Basin-Scale Geometric Focusing: A Probabilistic-Geometric Framework for Global Tsunami Hazard Assessment and the 2025 Kamchatka Peninsula Tsunami

Abdolali, Ali; Lam, Michael-Angelo Y.; Kadri, Usama; Malej, Matt; Filimonov, Maxim; Shi, Fengyan

doi:10.5194/egusphere-2025-6048

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https://doi.org/10.5194/egusphere-2025-6048

Preprints

03 Feb 2026

| 03 Feb 2026

Basin-Scale Geometric Focusing: A Probabilistic-Geometric Framework for Global Tsunami Hazard Assessment and the 2025 Kamchatka Peninsula Tsunami

Ali Abdolali, Michael-Angelo Y. Lam, Usama Kadri, Matt Malej, Maxim Filimonov, and Fengyan Shi

Abstract. We present a hybrid probabilistic-geometric framework that integrates probabilistic earthquake statistics with large-scale ray-tracing simulations to efficiently map global coastal tsunami exposure. Utilizing a catalog of historical tsunamigenic events and the Gutenberg-Richter relation, we derive probabilistic weights for over 9,000 rays released across potential fault zones. The simulated ray pathways reveal persisting bathymetry-driven energy convergence patterns that govern far-field coastal focusing and shadowing. The geometric framework's predictive power is demonstrated using the 2025 M8.8 Kamchatka Peninsula event. Validation against the 2025 M8.8 Kamchatka earthquake utilizes phase-corrected FUNWAVE-TVD simulations and in-situ DART observations. The resulting ray-based coastal focusing patterns display a substantial qualitative and quantitative spatial agreement (Spearman's ρ = 0.66) with the transoceanic maximum wave amplitudes from the high-fidelity FUNWAVE-TVD model. This agreement confirms the hybrid probabilistic-geometric approach as a scalable and computationally efficient tool for rapidly identifying coastal hotspots of transoceanic tsunami impact.

Received: 04 Dec 2025 – Discussion started: 03 Feb 2026

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Ali Abdolali, Michael-Angelo Y. Lam, Usama Kadri, Matt Malej, Maxim Filimonov, and Fengyan Shi

Status: final response (author comments only)

RC1:
'Comment on egusphere-2025-6048', Anonymous Referee #1, 29 May 2026
Review of the manuscript: “Basin-Scale Geometric Focusing: A Probabilistic-Geometric Framework for Global Tsunami Hazard Assessment and the 2025 Kamchatka Peninsula Tsunami”
Recommended decision: Major revisions
1. Summary of the manuscript
The manuscript proposes a hybrid probabilistic–geometric framework to identify coastal areas exposed to transoceanic tsunamis at global scale, combining Gutenberg–Richter-type seismic weighting with ray-tracing simulations. The central idea is to use ray density and coastal ray-termination points as a rapid proxy for bathymetry-induced focusing or shadowing. The approach is validated using the 2025 Kamchatka event through phase-corrected FUNWAVE-TVD simulations and comparison with DART and tide-gauge records. The work shows a reasonable spatial correlation between the geometric proxy and the maximum amplitudes obtained from the hydrodynamic model. The article is interesting and potentially useful as a rapid screening tool, although it still requires a more rigorous delimitation of its scope, of the probabilistic component, and of what can properly be referred to as “hazard assessment”.
2. Structure of the manuscript by sections
The introduction presents the problem of transoceanic tsunami propagation and the role of bathymetry in energy focusing and defocusing. It also justifies the use of ray tracing as an alternative to full numerical models and positions the contribution of the study.

Section 2: Probabilistic Tsunami Hazard Assessment. This section builds the probabilistic component from a historical catalogue, a global Gutenberg–Richter law, and a spatial KDE over a curve representing fault zones. The resulting output is an annual rate, λ, used as a weight for the rays.

Section 3: Ray Tracing Methodology. This section formulates the ray equations, describes the mesh and numerical implementation, and presents several global experiments designed to separate the effects of fault geometry, bathymetry, and probabilistic weighting.

Section 4: M8.8 Kamchatka Peninsula event. This section introduces two source scenarios (NOAA and USGS), describes the FUNWAVE simulation, applies a phase correction, and compares results with observations to evaluate the predictive capability of the geometric approach.

