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REVIEW 3 major objections 6 minor 88 references

A high-resolution discourse on seismic tomography

T0 review · 3 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Seismic tomography's published models of Earth's mantle diverge more than their formal error analyses indicate, and the paper argues the field should embrace this divergence as a Community Monte Carlo ensemble rather than pursue a single…

desk verdict A readable, honest perspective on tomographic uncertainty; the Community Monte Carlo proposal is a good idea that needs a sharper definition of sample diversity. read the letter →

arxiv 2501.14301 v1 pith:GXOYYVMA submitted 2025-01-24 physics.geo-ph physics.app-ph

Andreas Fichtner , Jeroen Ritsema , Solvi Thrastarson This is my paper · ORCID
classification physics.geo-phphysics.app-ph
keywords seismictomographyuncertaintyquantificationfull-waveforminversionmantleCommunityMonteCarlosubjectivemodelingchoicesgeodynamicinference
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper, written for researchers who use tomographic images without building them, argues that the uncertainty attached to seismic tomography is larger than the formal error bars of any single model suggest. The reason is that many individually small, reasonable choices—how to regularize the inversion, how to parameterize and discretize the Earth, how to treat the crust, what misfit function to use, how to scale poorly constrained parameters—compound into large model differences. The authors demonstrate this with a quiz in which five modern global models, built with different data and methods including full-waveform inversion, disagree on basic mantle features such as subducting slabs and mantle plumes. They conclude that converging on a single 'best' model is the wrong goal, and instead propose a Community Monte Carlo approach in which many deliberately diverse models, all explaining the seismic data, are assembled and propagated into geodynamic inferences with meaningful uncertainties.

What carries the argument

The load-bearing concept is the 'little choices' catalog of Section 4.3: regularization, inclusion or exclusion of model parameters, discretization and parameterization, crustal corrections, misfit functions, and empirical scaling of unmodeled parameters such as density and anisotropy. These choices, each defensible on its own, act as compounding degrees of freedom that make the set of plausible models much wider than any single inversion's resolution analysis admits. The proposed remedy, Community Monte Carlo, treats independent research groups as Monte Carlo samples over this subjective-choice space: each group's model is one draw, and the ensemble of dissimilar, data-fitting models maps the true uncertainty. The paper stresses the condition that the sampling only works when the models are sufficiently diverse.

What would settle it

A controlled community experiment would settle the claim: have several independent groups invert the same waveform data with freely chosen regularization, parameterization, and crustal corrections, then compare the spread of their resulting models with each group's formal resolution-based uncertainty. If the cross-group spread is no larger than the internal error estimates, the paper's central premise that subjective choices dominate tomographic uncertainty would be falsified.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central assertion is that the spread among independently published tomographic models is itself the most honest estimate of tomographic uncertainty, and that this spread is substantially larger than the misfit reductions and resolution matrices of individual inversions indicate. The paper traces that excess uncertainty to the 'artistic component' of tomography: the unavoidable, reasonable, and partly subjective decisions made at every stage of model construction. Because these decisions differ across research groups, the models they produce agree on widely reproduced features such as the plate-tectonic fabric of the upper mantle and the two large low-shear-velocity provinces at the base of the mantle, but disagree on the presence, sharpness, and position of features like slabs and plumes. The paper therefore advocates that the community stop aiming for similar models and instead deliberately cultivate a diverse ensemble of data-fitting models—Community Monte Carlo—which can serve as input to geodynamic simulations that carry genuine seismic uncertainties.

Load-bearing premise

The argument depends on the ensemble of community models being genuinely independent: if groups share starting models, data selections, and parameterization conventions, the observed model spread will underestimate the true uncertainty, and Community Monte Carlo will not map it out.

