.","key_machinery":"The central object is a transformer that encodes each period of the dispersion curve independently: linear layers encode period, phase velocity, and group velocity; position embeddings retain period ordering; transformer blocks model inter-period correlations; and a dense head outputs $v_s$ at fixed depth nodes. Because each period is a separate token, input length is arbitrary, so the network accepts curves of different period ranges without cropping, padding, or network modification. The physical constraint is a dynamic depth-alignment strategy that computes the sensitive depth range from the dispersion wavelengths as $z_{\\min} = \\min(C_1 \\lambda_p, C_2 \\lambda_g)$ and $z_{\\max} = C_3 \\max(\\lambda_p, \\lambda_g)$, with $C_1=1/3$, $C_2=1/2$, and $C_3=1.1$, and aligns the prediction depth span to that range. The paper reports that this alignment lowers zero-shot MAE from 98.53 to 72.78 m/s on CWD and from 91.20 to 73.27 m/s on CCD, showing that the depth-sensitivity constraint is what carries much of the transfer gain.","core_discovery":"The load-bearing discovery is that a transformer pretrained on synthetic dispersion curves derived from the global LITHO1.0 model transfers to regional crustal and upper-mantle targets without any labeled fine-tuning: on the Central and Western US dataset the zero-shot mean absolute error is 72.78 m/s and on the Continental China dataset it is 73.27 m/s, compared with 234.53 m/s and 233.61 m/s for the interpolated LITHO1.0 reference model. When a small fraction of labeled regional data is available, fine-tuning with fewer than two percent of samples yields errors of 33.84 m/s (108 samples, CWD) and 28.69 m/s (180 samples, CCD), both lower than the particle swarm optimization baseline of 42.77 m/s and 36.87 m/s. On real-world dispersion curves from the China Seismological Reference Model, the zero-shot model reconstructs large-scale features such as the Tibetan Plateau low-velocity zone, and fine-tuning further reduces data residuals. The paper presents DispFormer as a foundation-model-style tool: a single pretrained network that handles varying period ranges, missing values, and noisy observations without architectural change.","pith_inferences":["Editorial inference: if the zero-shot gains hold beyond crustal-mantle targets, DispFormer points toward a general 'initial-model prior' for other nonlinear geophysical inversions, such as magnetotelluric or gravity inversion, though the paper only hints at this extension and does not demonstrate it.","Editorial inference: a stronger test of the generalization claim would be a blind evaluation on a regional dataset deliberately outside the LITHO1.0 structural family, such as a sedimentary basin or shallow urban site with sharp velocity contrasts; Section 5.4 itself flags such shallow complex structures as a current limitation.","Editorial inference: the reported computational advantage over global search should be read as order-of-magnitude rather than exact, because the PSO baseline is a single implementation without multi-CPU parallelization, and a parallelized or hybrid search would narrow the gap.","Editorial inference: the per-period token design suggests a natural extension to joint inversion of multiple observables, such as phase velocity, group velocity, ellipticity, or receiver functions, by adding extra token types; the current model demonstrates only phase and group data."],"forward_implications":["Zero-shot DispFormer can seed linearized inversion with initial models better than interpolated LITHO1.0, potentially reducing both local-minima risk and the number of iterations in traditional workflows.","Few-shot fine-tuning with tens of labeled samples produces accuracy competitive with or better than a particle swarm optimization baseline while cutting inference time from hundreds of hours to about one second for an entire regional dataset.","Because the network accepts arbitrary period ranges and missing values, a single pretrained model can serve datasets with different period windows, including 10-60 s, 5-80 s, and 8-70 s, without architectural modification.","Fine-tuned DispFormer keeps MAE under roughly 50 m/s even with 10 percent Gaussian noise and up to 50 percent missing data, supporting deployment on typical noisy, incomplete field observations.","The dynamic depth-alignment constraint improves zero-shot transfer, making the pretraining-plus-alignment recipe a candidate template for other underdetermined geophysical inverse problems."],"supporting_citations":[{"why":"Supplies the LITHO1.0 global velocity model from which the 40,962 pretraining profiles are extracted.","marker":"Pasyanos et al. (2014)"},{"why":"Provides the empirical $v_p$-$v_s$ and density relationships used to build complete layered models for forward dispersion calculation.","marker":"Brocher (2005)"},{"why":"Computer Programs in Seismology generates the theoretical Rayleigh-wave phase and group dispersion curves used as pretraining and fine-tuning data.","marker":"Herrmann (2013)"},{"why":"Supplies the Central and Western US regional velocity profiles used for zero-shot and few-shot evaluation.","marker":"Shen, Ritzwoller, and Schulte-Pelkum (2013)"},{"why":"Supplies the Continental China regional velocity profiles used for zero-shot and few-shot evaluation.","marker":"Shen et al. (2016)"},{"why":"Provides the CSRM reference model and the real observed dispersion curves used for real-world generalization testing.","marker":"Xiao et al. (2024)"},{"why":"Provides the particle swarm optimization implementation used as the global-search baseline in the few-shot comparisons.","marker":"Luu (2023)"},{"why":"Validates the thin-layer parametrization with 0.5 km layers, which DispFormer adopts for its fixed-depth output grid.","marker":"Hu et al. (2020)"}],"fun_headline_variants":["Zero-shot transformer beats seismic baselines without labels","Pretrained transformer inverts seismic curves with zero labels","DispFormer: zero-shot seismic inversion from synthetic data","Physics-aware transformer outperforms seismic baselines"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The paper's transfer claims rest on the assumption that the synthetic LITHO1.0 pretraining distribution, together with the Brocher empirical scaling and CPS forward modeling, adequately represents the velocity structures and period-depth sensitivity of the regional targets; the paper itself states in Section 5.4 that some shallow or complex geological structures are not adequately represented in LITHO1.0.","fun_headline_variants_meta":{"raw":{"variants":["Zero-shot transformer beats seismic baselines without labels","Pretrained transformer inverts seismic curves with zero labels","DispFormer: zero-shot seismic inversion from synthetic data","Physics-aware transformer outperforms seismic baselines"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000309,"raw_usage":{"total_tokens":1822,"prompt_tokens":1061,"completion_tokens":761,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":677,"completion_tokens_details":{"reasoning_tokens":700}},"tokens_in":677,"tokens_out":761,"duration_ms":6782,"temperature":1.0,"reasoning_tokens":700,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T21:34:52.999309+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the identical zero-shot and few-shot protocol on a regional dataset whose velocity profiles contain sharp shallow contrasts or strong vertical heterogeneity, such as a sedimentary basin or a dense-array near-surface site, and compare MAE against the interpolated LITHO1.0 baseline; if zero-shot error rises to or above baseline, the generalization claim fails for that structure class. Alternatively, rerun the few-shot comparison against a multi-CPU parallelized particle swarm optimization with the same search range and iteration budget, and check whether the accuracy advantage survives.","supporting_citations":[{"cited_title":"APACrefauthors \\ 2023","cited_arxiv_id":null,"evidence_quote":"Provides the particle swarm optimization implementation used as the global-search baseline in the few-shot comparisons."}],"review_version":1}