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REVIEW 4 major objections 5 minor 18 references

Deep learning methods for modeling infrasound transmission loss in the middle atmosphere

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read An optimized 2D convolutional network predicts infrasound transmission loss over 4,000 km from combined temperature and wind fields with an average error of 8.6 dB at a fraction of the computational cost of parabolic-equation simulations.

desk verdict A useful 4,000-km extension of an existing CNN surrogate, but the headline 8.6 dB error is the best of eight runs, not the expected error, so the reporting needs a fix. read the letter →

arxiv 2506.06351 v1 pith:7633KAGK submitted 2025-06-02 eess.SP cs.AIcs.LG

Alexis Le Pichon , Alice Janela Cameijo , Samir Aknine , Youcef Sklab , Souhila Arib , Quentin Brissaud , Sven Peter Naesholm This is my paper
classification eess.SPcs.AIcs.LG PACS 43.28.+h
keywords infrasoundpropagationtransmissionlossconvolutionalneuralnetworkparabolicequationmiddleatmosphereeffectivesoundspeedratioInternationalMonitoringSystematmosphericreanalysis
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

The paper claims that a carefully tuned 2D convolutional neural network can stand in for expensive parabolic-equation simulations when predicting how much infrasound energy reaches the ground after traveling up to 4,000 km through the middle atmosphere. Given a range-dependent slice of temperature and wind fields together with a frequency between 0.1 and 3.2 Hz, the network outputs ground-level transmission loss with an average error of 8.6 dB against parabolic-equation simulations held out from training. This matters because the International Monitoring System infrasound network, built to verify compliance with the nuclear-test-ban treaty, needs fast estimates of which stations can detect which events, and full parabolic-equation runs are far too slow to explore the relevant parameter space. The work extends an earlier regional approach that covered 1,000 km to a four-times-longer range, and it feeds the network effective sound-speed ratio profiles so that the learned features correspond to the atmospheric waveguides that actually steer infrasound.

What carries the argument

The load-bearing object is the atmospheric slice: a two-dimensional field 120 km tall and 4,000 km long, built from vertical profiles sampled every 100 km and each reduced to the effective sound-speed ratio $$c_{\rm ratio}(z)=\frac{c_{\rm eff}(z)}{c_{0\rm km}},$$ which folds temperature and along-path wind into a single profile whose value of at least 1 marks a ducting layer that reflects infrasound back to the ground. Stacking 40 such profiles gives the network's $(1000\times 40)$ input matrix, deliberately not downsampled so that small-scale range dependence is preserved. The architecture is a 2D convolutional encoder — four tanh-activated stages with $3\times 3$ kernels growing from 32 to 256 channels, each followed by $2\times 2$ max-pooling — that compresses the slice into an $8\times 1\times 256$ latent map; the scalar frequency is concatenated to the flattened vector, and four fully connected layers (2048, 1024, 512, 400 units) with batch normalization, ReLU activations, and dropout at 40/30/20 percent regress 400 ground-level transmission-loss points spaced every 10 km. Training minimizes MSE with Adam at learning rate $10^{-4}$ decaying tenfold per epoch after the tenth, uses mini-batches of 32, and stops early on validation loss. The labels the network imitates come from the ePaPe parabolic-equation code at Padé order $M=7$, run on 36,454 slices assembled from reanalysis winds and temperatures below 80 km, climatological winds and temperatures above, and superimposed gravity-wave spectral perturbations.

What would settle it

Compare the network's transmission-loss maps against measured amplitudes at infrasound stations for a well-characterized source, such as the 15 January 2022 Hunga Tonga eruption that the paper itself maps. Driving the network with the same reanalysis fields and checking predicted attenuation against station recordings on paths of 2,000–4,000 km, especially on upwind paths where the network shows its largest errors, would reveal whether the 8.6 dB figure survives contact with the real atmosphere or only describes agreement with one parabolic-equation code.

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Extended reading notes

Core claim

The central claim is that a 7.4-million-parameter 2D convolutional network, fed with 120 km tall by 4,000 km long slices of the effective sound-speed ratio $c_{\rm ratio}(z)$ and a scalar frequency, reproduces ground-level transmission losses computed by the ePaPe parabolic-equation solver (Padé truncation order $M=7$, with standard atmospheric absorption) to an average error of 8.6 dB across the full 0.1–3.2 Hz band and across all wind conditions in a held-out test set of 3,645 atmospheric states. The figure rests on eight independent train/validation/test splits of 36,454 realistic atmospheric slices; the best run reached a normalized RMSE near 0.095 on both training and validation after 51 epochs. Errors grow with frequency — about 7.3 dB near 0.2 Hz, rising to about 11.6 dB at 2.5–3.2 Hz — and are larger for upwind cases, where the network's smoothing of fine spatial structure in the labels is most visible. As a demonstration, the network produces the 1.0 Hz attenuation map around the 15 January 2022 Hunga Tonga eruption, reproducing the geometry of the parabolic-equation map at negligible computational cost.