Editorial extensions

If this is right

  • Users of tomographic models should treat the divergence among independently produced models as a first-order uncertainty estimate rather than picking a single 'best' image.
  • Funding agencies and community efforts should reward methodological diversity and the production of intentionally different models, because convergence would hide uncertainty rather than reduce it.
  • Geodynamic inversions that assimilate tomographic structure should be run repeatedly, once per ensemble member, so that uncertainty in the seismic images propagates into an ensemble of plausible mantle-flow histories.
  • Formal resolution tests and misfit statistics remain necessary but are not sufficient: they describe data coverage and data fit for a fixed set of choices, not the true range of defensible models.
  • As data volumes grow and computational costs fall, the practical barrier to regular Monte Carlo sampling shrinks, making the complementary combination of regular and Community Monte Carlo increasingly feasible.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: one could operationalize diversity by measuring the statistical independence of the ensemble, for example through pair-wise differences between models, and use that to compute an effective sample size for the Community Monte Carlo.
  • Editorial inference: the same logic transfers to other data-assimilation fields: any inverse problem with many defensible algorithmic choices should report ensemble spread across independently constructed pipelines, not just pipeline-internal covariance.
  • Editorial inference: a targeted experiment varying one subjective choice at a time—say, regularization norm or crustal treatment—while holding data and method fixed would quantify how much each 'little choice' contributes, testing the paper's claim that the effects compound.
  • Editorial inference: if the proposal is adopted, a natural deliverable would be a probability-style statement for a given structure—such as '95 percent of data-fitting models contain a slab here'—which is more actionable for non-specialists than a single image with resolution lengths.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper is a pedagogical review and perspective on global seismic tomography aimed at non-specialists. It introduces the main data types (surface waves, body waves), the mathematical framework of travel-time tomography (Eqs. 1–13), finite-frequency and full-waveform approaches, and then argues that a large number of reasonable but subjective modeling choices (damping, parameterization, crustal corrections, misfit functions, etc.) accumulate into model differences that are larger than formal uncertainty analyses suggest. The authors support this claim by presenting five recent tomographic models (S40RTS, SEMUCB-WM1, SPiRaL, GLAD-M35, REVEAL) and a quiz based on visual comparison of slices. They conclude that producing similar models should not be the goal; instead, they propose a 'Community Monte Carlo' effort in which diverse groups deliberately generate dissimilar but data-fitting models, and they discuss how such ensembles could propagate meaningful uncertainties into geodynamic modeling. The paper ends with a glossary that satirically deflates jargon such as 'high-resolution'.

Significance. If the central argument is accepted, it offers a concrete community-level response to a recognized problem: model differences in tomography are often treated as noise rather than as signal about uncertainty. The pedagogical parts (ray theory, damping, resolution matrix, FWI scaling) are accurate and well suited for the target audience. The paper also deserves credit for explicitly stating the limitation of its own proposal ('Community Monte Carlo can map out the true uncertainties only when the samples are sufficiently diverse') and for citing established ensemble practices in climate and ice-sheet modeling (CMIP, ISMIP6). However, the paper is a perspective rather than a quantitative study: the claim that uncertainties are 'significantly larger' than formal estimates is supported by visual inspection of five hand-picked models and by citation, not by a direct comparison to formal uncertainty bounds, and the proposal lacks an operational definition of the sample space of subjective choices. These gaps are load-bearing because they concern exactly what the paper asks the community to adopt.

major comments (3)
  1. [Section 6.3] The Community Monte Carlo proposal lacks an operational definition of 'sufficiently diverse.' The paper asserts that groups 'sample the actual range of plausible models' and that current model differences already map out uncertainties, but Table 1 shows that the five models share largely the same global-network data and overlapping parameterization families (spherical harmonics, splines, spectral-element meshes) and common reference models such as PREM. Without a defined sample space of subjective choices and a coverage criterion, the proposal is unfalsifiable, and the current five-model ensemble cannot be shown to be an unbiased sample. I suggest specifying the axes of subjective choice (the paper already lists several in Section 4.3), a minimal experimental design (e.g., independent groups inverting common data with deliberately varied but justifiable choices), and a diagnostic for coverage, for example comparing the ensemble spread to the formal posterior uncertainty reported for GLAD-M35 (Cui et al., 2024).
  2. [Sections 1 and 2] The central assertion that 'the uncertainties in seismic tomography are significantly larger than estimated by individual practitioners based on statistical analyses' (Section 1) is not quantitatively supported. The evidence presented is visual: five models are shown to differ in Figs. 1-2, and the paper states that this 'indicates that uncertainties are large.' Yet the models differ in data selection, method, and parameterization simultaneously, so the displayed spread cannot be attributed to subjective choices alone, and no comparison is made to the formal uncertainty bounds published for at least one of the models (GLAD-M35 is described in the reference list as including uncertainty quantification). A direct comparison between the inter-model spread and the formal posterior standard deviations would provide a concrete test of the 'significantly larger' claim; without it, the claim should be explicitly framed as a testable hypothesis rather than an established conclusion.
  3. [Section 6.2] The paper states that 'it is impossible to exactly quantify how much lower [the true quality] is' relative to misfit-based measures. This admission is honest but weakens the paper's own central claim. If the magnitude cannot be quantified, the paper should say what evidence would suffice to establish the direction and rough magnitude of the effect and whether the 'Community Monte Carlo' proposal is intended to produce that evidence. Currently, the paper alternates between asserting that uncertainties are 'significantly larger' and denying that the difference can be quantified, leaving the reader without a clear sense of what would confirm or refute the thesis.
minor comments (6)
  1. [Section 3 heading] The section heading appears as 'SEISMIC DA TA' with an inserted space; this is presumably a typesetting artifact and should be corrected to 'SEISMIC DATA'.
  2. [Section 1] The phrase 'comparison of different tomographic model' is missing the plural 's'; it should read 'tomographic models.'
  3. [Title and Section 7] The title uses 'High-resolution' while the Glossary explicitly advises against using the term 'unless a precise definition can be provided.' If this is intentional irony, a footnote or a sentence in the Introduction would make the intent clearer; if not, the title is in tension with the paper's own advice.
  4. [Figures 1 and 2] The captions do not state whether all slices are plotted with the same color scale and amplitude range. Differences in color scaling across the five models could visually amplify or diminish apparent differences; stating that the color scale is common (or not) is important for interpreting the quiz.
  5. [Section 4.2.2] The Fresnel-zone width formula w ≈ 0.5*sqrt(v*l/f) is presented without derivation or citation; since the paper is aimed at non-experts, adding a brief reference or a one-sentence explanation would be helpful.
  6. [References] The reference for SPiRaL (Simmons et al., 2021) lacks page numbers (the entry ends at 'Geophys. J. Int. 227'); several other entries also omit DOIs or final page ranges, which is untypical for a journal submission.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the paper's central uncertainty argument is an empirical/community-practice observation, not a derivation that reduces to its own inputs.

