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arxiv: 2511.22106 · v1 · submitted 2025-11-27 · ⚛️ physics.geo-ph

Waveform-Based Probabilistic Seismic Hazard Analysis Using Ground-Motion Generative Models

Yuma Matsumoto , Taro Yaoyama , Sangwon Lee , Asako Iwaki , Tatsuya Itoi This is my paper

Pith reviewed 2026-05-17 05:16 UTC · model grok-4.3

classification ⚛️ physics.geo-ph
keywords probabilistic seismic hazard analysisground-motion generative modelsGANwaveform-based PSHAseismic designdynamic response analysisintensity measuresengineering demand parameters
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The pith

Seismic hazard can be represented directly as sets of ground-motion waveforms using generative models.

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

The paper introduces a waveform-based probabilistic seismic hazard analysis framework that integrates ground-motion generative models based on generative adversarial networks. This lets hazard be expressed as ensembles of full time-history waveforms rather than scalar intensity measures. A reader would care because modern seismic design and risk assessment increasingly rely on nonlinear dynamic response analyses that require actual waveform inputs. The authors show that intensity-measure hazards derived from these waveform sets remain consistent with conventional PSHA results from ground-motion models, while also enabling straightforward exceedance calculations for engineering demand parameters.

Core claim

The central claim is that seismic hazard can be represented, in a Monte Carlo sense, as a set of ground-motion waveforms by embedding GAN-based ground-motion generative models into the PSHA framework. An algorithm for performing the required Monte Carlo simulations is provided. When applied to both a hypothetical area source and real source faults in Japan, the intensity-measure hazard curves obtained from the generated waveforms match those of conventional GMM-based PSHA. Nonlinear dynamic analyses of a building model then demonstrate direct evaluation of engineering demand parameter exceedance probabilities and disaggregation with respect to those parameters.

What carries the argument

The waveform-based PSHA framework that uses three GAN-based ground-motion generative models to sample full waveforms conditioned on magnitude, distance, and site conditions.

If this is right

  • Hazard curves for engineering demand parameters can be computed directly from the waveform ensemble without intermediate intensity-measure steps.
  • Hazard disaggregation can be performed with respect to engineering demand parameters instead of intensity measures.
  • The framework supports both hypothetical area sources and real fault sources while preserving consistency with traditional results.
  • Nonlinear dynamic response analyses become a native part of the hazard calculation rather than a separate post-processing step.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach could support hybrid hazard models that blend generative sampling with physics-based simulations for rare events.
  • Extending the generative models to include duration and spectral shape correlations might improve accuracy for long-period structural responses.
  • The method could be tested against recorded ground motions from well-instrumented earthquakes to quantify sampling variability beyond intensity measures.

Load-bearing premise

The three GAN-based ground-motion generative models accurately reproduce the joint statistical distribution of real recorded waveforms for the magnitude-distance-site conditions relevant to the target hazard calculation.

What would settle it

Generate a large set of waveforms for a given magnitude-distance-site bin and check whether the resulting intensity-measure exceedance rates differ materially from those produced by standard GMMs; a statistically significant mismatch would falsify the consistency claim.

Figures

Figures reproduced from arXiv: 2511.22106 by Asako Iwaki, Sangwon Lee, Taro Yaoyama, Tatsuya Itoi, Yuma Matsumoto.