Load-bearing premise

The whole evaluation treats the outputs of one parabolic-equation simulation code, run with a specified Padé order and a standard atmospheric absorption model, as the true transmission loss over 4,000 km; if that code is inaccurate at long range or high frequency, or neglects real effects such as crosswinds and nonlinear propagation (which the paper acknowledges), the reported 8.6 dB error measures how faithfully the network copies the code, not how accurately it predicts real infrasound at the ground.

Editorial extensions

If this is right

  • Near-real-time attenuation maps around any known source become feasible: the Hunga Tonga demonstration produces the 1.0 Hz ground-level TL field over 2,000 km in milliseconds, where PE integration would take hours.
  • Because 4,000 km covers the roughly 1,700 km average spacing of IMS infrasound stations, a single trained network can draw complete detection-capability maps for the monitoring network.
  • Users should expect the most reliable predictions in downwind, low-frequency conditions: errors average about 7.3 dB near 0.2 Hz but about 11.6 dB at 2.5–3.2 Hz, and upwind cases skew toward the larger error classes.
  • Expressing inputs as effective sound-speed ratio profiles ties every prediction to the ducting structure of the atmosphere, the same quantity that determines whether rays are reflected back to the ground, improving interpretability over raw wind inputs.
  • The 8.6 dB headline figure comes from the best of eight cross-validation runs, each with its own train/validation/test split, so the reported average reflects a held-out test set rather than training data.

Reading between the lines

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

  • The decisive experiment this paper does not run is a test against measured infrasound: comparing the network's maps with real IMS recordings of well-characterized sources would separate 'faithful surrogate of one PE code' from 'accurate predictor of atmospheric infrasound,' and would likely reveal that the upwind, high-frequency residuals are not purely a CNN artifact.
  • Because errors concentrate in upwind and high-frequency cases, a deployable version of this tool would probably pair each prediction with a confidence flag or route those regimes back to a PE calculation; the paper proposes neither, though its own error histograms point to the need.
  • The claim that effective sound-speed ratio inputs improve interpretability is qualitative; a controlled ablation training the same architecture on raw wind profiles alone would quantify how much of the 8.6 dB comes from the input representation versus the deeper and wider network.
  • If the network's accuracy tracks whichever simulator generated its labels, the same architecture may serve as a universal fast surrogate for infrasound propagation: retraining it on normal-mode labels, which the authors list as a perspective, and comparing errors would show how much physics the network has actually internalized.
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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

4 major / 5 minor

Summary. The paper proposes an optimized 2D convolutional neural network (CNN) to predict ground-level infrasound transmission loss (TL) over 4000 km propagation ranges. Inputs are range-dependent atmospheric slices, represented as effective sound speed ratio c_ratio(z) profiles derived from ERA5/HWM-14/NRLMSIS-00 fields with added gravity-wave perturbations, concatenated with the frequency. Labels are TL curves computed with the NCPA ePaPe parabolic equation solver with Sutherland-Bass attenuation. The network is trained on 36,454 simulated slices and evaluated on a held-out test set. The authors report an average error of 8.6 dB in the 0.1–3.2 Hz band and demonstrate a near-real-time attenuation map for the 2022 Hunga Tonga eruption.

Significance. If the reported accuracy is robust, the method would be a practical tool for near-real-time infrasound detection-capability assessment, extending the prior regional-scale work of Brissaud et al. (2023) to global ranges. The paper's strengths include the use of realistic range-dependent atmospheric fields, frequency-conditioned inputs, and evaluation on data held out from training. However, the headline accuracy number is not supported as stated: it is taken from the best of eight cross-validation runs without reporting variability across runs, and it is internally inconsistent with the frequency-group error table. These issues must be addressed before the performance claim can be accepted.