Section 5: Conclusions. The conclusions summarize the findings and present the method as an efficient tool for prioritizing exposed areas. The closing section is generally clear, although in some places it overextends the actual scope of the method.

3. General comments
The article addresses a relevant problem with an attractive methodological combination: using ray tracing to capture the geometric organization of tsunami energy and adding seismic weighting to prioritize more likely sources. The validation with a real event and with a higher-fidelity hydrodynamic model adds credibility, and the comparison with real observations clearly improves the manuscript.

As currently presented, the method appears closer to an “exposure screening” tool, or a preliminary prioritization tool for transoceanic corridors, than to a complete Probabilistic Tsunami Hazard Assessment framework. Uncertainties are not propagated, aleatory and epistemic variability are not explicitly treated, and the final coastal indicator is a normalized geometric proxy rather than a directly interpretable physical intensity measure. I recommend either lowering the expectations in the title and abstract and moderating the conclusions (what would be enough), or substantially strengthening the probabilistic component.

The probabilistic formulation requires stronger justification. The use of a single global b-value, a completeness threshold selected by visual inspection, and a KDE over a curve constructed from epicentres substantially simplifies the problem. This simplification may be acceptable for an exploratory study, but it should be better justified, preferably through sensitivity analyses that help clarify the limitations of the approach.

The validation is promising but still limited for supporting global claims. The use of a single case study (the 2025 Kamchatka event) and one main spatial metric (Spearman’s ρ = 0.66) is a useful first step, but it is not sufficient to demonstrate general robustness. The manuscript would benefit from a more quantitative discussion of sensitivity to the selected wave period, the 500 m termination criterion, the effective source length and width, and the stability of the results with respect to ray-tracing parameters.

The manuscript would benefit from a more rigorous and consistent use of the terms hazard, exposure, and risk. In several places, the ray-based output is presented as “hazard”, whereas the actual model output is a normalized geometric proxy of coastal ray convergence. Unless exceedance probabilities of physical intensity measures are computed at coastal locations, the terminology should be adjusted toward “relative exposure”, “focusing potential”, or “screening-level hazard indicator”.

The writing is generally understandable, but in some places it is repetitive. The introduction repeats the computational-efficiency argument for ray tracing several times. The paragraphs around the discussion of numerical models, Satake (1988), and Tehranirad et al. (2015) could be shortened and merged into a more concise rationale.

The discussion of Figure 3 is informative but somewhat over-narrative. It could be shortened and made more quantitative, for example by reporting changes in normalized coastal focusing for selected regions rather than relying mainly on descriptive expressions.

