{"id":"dc3d7c1a-d8d6-40eb-aa1d-bcb9acf02590","arxiv_id":"2411.17997","paper_version":2,"verdict":"UNVERDICTED","confidence":"HIGH","novelty_score":2.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"An invited review of the author's Bayesian multi-model source inversion and PINN-based Bayesian tomography methods for propagating velocity-structure uncertainty, with no new results.","lead":"A seismologist reviews his own published methods for treating uncertain seismic velocity models in earthquake source inversions, using Bayesian ensembles and physics-informed neural networks. The review explains how quantifying velocity-model uncertainty can reduce bias and underestimation in inferred fault slip and hypocenters, but presents no new results.","discovery_kind":"review","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Section 4's 2.5D velocity-model extension omits along-strike structural uncertainty, so the integrated example only weakly supports the claim that the full pipeline quantifies propagated uncertainty.","rationale":"The reader's weakest assumption correctly identifies the 2.5D extension as the most vulnerable point of the paper's integrated application. The central methodological framework (Bayesian multi-model inversion and PINN-based Bayesian tomography) is reviewed from previously published work, so a flaw in one illustrative application does not invalidate the review's characterization of those methods. However, the abstract and Section 4 assert that the integrated approach 'appropriately accounts for' velocity-structure uncertainty, and that assertion is specifically supported by the 2.5D example. If along-strike velocity variations are significant, the propagated uncertainty is incomplete, so the example's support is weakened. This is a real, load-bearing limitation of the demonstration, but it is already partially acknowledged by the author as preliminary and simple. The verdict remains UNVERDICTED because the manuscript is an invited review article rather than a new research preprint; the concern does not change that classification or require rejection. It does suggest that readers should not treat the Section 4 results as a definitive validation of the full pipeline without examining the cited Agata et al. (2025) paper and testing the 2.5D assumption.","tokens_in":20561,"tokens_out":4342,"duration_ms":40344,"concrete_test":"Use a published 3D P-wave velocity model (e.g., Japan Integrated Velocity Structure Model or Nakanishi et al. 2018) to compute the along-strike velocity variation over the domain spanning the DONET nodes and the KI03 line. If the along-strike variation exceeds the local standard deviation of the KI03 ensemble velocity models, the 2.5D prior is underdispersed. Alternatively, rerun the Bayesian multi-model hypocenter determination with a 3D ensemble generated by adding realistic along-strike perturbations (e.g., Gaussian random fields with a plausible correlation length) to the 2.5D extension, and check whether the posterior hypocentral depth uncertainty widens or the mean shifts by more than one posterior standard deviation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The integrated demonstration in Section 4 builds the 3D velocity structure by extending the 2D ensemble estimated along refraction line KI03 in the direction perpendicular to the trench to create a '2.5D structure.' This means the ensemble only samples uncertainty within the 2D plane of the line; any along-strike (trench-parallel) velocity heterogeneity is completely absent from the prior. The DONET stations and the hypocenter of the 2016 Mw 5.9 event are not exactly on KI03, so their travel times are computed with velocity models that may be systematically wrong in exactly the dimension that the ensemble does not represent. If the true velocity structure varies along strike between the line and the stations, the posterior over hypocenter location will be overconfident and potentially biased, undermining the paper's statement that considering subsurface structural uncertainties 'improved' the bias and underestimation. The paper honestly labels the example as simple and preliminary, and the methodological claims of Sections 2 and 3 rest on already-published work, but the integrated application is the only demonstration that the full chain (Bayesian tomography ensemble feeding Bayesian multi-model source inversion) quantitatively captures structural uncertainty. A failure of the 2.5D assumption would leave that claim untested.