major comments (4)
  1. [Section 4, Figure 3 and Table 1] The reported average error of 8.6 dB is the test-set error of the 'best network among the eight runs' of the cross-validation, not the average over runs. Selecting the run with the best validation performance and reporting its test error introduces a selection artifact: the reported number is an optimistic estimate of expected generalization. The paper gives no mean, standard deviation, or range of test errors across the eight folds, so the reader cannot determine whether 8.6 dB is typical. The authors should report the distribution of test errors across all folds and base the headline claim on the mean (or median) with uncertainty.
  2. [Section 4, Table 1] The claimed average error of 8.6 dB is inconsistent with the frequency-group errors reported in Table 1. Weighting the 'average mean-RMSE-4000-km' values by the corresponding number of cases gives approximately 9.5 dB, not 8.6 dB. If the 8.6 dB figure is an unweighted average of the 12 group means, that is not the per-sample average error and should be clearly stated and justified. This discrepancy directly affects the paper's central quantitative claim and must be resolved.
  3. [Sections 1 and 4] The paper claims to 'enhance' and 'optimize' the architecture of Brissaud et al. (2023), but no head-to-head comparison with that method is presented on the same data, same propagation range, or even on comparable held-out splits. The statement that the 8.6 dB error is 'comparable with the average 5 dB error obtained by Brissaud et al. 2023' is not evidence of improvement because the ranges and datasets differ. A direct comparison (e.g., retraining the prior network on the 4000 km dataset, or evaluating both on a common test set) is needed to support the claimed optimization.
  4. [Section 2.2 and Figure 6] The evaluation is entirely against PE-simulation labels, and the paper acknowledges that the PE model neglects nonlinear propagation and crosswinds. The Hunga Tonga map in Figure 6 is presented as an application, but no comparison with actual infrasound observations is made. While the paper frames its contribution as a surrogate for PE simulations, the title and abstract claim to model real infrasound transmission loss. The authors should either temper the real-world claims or provide at least a qualitative validation against a real event.
minor comments (5)
  1. [Global] There are recurring typos, including 'Similary' instead of 'Similarly' (Sections 2.1, 3), 'histogramms' instead of 'histograms' (Section 4), and inconsistent notation for c_ratio(z) versus cratio(z).
  2. [Section 2.1] The description of the input matrix dimension as '(1000×40)' is not explained: it is unclear whether the 1000 dimension corresponds to altitude levels or distance samples. Please clarify the coordinate axes of the input slices.
  3. [Section 3] The sentence on learning rate decay is ambiguous: 'decreasing by a factor of 10 at each iteration from the tenth' could be read as decaying every iteration after the tenth, which would be extremely fast. Please specify the exact decay schedule.
  4. [Section 4] The text says 'a training loss of 0.0953 and a validation loss of 0.0949 were reached at the 51st epoch,' but these are normalized MSE values, not RMSE. Please clarify which quantity is plotted in Figure 3 and which is reported here.
  5. [General] No code, data, or trained-model availability statement is provided. Given the reproducibility importance of the exact dataset split and preprocessing, the authors should consider releasing the code and the preprocessed dataset.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the CNN is trained on PE labels and tested on held-out PE labels; self-citations are architectural background, not load-bearing evidence.

full rationale

The derivation chain is explicit and non-circular: atmospheric slices from ERA5/HWM/NRLMSIS are used to compute effective sound-speed ratio profiles, PE simulations with the ePaPe code generate the transmission-loss labels, and the optimized 2D-CNN is trained with an MSE loss and then evaluated on a held-out testing set. Section 4 states that 'testing data correspond to samples never seen before, used to measure network's generalization capabilities', so the headline 8.6 dB error is not computed on training data. The paper is also transparent that the labels are PE simulations, not measurements: Section 2.2 notes that PEs 'neglect non-linear propagation and crosswinds effects', which is a physical-fidelity limitation rather than circularity. The self-citation to Brissaud et al. 2023 is used as an architectural and methodological baseline ('optimized version of the 2D-CNN originally developed by Brissaud et al. 2023'), not as a proof or uniqueness argument for the new result. The main non-circular statistical concern is that the reported error is from 'the best network among the eight runs' rather than an average over folds, which affects the interpretation of the 8.6 dB figure but does not make the derivation circular.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central result rests on one large fitted surrogate (7.4 million CNN parameters), several hand-chosen training hyperparameters, and a chain of atmospheric and propagation modeling assumptions. The main load-bearing external inputs are the PE solver, the reanalysis and climatology composite, and the synthetic gravity wave perturbation model. No new physical entities are introduced.