4. Main comment
My main concern is that the manuscript currently makes claims that are broader than what is demonstrated by the analysis. In its present form, the work reasonably validates a geometric proxy for transoceanic coastal exposure, but not a complete global probabilistic hazard framework. This distinction is important because it affects the title, the abstract, and the interpretation of the results. The authors should either substantially reinforce the probabilistic treatment and uncertainty quantification, or reformulate the scope of the manuscript as a global screening/prioritization tool for transoceanic tsunami exposure.
5. Specific comments
Lines 1–3 (title): There is a missing space in “AProbabilistic-Geometric”. In addition, the title is somewhat too ambitious. I suggest replacing “Global Tsunami Hazard Assessment” with “Global Tsunami Exposure Screening” or an equivalent formulation, unless the probabilistic component is substantially strengthened.
Lines 5–10 (abstract): The abstract works well overall, but it mixes “hazard”, “exposure”, and “coastal focusing patterns” as if they were equivalent. The authors should clarify from the outset what variable the ray model predicts and what it does not predict.
Lines 22–33: The exclusion of non-seismic tsunamis and nearshore processes is well motivated, for which decisions is the method suitable? And not?.
Lines 35–55: This part repeats the justification for ray tracing several times. It could be shortened considerably without losing content. The central argument is already clear from the references to Satake (1988) and Tehranirad et al. (2015).
Lines 61–75: The introduction of the probabilistic component is well placed, but a sentence is needed to clarify that λ is not a direct probability of coastal amplitude exceedance.
Lines 94–106: In Figure 1 and its caption, magnitude is described as being on the “Richter scale”. For large events, this should be revised and the appropriate magnitude scale should be used, most likely Mw. In addition, “AMagnitude of Completeness” requires typographical correction.
Lines 109–126: The construction of the curve Γ and the KDE is a delicate parts of the manuscript. how Γ is generated?,
Lines 184–191: The normalized ray termination count is used as a proxy for amplitude. This is a crucial assumption and deserves a more nuanced discussion. Is it a proxy for maximum amplitude, incident energy, or relative probability of impact?
Lines 230–240: The summary of the Kamchatka event includes information on impacts and damage that should be supported by specific references if retained.
Lines 284–303: The phase correction appears useful, but the current presentation mixes several elements (compressibility, elasticity, shortest path, and DART observations) in a dense block. I suggest separating more clearly the method, the data, and the result of the correction.
Lines 333–340: Spearman’s ρ = 0.66. How many coastal points are used? What is the statistical significance? Does it change if selected regions are excluded or if the coastal proximity criterion is modified?
6. Typos and local style improvements
Review spacing and typographical errors throughout the manuscript, including “large-scale ray-tracing”, “farfield”, “AMagnitude”, and “wether”.
Standardize the use of “far-field” and “near-field” throughout the text.
7. Final assessment
I recommend Major revisions. The manuscript presents an interesting and potentially useful probabilistic–geometric framework for the rapid identification of transoceanic tsunami focusing corridors. The combination of recurrence-based source weighting, ray tracing, FUNWAVE simulations, and observational comparison is valuable. However, the current framing is broader than what the analysis demonstrates. In particular, the manuscript should more clearly distinguish between probabilistic tsunami hazard assessment, exposure screening, and relative geometric focusing. The probabilistic component remains simplified, the uncertainty and sensitivity analysis is limited, and the validation relies mainly on one event and one principal spatial correlation metric. These issues affect the interpretation of the results and the claims made in the title, abstract, and conclusions. I consider major revision appropriate. The manuscript has clear potential if the scope is reframed and the methodological assumptions are better justified.
Citation: https://doi.org/10.5194/egusphere-2025-6048-RC1
RC2:
'Comment on egusphere-2025-6048', Anonymous Referee #2, 11 Jun 2026
REVIEW OF egusphere-2025-6048
Title: Basin-Scale Geometric Focusing: A Probabilistic-Geometric Framework for Global Tsunami Hazard Assessment and the 2025 Kamchatka Peninsula Tsunami Authors: A. Abdolali, M.-A. Y.-H. Lam, U. Kadri, M. Malej, M. Filimonov, F. Shi
Recommendation: Major revisions
GENERAL COMMENTS
This manuscript presents a hybrid probabilistic-geometric framework that couples a simplified Probabilistic Tsunami Hazard Assessment (PTHA) with global wave ray tracing to map far-field coastal tsunami exposure and validates the approach against the 2025 M8.8 Kamchatka event using FUNWAVE-TVD simulations, DART records, and tide-gauge observations.
The paper is clearly written, timely, and addresses a genuine operational need: a computationally cheap screening tool to prioritise where expensive high-fidelity inundation modelling should be applied. The experimental design that isolates fault geometry, bathymetric refraction, and recurrence weighting (Fig. 3) is clean and pedagogically effective, and the multi-source validation (numerical model + two independent observational networks) is in my opinion a good practice. I also found valuable the explicit phase-lag correction for ocean compressibility, sea-floor elasticity and background density, which is applied transparently as a purely kinematic time-shift.
That said, I have several concerns that, in my view, require major revision before the paper could be considered for publication. They can be divided into three groups: (i) the physical completeness of the ray-based amplitude proxy and the treatment of caustics; (ii) a mismatch between the probabilistic claims and what the method actually delivers; and (iii) the strength of the validation and its supporting statistics relative to the "global" and "rigorous" framing; plus some additional methodological and presentation issues (comments 6-8).
None of these is fatal, and I think all are addressable within the scope of the study.
The amplitude proxy is physically incomplete (ray-tube spreading / energy flux). The hazard proxy is the normalised count of ray terminations along the coast. A count is not an amplitude: two coastal segments receiving the same number of rays can experience very different wave heights depending on the geometric convergence of the ray tube. Classical geometrical optics provides a natural amplitude estimate via conservation of energy flux within the ray tube (the spreading Jacobian), optionally combined with Green's law toward shallower water. By using a count rather than a ray-tube-based energy-flux estimate, the manuscript leaves the most quantitatively valuable part of the method untapped and weakens the link between the proxy and the FUNWAVE maximum-amplitude envelope it is compared against. I would recommend either (a) implementing an energy-flux / ray-tube amplitude estimate, or (b) explicitly justifying the count proxy and discussing the conditions under which count density and amplitude diverge.