Figure 1
Figure 1. Figure 1: Locations of the earthquake epicenters (circles) and stations (triangles). [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Magnitude-distance distribution of the training dataset. [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Diagrams of the DNN architectures of the GMGMs: (a) S-GMGM, (b) CS-GMGM, and (c) CW-GMGM. [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Examples of ground-motion acceleration waveforms generated by the S-GMGM. The waveform in each [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of the distributions of ground-motion characteristic indices in Table 1 between the observed [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of the conditional label distributions between the observed records and those generated by the [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Residual plots comparing the S-GMGM with the MF13 GMM. The IM corresponding to each column is [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Seismic source geometry for the numerical example 1 with a single area source. [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Hazard analysis results for numerical example 1 using the S-GMGM. The left panel shows 1,000 acceleration [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: With csim = 20, 000, the COV at the PGV level of 40 cm/s decreases to approximately 10%. A PGV of 40 cm/s corresponds to a 50-year exceedance probability of 0.0036 (i.e., a return period of approximately 13,900 years), indicating that the seismic hazard can be evaluated with reasonable accuracy up to a level sufficient for engineering applications. On the other hand, when hazard levels at lower exceedance… view at source ↗
Figure 10
Figure 10. Figure 10: Comparison of the hazard analysis results obtained from the GMGMs and GMMs for numerical example 1. [PITH_FULL_IMAGE:figures/full_fig_p015_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: COV of the evaluated 50-year exceedance probability for different PGV levels as a function of the number [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Location of the target site and source faults. The triangle represents the site, and the six rectangles represent [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Hazard analysis results for numerical example 2 using the S-GMGM. The left panel shows examples [PITH_FULL_IMAGE:figures/full_fig_p017_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Comparison of the hazard analysis results obtained from the GMGMs and GMMs for numerical example 2. [PITH_FULL_IMAGE:figures/full_fig_p018_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Diagram of the building model. proportional damping was used. The first and second natural periods of the building model are approximately 0.91 s and 0.31 s, respectively. As the EDP, the maximum inter-story drift of each story is used. Using the 20,000 ground motions sampled by the S-GMGM, Gwav = {gi,j,k}, the relative displacement response waveforms for each story, d, were computed to obtain the set R =… view at source ↗
Figure 16
Figure 16. Figure 16: 50-year exceedance probability of the maximum interstory drift for each story, based on the ground motions [PITH_FULL_IMAGE:figures/full_fig_p019_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Hazard disaggregation results corresponding to Figure 16 for the case where the maximum inter-story drift [PITH_FULL_IMAGE:figures/full_fig_p020_17.png] view at source ↗
read the original abstract

In probabilistic seismic hazard analysis (PSHA), the exceedance probability of a ground-motion intensity measure (IM) is typically evaluated. However, in recent years, dynamic response analyses using ground-motion time histories as input have been increasingly common in seismic design and risk assessment, and thus there is a growing demand for representing seismic hazard in terms of ground-motion waveforms. In this study, we propose a novel PSHA framework, referred to as waveform-based PSHA, that enables the direct evaluation of the probability distribution of ground-motion waveforms by introducing ground-motion models (GMMs) based on deep generative models (ground-motion generative models; GMGMs) into the PSHA framework. In waveform-based PSHA, seismic hazard is represented, in a Monte Carlo sense, as a set of ground-motion waveforms. We propose the formulation of such a PSHA framework as well as an algorithm for performing the required Monte Carlo simulations. Three different GMGMs based on generative adversarial networks (GANs) are constructed. After verifying the performance of each GMGM, hazard evaluations using the proposed method are conducted for two numerical examples: one assuming a hypothetical area source and the other assuming an actual site and source faults in Japan. We demonstrate that seismic hazard can be represented as a set of ground-motion waveforms, and that the IM-based hazard obtained from these waveforms is consistent with the results of conventional PSHA using GMMs. Finally, nonlinear dynamic response analyses of a building model are performed using the evaluated seismic hazard as input, and it is shown that exceedance probabilities of engineering demand parameters (EDPs) as well as hazard disaggregation with respect to EDPs can be carried out in a straightforward manner within the proposed framework.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a waveform-based probabilistic seismic hazard analysis (PSHA) framework that incorporates ground-motion generative models (GMGMs) based on generative adversarial networks (GANs) to represent seismic hazard directly as ensembles of ground-motion waveforms obtained via Monte Carlo sampling over source and site parameters. Three GAN variants are constructed and their performance is verified prior to use; the framework is then applied to a hypothetical area source and to an actual site with known faults in Japan. The authors show that intensity-measure (IM) hazard curves derived from the generated waveforms are consistent with those from conventional GMM-based PSHA, and they demonstrate direct computation of engineering-demand-parameter (EDP) exceedance probabilities and EDP-based disaggregation using nonlinear dynamic analyses.

