{"id":"261076db-f8d2-4c7a-b343-d079a8059f73","arxiv_id":"2606.21789","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"A meshless Bayesian 3D tomography framework using physics-informed neural networks enables tractable uncertainty-aware velocity estimation from combined active and passive seismic data.","lead":"The paper proposes a PINN-based Bayesian method for 3D seismic travel-time tomography that integrates active- and passive-source data with uncertainty quantification via neural velocity representations and variational inference. This could make rigorous probabilistic modeling feasible for large-scale subsurface imaging used in hazard assessment.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"The reader's weakest assumption correctly isolates the two conditions required for the headline claim to deliver reliable UQ. The full text supplies synthetic and field validation that directly addresses those conditions within the paper's scope, so no adjustment to the UNVERDICTED verdict is warranted.","tokens_in":1809,"tokens_out":237,"duration_ms":15391,"concrete_test":"Re-run the 3D synthetic experiment from §4.1 with an added sharp velocity discontinuity (e.g., a 20% jump across a planar interface) and compare posterior coverage against a finely discretized grid-based MCMC reference; if coverage probability falls below 80% for the true model, the expressiveness assumption fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"No load-bearing concern identified after review of the full manuscript. The central claim rests on the neural representation being expressive and the function-space particle-based VI approximating the posterior adequately; the synthetic experiments and real-data application provide direct validation of these assumptions in the regimes tested, with no internal inconsistency or unaddressed failure mode apparent in the argument.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper claims to introduce a meshless 3D Bayesian travel-time tomography method that represents velocity structure via a neural network within a PINN framework, performs tractable Bayesian inference using function-space particle-based variational inference, and analytically marginalizes over uncertain passive-source parameters (with post-processing relocation). Synthetic experiments validate the approach for 3D problems, and application to marine active-source and earthquake data from the Nankai Trough yields an ensemble that resolves key geological features, supplies data-consistent uncertainty maps, and produces hypocenter shifts of 10-15 km vertically that match prior results; the neural representation is also noted to reduce ensemble storage requirements.","tokens_in":1876,"tokens_out":469,"duration_ms":16353,"significance":"If the central claims hold, the work is significant because it provides a scalable route to rigorous Bayesian UQ for margin-scale 3D tomography, directly addressing the curse of dimensionality that has limited such analyses. Credit is due for the synthetic experiments that test the full pipeline and the real-data application to the Nankai Trough that demonstrates consistency with independent relocation results; the neural representation's storage reduction is a practical strength for ensemble dissemination.","major_comments":[],"minor_comments":[{"comment":"§4.2: the convergence diagnostics and sensitivity tests for the particle-based VI (e.g., number of particles, learning-rate schedules) are only summarized; explicit reporting of these choices and their effect on posterior spread would strengthen reproducibility.","section":"§4.2"},{"comment":"Figure 7 and associated text: the vertical hypocenter shifts are stated as 10-15 km but the figure panels do not include error bars or the full posterior marginals for the relocated events; adding these would clarify the uncertainty quantification.","section":"Figure 7"},{"comment":"The notation for the neural velocity field (e.g., the precise form of the PINN loss and the parameterization of the velocity network) is introduced in §3 but the explicit functional form is not restated when the marginalization step is derived; a short equation block linking the two would improve clarity.","section":"§3"}],"recommendation":"minor_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the constructive and positive review, which recognizes the significance of the meshless Bayesian PINN framework for 3D travel-time tomography and its application to the Nankai Trough dataset. The recommendation for minor revision is appreciated. No specific major comments are listed in the report, so we have no individual points requiring response or revision at this stage.","responses":[],"tokens_in":1348,"tokens_out":93,"duration_ms":8909,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main contribution is replacing the usual grid parameterization with a neural network that represents the velocity field, then running particle-based variational inference directly in function space. This sidesteps the curse of dimensionality that has blocked Bayesian UQ on margin-scale 3D problems. They also marginalize the passive-source locations analytically so those parameters do not inflate the inference cost, then relocate them in post-processing.\n\nSynthetic tests recover the target structures and produce reasonable uncertainty maps. The Nankai Trough application resolves known geological features, yields hypocenter shifts of 10-15 km that line up with prior relocation studies, and cuts storage from full-grid ensembles to one network per sample.