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This invited review article, written as an English preprint of a manuscript submitted to Zisin (Journal of the Seismological Society of Japan), synthesizes the author's program for quantifying uncertainty in seismic velocity structure and propagating it into earthquake source inversion. Section 2 presents Bayesian multi-model source inversion, where ensembles of structural models are marginalized via Monte Carlo integration, including an application to long-term slow slip events in the Bungo Channel. Section 3 introduces a Bayesian traveltime tomography method based on physics-informed neural networks (PINNs) with function-space particle-based variational inference, together with numerical experiments. Section 4 describes a preliminary integrated application to hypocenter determination of the 2016 Mw 5.9 earthquake off Mie Prefecture, in which a 2D velocity structure ensemble estimated along refraction line KI03 is extended along-strike to form a '2.5D' velocity model for travel-time calculations. Section 5 gives future prospects involving scientific machine learning. The paper is a review and does not present new results; its central message is that velocity-structure uncertainty is routinely ignored in source inversion, leading to biased and overconfident estimates, and that the author's Bayesian approaches can materially improve this situation.","tokens_in":20959,"tokens_out":5826,"duration_ms":50484,"significance":"If the claims are accepted, the paper offers a coherent, well-illustrated summary of an important methodological direction: moving from single velocity models to explicit ensembles in earthquake source inversion. A particular strength is the emphasis on the theoretical connection between Green's-function error covariance and Bayesian marginalization over structural parameters, presented in Section 2.1. The proposal to use function-space particle-based variational inference for PINN-based tomography (Section 3.2) is a plausible response to the known multimodality and prior-specification problems of weight-space B-PINNs, and the numerical experiments reported in Section 3.3 show the method can produce smooth, continuous velocity samples that are suitable for downstream use. The paper is honest in labeling the integrated example in Section 4 as preliminary, and it correctly points to the published work (Agata et al. 2021, 2022, 2023, 2025) for details. Its value to the readership of Zisin is likely to be high, given the award-context and the didactic style.","major_comments":[{"comment":"The integrated application constructs the 3D velocity structure by extending the 2D ensemble estimated along refraction line KI03 perpendicular to the trench ('2.5D structure'). This means the ensemble only samples structural uncertainty within the 2D plane of that line; trench-parallel (along-strike) heterogeneity is entirely absent from the prior. The nine DONET stations and the hypocenter of the 2016 Mw 5.9 earthquake are not located exactly on KI03, so their travel times are computed using velocity models that could be systematically biased in the very dimension that the ensemble does not represent. Consequently, the posterior uncertainty of the hypocenter may be overconfident, and the claim in Section 4 that accounting for structural uncertainty 'improved' the bias and underestimation is not quantitatively supported by the material in this manuscript. The author should add a clear caveat about the 2.5D limitation and, where possible, indicate how along-strike variability could influence the reported conclusions (e.g., by referencing any sensitivity analysis in Agata et al. 2025).","section":"Section 4 (paragraphs 2-3)"},{"comment":"The computation of the gradient ∇_v log p(v|d) is the technical core of the proposed PINN-based Bayesian traveltime tomography method, because the likelihood depends on the velocity structure only through the travel-time network f_T. The manuscript states that 'the discrete adjoint method' is used but omits the details, deferring to Agata et al. (2023). While a review may refer to the original paper, this omission leaves the reader unable to assess the method's practicality and scalability, which are central to the claimed advantages over HMC-based B-PINNs. The author should at least sketch the adjoint formulation, explain how f_T enters the gradient, and state the computational cost relative to the forward eikonal solve.","section":"Section 3.2"},{"comment":"The comparison between the proposed Bayesian multi-model slip estimate and the smoothing-constrained, single-structure estimate is summarized as 'It is evident that our estimation results better correspond to the distribution of deep tectonic tremors.' This is a visual, qualitative assessment without a quantitative measure, and it is based on a single event. To support the claim that the method reduces instability and improves physical interpretability, the review should specify a metric (e.g., spatial correlation between ΔCFS and tremor density) or explicitly label the comparison as qualitative and preliminary.","section":"Section 2.3"}],"minor_comments":[{"comment":"The sentence 'as described in Section,' near the end of the first paragraph of Section 5 is missing the section number; it should read 'Section 4'.","section":"Section 5"},{"comment":"The title of Section 4 ends with a colon ('... Earthquake Source Inversion:'), which is incomplete and should be removed.","section":"Section 4 (title)"},{"comment":"The caption contains the sentence 'Pink and magenta circles mark locations designated for further visualizations, which are not included in this article.' This is a leftover from the original figure and should be deleted or replaced with an appropriate description.","section":"Figure 1 caption"},{"comment":"The phrase 'quasi-analytical solution' should be clarified; either 'analytical solution' or 'semi-analytical solution' would be clearer, and the intended meaning should be stated explicitly.","section":"Section 3.3"},{"comment":"The reference list has minor formatting issues, such as the missing space between 'Phys. Rev. Lett.' and the next entry, and 'Hallo, M., and F. Gallovič, 2016' is concatenated with the following reference. These should be corrected for consistency.