Caustics in the deep ocean are not addressed. Rays are terminated at 500 m depth to avoid nearshore caustics, but caustics (ray crossings) also form in the open ocean - precisely at the focusing zones that are the object of the study, where geometrical optics formally diverges (unbounded amplitude). The manuscript should state how deep-water caustics are detected and handled (e.g. amplitude capping or a Maslov/Gaussian-beam correction) and discuss the implications for the reliability of the identified hotspots. I may be missing something here, but I could not find any mention to this issue in the manuscript.

The "probabilistic" component reduces to a recurrence rate and yields no hazard curves. The authors themselves show (L137-143) that with a single global b-value and a uniform magnitude range, the energy-weighted field reduces to a constant multiple of the recurrence rate (Lambda = C*lambda). There is no logic tree, no epistemic uncertainty, no zone-dependent maximum magnitude, and no slip distribution; the final product is a normalised 0-1 ray-count field rather than amplitudes at given return periods. The claim of "a probabilistic interpretation of exposure consistent with modern hazard assessment standards" therefore overstates the method relative to the state of the art (e.g. Davies et al., 2018, which is cited). I recommend either producing actual hazard quantities (amplitude vs. return period) or reframing the contribution honestly as a recurrence-weighted exposure screening and moderating the PTHA language accordingly.

Single-event validation does not support a "global / rigorously validated" claim. The validation rests on one source region (Kuril-Kamchatka). A global framework should be tested across basins and source geometries. I strongly recommend adding at least one validation case in a different setting (e.g. Tohoku 2011, Maule 2010, or Sumatra-Andaman 2004) before claiming global applicability, and softening "rigorously validated" if only one case is retained.

Statistical rigour of Spearman rho = 0.66. rho = 0.66 is a moderate monotonic association (~44% of rank variance). No confidence interval or significance test is reported, and co-located coastal pairs are strongly spatially autocorrelated, which inflates the effective sample size and apparent significance. I would ask the authors to report a confidence interval, to use a resampling scheme that accounts for spatial autocorrelation (e.g. block bootstrap or an effective-N correction), and to show the sensitivity to the coastal sampling/binning choices.

Dispersion and the handling of multiple wave periods. Each ray is assigned a period between 15 min and 3 h, but the manuscript does not explain how the different periods are aggregated into the final field, nor how the non-dispersive assumption is reconciled with the use of a dispersive Boussinesq model (FUNWAVE) as the reference. Over transoceanic distances frequency dispersion is not negligible. Please clarify the period-aggregation procedure and discuss the dispersion assumption quantitatively.

Code and data availability. For a methods paper whose central contribution is the ray-tracing framework, "available from the corresponding author upon request" does not meet FAIR requirements. Only the pre-existing FUNWAVE-TVD code is released. Depositing the ray-tracing code and the derived datasets in a citable repository with a DOI (e.g. Zenodo) is necessary to meet FAIR standards.

Writing economy. While reading the introduction I had the feeling of being told three times why ray tracing is cheaper than full numerical modelling; the point is made at L35-39, again around L40-44 (Satake) and once more at L44-55 (Tehranirad et al.). Once is enough, and the introduction would gain pace if these passages were merged. Something similar happens with Section 3.3: the description of Figure 3 reads like a guided tour ("a striking artifact", "a very different picture emerges", "dismantled almost entirely"). Since all panels share the same normalised 0-1 coastal scale, the authors have the numbers at hand: stating, for two or three regions (NE Australia, the Pacific Northwest, Chile), by how much the coastal metric actually changes between panels b and d would replace adjectives with evidence and make the case far more convincing.