full rationale

This paper is a perspective and review, not a derivation with fitted parameters or quantitative predictions. The central claim that tomographic uncertainties are larger than individual statistical analyses suggest is supported by comparing five independently constructed models (Section 2, Figs. 1, 2 and 9) and by cataloguing the many subjective choices involved in tomography (Section 4.3). It does not depend on a self-referential theorem or on a fitted parameter being renamed as a prediction. The proposed Community Monte Carlo is explicitly conditional: 'Community Monte Carlo can map out the true uncertainties only when the samples are sufficiently diverse' (Section 6.3), and Section 6.2 concedes 'it is impossible to exactly quantify how much lower it is.' These statements acknowledge the main limitation rather than concealing it. Self-citations appear throughout, including REVEAL (Thrastarson et al., 2024) and nullspace shuttles (Fichtner and Zunino, 2019), but they serve as examples or supporting references; the argument does not require any specific author-only prior result to be correct. Even if REVEAL or the cited nullspace-shuttle work were removed, the model-diversity observation and the recommendation to produce more dissimilar models would stand on the other examples and on the general logic of subjective choices in ill-posed inverse problems. No uniqueness theorem is imported from the authors' own prior work, and no ansatz is smuggled in via self-citation. The paper is therefore self-contained as an argument about community practice, and the honest finding is no significant circularity.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

The paper introduces no free parameters or invented physical entities. Its argument rests on three domain assumptions about model plausibility, the origin of model differences, and the representativeness of the model ensemble; the third is explicitly conditional in the text.

assumptions (3)
  • domain assumption Tomographic models that fit the seismic data to within estimated errors are all equally acceptable representations of Earth structure.
    The paper's argument that model diversity should be embraced presumes that no single model is favored by the data alone, so differences reflect subjective choices. Stated in Sections 4.1.2, 4.3, and 6.2.
  • domain assumption The differences among published tomographic models are primarily due to subjective methodological choices rather than to data errors or noise.
    Stated in Section 6.3 ('model differences must exist because model uncertainties due to (i) data coverage and quality and (ii) the range of justifiable technical choices exist') and supported by cited work (Valentine and Trampert, 2016).
  • domain assumption The existing set of research groups and models provide a sufficiently independent sampling of the space of subjective choices to map true uncertainties.
    The Community Monte Carlo proposal depends on diversity being representative; the paper itself flags this as a condition in Section 6.3: 'Community Monte Carlo can map out the true uncertainties only when the samples are sufficiently diverse.'