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"This is an invited review article for Zisin, and as such its scope is appropriate. However, the manuscript is almost entirely based on the author's own published work, and the review would be strengthened by a more balanced discussion of alternative methods and explicit limitations. The integrated example in Section 4 is the only place where the full Bayesian-tomography-to-source-inversion chain is demonstrated, and its 2.5D approximation raises a substantive concern that should be addressed before acceptance. I also recommend that the editor verify the completeness of the English preprint, including the missing section number and the figure-caption leftover, prior to final publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This is an invited review article, not a research preprint. It summarizes the author's own Bayesian multi-model source inversion and PINN-based Bayesian traveltime tomography, and it does that job about as well as a self-review can. The Section 2 derivations are clean, the connection between Duputel-style covariance weighting and full marginalization is made carefully, and Table 1, comparing HMC-based B-PINN with function-space ParVI, is genuinely useful. The paper is also honest about where things stand: Section 5 explicitly calls the integrated example “very simple” and lists 3D extensions as future work.\n\nWhat is not here: no new data, no new derivations, no code. Everything substantive is deferred to the cited papers (Agata et al. 2021, 2022, 2023, 2025). That is fine for a review, but the abstract overstates. It tells you the integrated application improved bias and uncertainty, yet the actual demonstration is not in this paper—you must go to the published paper, and the brief Section 4 description is unbacked. Notably, the abstract was added for the English preprint and is not part of the original Japanese manuscript, which may explain this mismatch.\n\nThe biggest soft spot is the 2.5D velocity model in Section 4. The ensemble is estimated along refraction line KI03 and extended perpendicular to the trench; along-strike (trench-parallel) heterogeneity is not sampled. The DONET stations and the 2016 hypocenter are not exactly on the line, so travel times for those stations are computed with velocity models that are systematically blind in the along-strike dimension. That means the propagated uncertainty understates the true structural uncertainty for this application. The paper labels the example preliminary, which mitigates the issue, but it still means the claim that the full pipeline captures structural uncertainty is only weakly supported by the integrated demo.\n\nThe citation pattern is heavy on the author's own work, but that is expected for a self-review and not a flaw. The math is standard and consistent, and the summaries match the cited literature. The free parameters you listed (particle counts, Dirichlet alpha, GP correlation length, ensemble size) are all in the original papers; the review does not hide them.\n\nWho is this for? A student or colleague who wants a quick map of how Bayesian multi-model source inversion and PINN-based tomography fit together. It is worth a careful read for that purpose. I would not cite it as the methods source; the original papers carry the evidence. If this were a submitted research paper, I would desk reject it for lack of new results, but as an invited review it has already passed journal review and is acceptable. My advice: read it if you are in the subduction-zone source inversion world, but do not rely on Section 4 for quantitative conclusions—go to Agata et al. 2025 and check the 2.5D limitation against the actual station geometry.","headline":"A clear self-review with genuinely useful framing, but no new evidence, and the integrated 2.5D example understates along-strike structural uncertainty.","tokens_in":21336,"tokens_out":3073,"would_cite":false,"duration_ms":28592,"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":"This review establishes that earthquake source inversions ignoring seismic velocity uncertainty are biased and overconfident, and that a Bayesian multi-model inversion fed by PINN-based tomography quantifies and propagates that…","keywords":["earthquake source inversion","uncertainty propagation","Bayesian estimation","Bayesian traveltime tomography","physics-informed neural network","scientific machine learning","ensemble modelling","hypocenter determination"],"falsifier":"A numerical experiment with a synthetic 3D velocity model containing strong along-trench heterogeneity: generate travel times, estimate the 2.5D