SPECIFIC COMMENTS (by line)
L3, L73, L184: "over 9,000", "more than 9,000", and "In total, 9,000 rays were released" are inconsistent. Please use a single exact figure throughout the paper.
L50-54 and 157-160: The argument that seismic tsunamis are "ideal for the geometric optics approach" because they are non-dispersive is reasonable, but it sits in tension with using a dispersive Boussinesq model as ground truth. Please reconcile.
L137-143 (magnitude-energy paragraph): The demonstration that Lambda = C*lambda is honest and welcome, but it undercuts the "probabilistic" framing; this should be reflected in the abstract and conclusions (see General comment 3).
L103-108: b = 1.05 from 212 events with Mc = 7.4 determined "by visual inspection". Please justify Mc more quantitatively (e.g. maximum-curvature or goodness-of-fit method) and report the uncertainty on b.
L117-125: KDE with sigma = 500 km is justified by rupture length, and 400-600 km is said to give similar patterns. It would be good to see this sensitivy shown quantitatively, even as supplementary material.
Figure 1 caption (around L94-98): magnitude is described as being on the "Richter scale". For the large events that dominate this catalogue, moment magnitude (Mw) is the appropriate scale and should be used instead.
L168-172 and L270-271: "1 arc-second resolution" for GEBCO 2025 contradicts the cited reference (L408), which states 15 arc-second intervals. The same error is repeated at L270-271 ("downscaled from a resolution of 1 arc-second to 4 arc-minutes"). Please correct this factual inconsistency in both places and confirm the actual resolution used.
L168-173: Ray-tracing mesh resolution is 10-28 km. The seamounts and fracture zones responsible for focusing may be under-resolved, and barycentric interpolation with precomputed gradients smooths exactly those features. Please add a ray-tracing mesh-resolution sensitivity test (a FUNWAVE resolution test is already provided, L278-280; an equivalent for the rays is needed).
L179-184: Rays are emitted perpendicular to the fault and oceanward only. Real radiation directivity depends on slip distribution and dip. Please discuss the impact of this simplification on the radiation pattern.
L181-184: The 500 m termination depth is a key parameter; please justify the choice and test sensitivity (see General comment 2 on caustics).
L230-240: the Kamchatka event summary reports specific run-up heights, casualties, and damage. These should be supported by explicit references if retained.
L278-280: The sensitivity simulations are described as being conducted on "higher resolution 8 and 16 arc-minute grids", but 8 and 16 arc-minutes are coarser than the 4 arc-minute production grid, not finer. Either this is a typo ("coarser") or the sensitivity test only explores lower resolutions, in which case the stated conclusion that 4 arc-minutes is "adequate" is not supported by a convergence test toward finer grids. Please clarify.
L334-340: Please specify exactly how co-located FUNWAVE-ray pairs are extracted (segment length, number of points, near-field exclusion criterion) and report the statistics described in General comment 5. In particular, please detail the near-field exclusion criterion applied; near the Kamchatka source region, the ray-tracing approximation breaks down due to initial source dynamics and strong diffraction, meaning near-field coastal segments must be strictly excluded to avoid biasing the global far-field statistical correlation.
L356-384 (Conclusions): Language such as "rigorously validated", "robust", and "defensible" should be moderated given rho = 0.66 and the single-event validation.
TECHNICAL CORRECTIONS
L137: "wether" -> "whether".
Ensure all figure colour scales state explicitly that the coastline metric is a normalised ray-count proxy (0-1), not wave amplitude, to avoid reader misinterpretation.
Citation: https://doi.org/10.5194/egusphere-2025-6048-RC2

Ali Abdolali, Michael-Angelo Y. Lam, Usama Kadri, Matt Malej, Maxim Filimonov, and Fengyan Shi

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Short summary

This study introduces a hybrid tsunami risk method that fuses probabilistic hazard assessment with ray tracing to enable rapid global mapping. Using historical tsunamigenic earthquake statistics, it identifies how bathymetry focuses wave energy into convergence hotspots. Validated with the 2025 M8.8 Kamchatka event, high-fidelity Boussinesq outputs showed strong observational skill, offering a robust basis for quick hazard evaluation and coastal resilience planning.


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