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Pith. "Pith review of A high-resolution discourse on seismic tomography." pith.science (2026). https://pith.science/paper/GXOYYVMA

@misc{pith2026250114301,
  author       = {Pith},
  title        = {Pith review of: A high-resolution discourse on seismic tomography},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GXOYYVMA}},
  note         = {Machine review of arXiv:2501.14301}
}
read the original abstract

Advances in data acquisition and numerical wave simulation have improved tomographic imaging techniques and results, but non-experts may find it difficult to understand which model is best for their needs. This paper is intended for these users. We argue that our notion of best is influenced by the extent to which models satisfy our biases. We explain how the basic types of seismic waves see Earth structure, illustrate the essential strategy of seismic tomography, discuss advanced adaptations such as full-waveform inversion, and emphasize the artistic components of tomography. The compounding effect of a plethora of reasonable, yet subjective choices is a range of models that differ more than their individual uncertainty analyses may suggest. Perhaps counter-intuitively, we argue producing similar tomographic models should not be the goal of seismic tomography. Instead, we promote a Community Monte Carlo effort to assemble a range of dissimilar models based on different modeling approaches and subjective choices, but which explain the seismic data. This effort could serve as input for geodynamic inferences with meaningful seismic uncertainties.

Figures

Figures reproduced from arXiv: 2501.14301 by the authors.

Figure 1
Figure 1. Collection of ten unlabeled vertical slices, 60◦ wide and from the core-mantle boundary (CMB) to 50 km depth, through five recent global S velocity models (Ritsema et al., 2011; French and Romanowicz, 2014; Simmons et al., 2021; Cui et al., 2024; Thrastarson et al., 2024). Shown is the variation of S-wave velocity ∆vs relative to the absolute S-wave velocity vs in the spherically symmetric Earth model PREM (Dziewons… view at source ↗
Figure 2
Figure 2. Collection of ten unlabeled vertical slices, 60◦ wide and from the core-mantle boundary (CMB) to 50 km depth, through five recent global S velocity models (Ritsema et al., 2011; French and Romanowicz, 2014; Simmons et al., 2021; Cui et al., 2024; Thrastarson et al., 2024). Shown is the variation of S-wave velocity ∆vs relative to the absolute S-wave velocity vs in the spherically symmetric Earth model PREM (Dziewons… view at source ↗
Figure 3
Figure 3. (a) Vertical, radial, and transverse ground displacement records of the April 2, 2024 Taiwan earthquake at seismic station ANMO (Albuquerque, New Mexico) at a distance of 106◦. Several high-amplitude seismic signals are indicated in the hour-long record. (b) Ray paths of several shear waves, plotted for earthquakes at different locations, for better visibility. In the lower-right section of the globe are S (red), Sd… view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: (a) Vertical-component seismogram of the September 8, 2023 Morocco earthquake recorded at LSZ (Lusaka, Zambia) at an epicentral distance of 58◦. The upper trace shows the unfiltered waveform. The second, third, fourth, fifth, and sixth trace (from the top) are filtered…
Figure 5
Figure 5. Figure 5: Variation of the Rayleigh-wave phase velocity at periods of 40 s (a), 100 s (b), and 200 s (c). The normalized sensitivity of Rayleigh-wave velocity to shear-wave velocity in the upper 1000 km of the mantle is plotted on the top left. fundamental-mode surface wave in F…
Figure 6
Figure 6. Figure 6: (a) Transverse-component recordings of the diffracted S wave, Sdiff, generated by (top) the March 9, 1994 Fiji Islands earthquake recorded at HRV (Harvard, Massachussets, U.S.A.) and (bottom) the May 30, 2015 Bonin Islands earthquake recorded at BFO (Black Forest Obser…
Figure 7
Figure 7. Figure 7: Schematic illustration of tomography basics. a) Our domain of interest is discretized into 9 cells. The slowness anomaly ∆sj within each cell j is constant. A ray path (black line) connects a source and a receiver. The length of the ray segment within the j th cell is …
Figure 8
Figure 8. Figure 8: Illustration of finite-frequency effects using a numerical simulation of a wave (amplitudes in gray scale) with a dominant frequency of 2 Hz and a background velocity of 6 km/s. The source is indicated by a black star, and the receiver by a black triangle. a) Wavefront…
Figure 9
Figure 9. Figure 9: Horizontal slices through five recent global S velocity models, S40RTS (Ritsema et al., 2011), SEMUCB-WM1 (French and Romanowicz, 2014), SPiRaL (Simmons et al., 2021), GLAD-M35 (Cui et al., 2024) and REVEAL (Thrastarson et al., 2024). mantle. The mantle between 1000 km…

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.