ensemble exactly as in the paper, and check whether the resulting posterior hypocenter interval covers the true hypocenters in repeated realizations; if the coverage is below the nominal probability, the 2.5D propagation undercounts uncertainty. A field-based test would compare the ensemble posterior for the 2016 Mie event with an independent absolute depth constraint from a borehole or local dense array.","tokens_in":20363,"feed_emoji":"🌏","tokens_out":9556,"duration_ms":78311,"temperature":0.7,"pith_summary":"This review article makes the case that ignoring uncertainty in the seismic velocity structure, as standard source inversions do, systematically biases inferred fault slip and earthquake source parameters and makes their uncertainties too small. The author's remedy is a two-stage Bayesian pipeline: an ensemble of velocity structure models is generated by Bayesian traveltime tomography based on physics-informed neural networks, then a Bayesian multi-model source inversion marginalizes over that ensemble without requiring Gaussian noise or linearized Green's functions. The numerical experiments and applications to slow slip events in the Bungo Channel and the 2016 Mie-ken Nansei-oki earthquake support the claim that the pipeline removes the bias and produces uncertainties that are neither overconfident nor inflated. If correct, this would make source-inversion results more trustworthy for understanding fault behavior and for hazard assessment.","feed_headline":"Ignoring velocity-model error skews quake source estimates","feed_subtitle":"Bayesian multi-model inversion fed by PINN tomography puts that uncertainty into fault-slip and hypocenter error bars.","key_machinery":"Bayesian multi-model estimation: rather than solving the source inversion with one chosen velocity model, it forms the posterior $p(\\mathbf m|\\mathbf d)$ as a Monte Carlo average of likelihoods over an ensemble of structure models $\\{\\boldsymbol\\phi^{(n)}\\}$, i.e. $p(\\mathbf m|\\mathbf d)\\simeq \\kappa \\frac{1}{N}\\sum_n p(\\mathbf d|\\mathbf m,\\boldsymbol\\phi^{(n)})p(\\mathbf m)$, which requires neither Gaussian data errors nor linear Green's functions. The companion machinery is PINN-based Bayesian traveltime tomography in function-space particle-based variational inference: the velocity structure is represented by a neural network, the posterior is approximated by particles interacting through Stein variational gradient descent in the output (function) space, and the gradient of the likelihood with respect to velocity is computed with the discrete adjoint method. The eikonal equation is enforced through the factored ansatz $T=T_0/\\tau$ with $1/\\tau$ approximated by the network, which removes the source singularity.","core_discovery":"The central claim is that velocity-structure uncertainty can be quantified as an ensemble and then propagated into earthquake source inversion by Monte Carlo marginalization, and that this removes the biases and underestimation of uncertainty that occur when a single velocity model is assumed. The paper shows that the two previously separate approaches, treating Green's-function errors through a data covariance matrix and jointly estimating source and structure parameters, are mathematically equivalent under Gaussian and linear assumptions, and that the multi-model method generalizes both by sampling the marginalized posterior directly. On the tomography side, the paper introduces a PINN-based Bayesian traveltime tomography that performs Bayesian inference in the function space of the neural network, using particle-based variational inference, so the velocity structure is a continuous function and the posterior samples are suitable as input to the source inversion. In the integrated application, the posterior ensemble of 2D P-wave velocity structures from refraction line KI03 was extended in a 2.5D sense and used for Bayesian hypocenter determination of the 2016 Mw 5.9 event off Mie; the result was a deeper mean hypocenter with larger uncertainty than the single-model estimate, and consistency with the uncertain depth of reflectors from a seismic reflection survey.","pith_inferences":["If the paper is right, the same Monte Carlo marginalization recipe should transfer to other inverse problems with uncertain forward models, such as tsunami waveform inversion or volcano deformation modeling, whenever an ensemble of medium parameters can be produced.","A testable extension suggested by the paper is to use the posterior over velocity structures to derive a probability that the 2016 Mie event ruptured the plate interface, rather than deciding it by comparing a single hypocenter with a single depth-converted reflector.","The function-space ParVI trick may be the more general contribution: any PDE-constrained Bayesian inversion where the physically meaningful prior lives on the solution field, not the network weights, could use the same scheme.","Because the integrated case rests on the 2.5D assumption, a natural next experiment is to build a full 3D ensemble with along-trench heterogeneity and check whether the reported deepening and uncertainty interval