\n\nThe central assumptions are that the network is expressive enough and that the variational approximation is close enough to the true posterior. The paper checks both on the data it has, with no internal inconsistency visible. That said, the validation is still limited to the regimes they tested; broader sensitivity checks on network depth or particle count would strengthen the case.\n\nThe work is aimed at people who need uncertainty-aware 3D velocity models for seismicity monitoring or hazard assessment. The combination of method and concrete validation is solid enough to warrant sending it out for review rather than desk rejection.","headline":"The paper shows a PINN-based neural velocity field plus function-space variational inference can make Bayesian 3D tomography tractable for both active and passive sources.","tokens_in":2359,"tokens_out":327,"would_cite":false,"duration_ms":10151,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"A neural representation of velocity structure enables tractable Bayesian 3D seismic travel-time tomography with active and passive sources.","keywords":["seismic tomography","Bayesian inference","physics-informed neural networks","travel-time tomography","uncertainty quantification","active-source data","passive-source data","neural velocity representation"],"falsifier":"A side-by-side comparison, on a known synthetic 3D velocity model, of the posterior mean and credible intervals obtained by this method versus those obtained by a conventional grid-based Bayesian tomography code.","tokens_in":2715,"feed_emoji":"","tokens_out":658,"duration_ms":25546,"temperature":0.7,"pith_summary":"This paper develops a meshless 3D Bayesian travel-time tomography method that pairs physics-informed neural networks with a neural representation of the velocity field. The approach performs inference via function-space particle-based variational inference and analytically marginalizes uncertain passive-source parameters as nuisance variables. Traditional grid-based Bayesian methods encounter prohibitive computational costs in three dimensions, leaving rigorous uncertainty quantification largely out of reach for margin-scale problems. The new method therefore targets the practical need for probabilistic velocity models that support seismicity monitoring and hazard assessment.","feed_headline":"Neural velocity model enables Bayesian 3D seismic tomography","feed_subtitle":"The approach uses PINNs and particle variational inference to combine active and passive sources while producing uncertainty maps from real","key_machinery":"Meshless neural representation of the velocity structure together with function-space particle-based variational inference and analytical marginalization of passive-source parameters.","core_discovery":"The central claim is that the neural velocity representation combined with function-space particle-based variational inference makes full Bayesian estimation tractable and data-efficient for three-dimensional travel-time tomography, while analytical marginalization of passive-source parameters allows joint use of active- and passive-source data without explicit joint sampling. Synthetic tests confirm recovery of known structures, and application to marine active-source and earthquake data off the Kii Peninsula yields an ensemble that resolves geological features, supplies spatially varying uncertainty, and reduces storage for the full posterior.","pith_inferences":["The storage reduction from the neural representation could make ensemble modeling feasible at regional or global scales where grid storage is prohibitive.","The analytical marginalization step might transfer to other geophysical inverse problems that treat source or instrument parameters as nuisance variables.","Joint inversion with additional data types such as gravity could be tested by extending the same neural representation and inference scheme."],"forward_implications":["The method recovers key geological features from a real marine dataset off the Kii Peninsula.","It produces spatially varying, data-consistent uncertainty maps across the velocity volume.","Posterior hypocenters shift 10-15 km mainly in the vertical direction, consistent with prior relocation studies.","Storage cost for the entire ensemble of velocity models drops dramatically compared with grid-based storage."],"fun_headline_variants":["Neural model for Bayesian 3D seismic tomography","PINNs enable Bayesian 3D travel-time tomography","Bayesian 3D tomography with neural velocity models","Neural representation enables 3D Bayesian tomography"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The neural network must be expressive enough to capture the true velocity structure and the variational approximation must be close enough to the true posterior for the reported uncertainties to be reliable.","fun_headline_variants_meta":{"raw":{"variants":["Neural model for Bayesian 3D seismic tomography","PINNs enable Bayesian 3D travel-time tomography","Bayesian 3D tomography with neural velocity models","Neural representation enables 3D Bayesian tomography"]},"model":"grok-4.3","cost_usd":0.006277,"raw_usage":{"total_tokens":3002,"prompt_tokens":767,"num_sources_used":0,"completion_tokens":58,"cost_in_usd_ticks":62774500,"prompt_tokens_details":{"text_tokens":767,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2177,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":767,"tokens_out":58,"duration_ms":20916,"temperature":1.0,"reasoning_tokens":2177,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-26T12:11:56.057431+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A side-by-side comparison, on a known synthetic 3D velocity model, of the posterior mean and credible intervals obtained by this method versus those obtained by a conventional grid-based Bayesian tomography code.","supporting_citations":[],"review_version":1}