free parameters (4)
  • CNN trainable weights and biases = 7,425,682 parameters, values learned during training
    The surrogate's predictive function is entirely determined by these fitted parameters, making them the largest set of free parameters in the paper.
  • Training hyperparameters = learning rate 0.0001, decay by 10 from epoch 10, patience 25, batch size 32, dropout 40/30/20 percent
    These values are chosen by hand and affect the reported test error; no sensitivity analysis is provided.
  • Gravity wave perturbation model parameters = not specified
    Section 2.1 adds fine perturbations using the Gardner et al. 1993 spectral model, but the paper does not give amplitudes, cutoffs, seeds, or realization counts, even though these perturbations shape the input dataset and the reported errors.
  • Dataset sampling choices = 1 degree horizontal resolution, profiles every 100 km, latitudes -40 to 70, longitudes -150 to 165, years 2010 to 2020
    These choices define the domain of the claim; the model is only shown to work for this sampling and coverage.
assumptions (5)
  • domain assumption Parabolic equation simulations with effective sound speed approximation are an adequate model for transmission loss over 4,000 km in the middle atmosphere.
    Invoked in Section 2.2 and Equation 2; all labels and all evaluation numbers are PE outputs, so the central claim is conditional on this.
  • domain assumption The composite atmospheric representation from ERA5, HWM-14, NRLMSISE-00, plus synthetic gravity wave perturbations, is realistic enough to represent the propagation scenarios of interest.
    Section 2.1 constructs all inputs this way; if the composite misses relevant atmospheric variability, the network cannot learn true transmission loss behavior.
  • domain assumption The 36,454 slices can be split into independent training, validation, and test sets without spatial or temporal leakage.
    Section 4 describes an 70/20/10 split with eight cross-validation runs, but gives no details on preventing nearby or same-date slices from appearing in both training and test sets.
  • domain assumption The effective sound speed ratio field alone, computed from temperature and along-path wind, contains enough information to predict ground-level transmission loss.
    Equation 1 defines the input; the model never sees cross-path winds, full wind vectors, or other atmospheric fields, so this reduction is load-bearing.
  • domain assumption Sutherland-Bass absorption and the NCPA ePaPe solver with Padé coefficient M=7 produce accurate attenuation for 0.1 to 3.2 Hz over 4,000 km.
    Section 2.2 uses these models to generate labels; errors in either propagate directly into the reported 8.6 dB figure.

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Cite this review

Pith. "Pith review of Deep learning methods for modeling infrasound transmission loss in the middle atmosphere." pith.science (2026). https://pith.science/paper/7633KAGK

@misc{pith2026250606351,
  author       = {Pith},
  title        = {Pith review of: Deep learning methods for modeling infrasound transmission loss in the middle atmosphere},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7633KAGK}},
  note         = {Machine review of arXiv:2506.06351}
}
read the original abstract

Accurate modeling of infrasound transmission losses (TLs) is essential to assess the performance of the global International Monitoring System infrasound network. Among existing propagation modeling tools, parabolic equation (PE) method enables TLs to be finely modeled, but its computational cost does not allow exploration of a large parameter space for operational monitoring applications. To reduce computation times, Brissaud et al. 2023 explored the potential of convolutional neural networks trained on a large set of regionally simulated wavefields (< 1000 km from the source) to predict TLs with negligible computation times compared to PE simulations. However, this method struggles in unfavorable initial wind conditions, especially at high frequencies, and causal issues with winds at large distances from the source affecting ground TLs close to the source. In this study, we have developed an optimized convolutional network designed to minimize prediction errors while predicting TLs from globally simulated combined temperature and wind fields spanning over propagation ranges of 4000 km. Our approach enhances the previously proposed one by implementing key optimizations that improve the overall architecture performance. The implemented model predicts TLs with an average error of 8.6 dB in the whole frequency band (0.1-3.2 Hz) and explored realistic atmospheric scenarios.

Figures

Figures reproduced from arXiv: 2506.06351 by the authors.

Figure 1
Figure 1. Mean cratio(z) over 4000 km and 25 % and 75 % quantiles for two scenarios. the troposphere (Chunchuzov et al. 2019 [9]). These fine perturbations are added to the 36454 slices using a range-dependant spectral model (Gardner et al. 1993 [10]). Each realisation of this model is superimposed to the original atmospheric specifications and considerably increase the variability and the complexity of the initial conditions… view at source ↗
Figure 2
Figure 2. Optimized 2D-CNN’s architecture, containing 7425682 trainable parameters [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Training and validation metrics reached by the best network among the eight runs of the [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Examples of predicted and expected TLs (dB) on the best run’s testing set. [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: Global comparisons between 3645 predicted TLs (top-right) and their corresponding [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: PE simulations and predicted attenuations maps at 0 km altitude and 1.0 Hz - Hunga [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

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Reference graph

Works this paper leans on

18 extracted references · 17 canonical work pages

  1. [1]

    Brissaud, SV

    Q. Brissaud, SV . Näsholm, A. Turquet, and A. Le Pichon. Predicting infrasound transmission loss using deep learning.Geophysical Journal International, 232(1):274–286, 2023

    work page 2023

  2. [2]