survive."],"forward_implications":["Any source inversion that pre-selects a single velocity model should be re-examined with the ensemble approach, since the paper identifies this as a major source of bias and underestimated uncertainty.","The velocity-structure ensemble produced by PINN-based Bayesian tomography is smooth and continuous, so it can be fed directly into multi-model source inversion without the artificial discontinuities of trans-dimensional Voronoi tomography.","Including structure uncertainty makes strong smoothing priors on fault slip unnecessary, because part of the instability that smoothing was meant to suppress comes from unmodeled structure error.","The integrated hypocenter application demonstrates that posterior depth intervals, not single hypocenters, are the right output when structure is uncertain; the 2016 Mie event's hypocenter became deeper and more uncertain.","The same pipeline can be scaled to 3D velocity structures and to pre-built seismogenic-zone ensemble models, making the approach a practical replacement for single-model source inversions."],"supporting_citations":[{"why":"This work introduced treating Green's-function errors as an off-diagonal data-error covariance in source inversion, the ancestor of the covariance approach.","marker":"Yagi & Fukahata (2011)"},{"why":"This work derived the prediction-uncertainty covariance from the sensitivity of Green's functions to structure parameters; the review shows this is equivalent to marginalizing over structure under Gaussian and linear assumptions.","marker":"Duputel et al. (2014)"},{"why":"This work propagated an ensemble of velocity models from Bayesian tomography into seismic event location, the direct precedent for multi-model hypocenter determination.","marker":"Gesret et al. (2015)"},{"why":"This work established the Bayesian multi-model fault-slip framework and proved the mathematical equivalence of the covariance and joint-estimation approaches.","marker":"Agata et al. (2021)"},{"why":"This work applied the multi-model method to Bungo Channel long-term slow slip events, showing that structure uncertainty removes the need for strong smoothing priors.","marker":"Agata et al. (2022)"},{"why":"This work proposed PINN-based Bayesian traveltime tomography in velocity function space using Stein variational gradient descent and the discrete adjoint.","marker":"Agata et al. (2023)"},{"why":"This work supplied function-space particle optimization for Bayesian neural networks, the inference machinery behind the tomography.","marker":"Wang et al. (2019)"},{"why":"This work introduced physics-informed neural networks, the forward modeling engine for the eikonal tomography.","marker":"Raissi et al. (2019)"},{"why":"This work integrated the tomography ensemble with Bayesian multi-model hypocenter determination for the 2016 Mie event, the paper's key application.","marker":"Agata et al. (2025)"}],"fun_headline_variants":["Velocity uncertainty ignored? Quake source errors understated","Quantify velocity uncertainty to fix quake source error bars","Bayesian inversion folds velocity uncertainty into quake source estimates","Seismic velocity uncertainty propagates into quake source error bars"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the velocity ensemble honestly spans the plausible structures, which in the integrated application reduces to assuming the 2D profile from refraction line KI03 can be extended without along-trench variation to build the 2.5D model used for hypocenters.","fun_headline_variants_meta":{"raw":{"variants":["Velocity uncertainty ignored? Quake source errors understated","Quantify velocity uncertainty to fix quake source error bars","Bayesian inversion folds velocity uncertainty into quake source estimates","Seismic velocity uncertainty propagates into quake source error bars"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00157,"raw_usage":{"total_tokens":6274,"prompt_tokens":956,"completion_tokens":5318,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":572,"completion_tokens_details":{"reasoning_tokens":5251}},"tokens_in":572,"tokens_out":5318,"duration_ms":32070,"temperature":1.0,"reasoning_tokens":5251,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T11:36:57.602294+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A numerical experiment with a synthetic 3D velocity model containing strong along-trench heterogeneity: generate travel times, estimate the 2.5D ensemble exactly as in the paper, and check whether the resulting posterior hypocenter interval covers the true hypocenters in repeated realizations; if the coverage is below the nominal probability, the 2.5D propagation undercounts uncertainty. A field-based test would compare the ensemble posterior for the 2016 Mie event with an independent absolute depth constraint from a borehole or local dense array.","supporting_citations":[{"cited_title":"Isometric immersions with flat normal bundle between space forms","cited_arxiv_id":"2008.03929","evidence_quote":"This work supplied function-space particle optimization for Bayesian neural networks, the inference machinery behind the tomography."}],"review_version":1}