    J. Marty. The ims infrasound network: current status and technological developments. Infrasound monitoring for atmospheric studies, pages 3–62, 2019

    work page 2019

  3. [3]

    Waxler, C

    R. Waxler, C. Hetzer, JD. Assink, and D. Velea. chetzer-ncpa/ncpaprop-release: Ncpaprop v2

    work page

  4. [4]

    0 (v2. 1. 0).Zenodo, 2021

    work page 2021

  5. [5]

    Le Pichon, L

    A. Le Pichon, L. Ceranna, and J. Vergoz. Incorporating numerical modeling into estimates of the detection capability of the ims infrasound network.Journal of Geophysical Research: Atmospheres, 117(D5), 2012. Proceedings of INTER-NOISE 2024

    work page 2012

  6. [6]

    Vorobeva, M

    E. Vorobeva, M. De Carlo, A. Le Pichon, PJ. Espy, and SP . Nasholm. Microbarom radiation and propagation model assessment using infrasound recordings: a vespagram-based approach. Annales Geophysicae Discussions, 2020:1–22, 2020

    work page 2020

  7. [7]

    Hersbach, B

    H. Hersbach, B. Bell, P . Berrisford, S. Hirahara, A. Horanyi, J. Munoz-Sabater, J. Nicolas, C. Peubey, R. Radu, D. Schepers, et al. The era5 global reanalysis.Quarterly Journal of the Royal Meteorological Society, 146(730):1999–2049, 2020

    work page 1999

  8. [8]

    Drob, JT

    DP . Drob, JT . Emmert, JW . Meriwether, JJ. Makela, E. Doornbos, M. Conde, G. Hernandez, J. Noto, KA. Zawdie, SE. McDonald, et al. An update to the horizontal wind model (hwm): The quiet time thermosphere.Earth and Space Science, 2(7):301–319, 2015

    work page 2015

Show all 18 references
  1. [9]

    Picone, AE

    JM. Picone, AE. Hedin, DP . Drob, and AC. Aikin. Nrlmsise-00 empirical model of the atmosphere: Statistical comparisons and scientific issues.Journal of Geophysical Research: Space Physics, 107(A12):SIA–15, 2002

    2002

  2. [10]

    Chunchuzov and S

    I. Chunchuzov and S. Kulichkov. Internal gravity wave perturbations and their impacts on infrasound propagation in the atmosphere.Infrasound monitoring for atmospheric studies: Challenges in middle atmosphere dynamics and Societal Benefits, pages 551–590, 2019

    2019

  3. [11]

    Gardner, CA

    CS. Gardner, CA. Hostetler, and SJ. Franke. Gravity wave models for the horizontal wave number spectra of atmospheric velocity and density fluctuations.Journal of Geophysical Research: Atmospheres, 98(D1):1035–1049, 1993

    1993

  4. [12]

    Sutherland and HE

    LC. Sutherland and HE. Bass. Atmospheric absorption in the atmosphere up to 160 km.The Journal of the Acoustical Society of America, 115(3):1012–1032, 2004

    2004

  5. [13]

    LeCun, Y

    Y. LeCun, Y. Bengio, and G. Hinton. Deep learning.nature, 521(7553):436–444, 2015

    2015

  6. [14]

    Glorot and Y

    X. Glorot and Y. Bengio. Understanding the difficulty of training deep feedforward neural networks.Proceedings of the thirteenth international conference on artificial intelligence and statistics, pages 249–256, 2010

    2010

  7. [15]

    Rahaman, A

    N. Rahaman, A. Baratin, D. Arpit, F . Draxler, M. Lin, F . Hamprecht, Y. Bengio, and A. Courville. On the spectral bias of neural networks.International conference on machine learning, pages 5301–5310, 2019

    2019

  8. [16]

    Brachet, D

    N. Brachet, D. Brown, R. Le Bras, Y. Cansi, P . Mialle, and J. Coyne. Monitoring the earth’ s atmosphere with the global ims infrasound network.Infrasound monitoring for atmospheric studies, pages 77–118, 2010

    2010

  9. [17]

    Matoza, D

    RS. Matoza, D. Fee, JD. Assink, AM. Iezzi, DN. Green, K. Kim, L. Toney, T . Lecocq, S. Krishnamoorthy, J-M. Lalande, et al. Atmospheric waves and global seismoacoustic observations of the january 2022 hunga eruption, tonga.Science, 377(6601):95–100, 2022

    2022

  10. [18]

    Z. Li, N. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. Stuart, and A. Anandkumar. Fourier neural operator for parametric partial differential equations.arXiv preprint arXiv:2010.08895, 2020

    2010 arXiv

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