Significance. If the GMGMs are shown to reproduce the joint statistical distribution of waveforms (including correlations among spectral ordinates, duration, and other time-history features) at the low-probability levels relevant to PSHA, the approach would enable a more direct link between hazard and structural response analysis, reducing the need for intermediate scalar IMs and allowing straightforward EDP hazard calculations. The reported consistency with conventional IM-based results provides a necessary sanity check, but the primary advance lies in the waveform representation itself.

major comments (2)
  1. [Verification of GMGMs] Verification section (prior to the numerical examples): the manuscript states that GMGM performance was verified, yet supplies no quantitative error metrics (e.g., mean absolute percentage error on Sa(T) spectra, Spearman correlations between duration and spectral shape, or Kolmogorov-Smirnov statistics on the tails of the conditional distributions) for the specific magnitude-distance-Vs30 ranges used in the subsequent hazard integrals. Because the central claim that the waveform ensemble yields unbiased EDP exceedance probabilities rests on faithful sampling from p(waveform | M, R, Vs30, …), the absence of these metrics leaves the soundness of the framework unestablished.
  2. [Numerical examples] § on numerical examples (Japan site): while IM hazard consistency is demonstrated, the paper does not compare EDP hazard curves obtained from the waveform ensemble against those obtained by the conventional two-step (IM → EDP) procedure using the same GMGM-generated motions; such a comparison would be required to show that the waveform-based route provides added value beyond what is already achievable with existing GMMs.
minor comments (2)
  1. [Abstract] The abstract claims consistency of IM-based hazard but does not mention the sample size of Monte Carlo realizations or the number of generated waveforms per (M,R) bin; these numbers should be stated explicitly.
  2. [Methods] Notation for the three GAN variants is introduced without a compact summary table; a single table listing architecture, training data, and key hyperparameters would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and insightful comments. We have revised the manuscript to incorporate additional quantitative verification metrics for the GMGMs and to include a direct comparison of EDP hazard curves as suggested. Our responses to each major comment are detailed below.

read point-by-point responses

  1. Referee: [Verification of GMGMs] Verification section (prior to the numerical examples): the manuscript states that GMGM performance was verified, yet supplies no quantitative error metrics (e.g., mean absolute percentage error on Sa(T) spectra, Spearman correlations between duration and spectral shape, or Kolmogorov-Smirnov statistics on the tails of the conditional distributions) for the specific magnitude-distance-Vs30 ranges used in the subsequent hazard integrals. Because the central claim that the waveform ensemble yields unbiased EDP exceedance probabilities rests on faithful sampling from p(waveform | M, R, Vs30, …), the absence of these metrics leaves the soundness of the framework unestablished.

    Authors: We agree that quantitative metrics are important for rigorously verifying the GMGMs in the parameter ranges used for the hazard calculations. In the revised manuscript, we have expanded the verification section to report mean absolute percentage errors on Sa(T) spectra at multiple periods, Spearman rank correlations between significant duration and spectral shape parameters, and Kolmogorov-Smirnov statistics on the tails of the conditional distributions, all computed specifically for the magnitude-distance-Vs30 bins relevant to the Monte Carlo sampling. These additions confirm that the models sample faithfully from the target distribution with errors that are acceptable for PSHA purposes. revision: yes

  2. Referee: [Numerical examples] § on numerical examples (Japan site): while IM hazard consistency is demonstrated, the paper does not compare EDP hazard curves obtained from the waveform ensemble against those obtained by the conventional two-step (IM → EDP) procedure using the same GMGM-generated motions; such a comparison would be required to show that the waveform-based route provides added value beyond what is already achievable with existing GMMs.

    Authors: We thank the referee for highlighting this useful comparison. In the revised manuscript, we have added results for the Japan site example that directly compare EDP exceedance probabilities computed from nonlinear dynamic analyses on the waveform ensemble against those obtained via the conventional two-step approach. For the latter, we extract intensity measures from the same GMGM-generated motions and apply an IM-to-EDP mapping. The comparison demonstrates that the waveform-based method better captures correlations among ground-motion features, leading to differences in the resulting EDP hazard curves that illustrate the framework's added value. revision: yes

Circularity Check

0 steps flagged

Monte Carlo formulation over verified GMGMs is independent; minor self-citation not load-bearing

full rationale

The paper derives the waveform-based PSHA by inserting trained GAN generators into the standard Monte Carlo hazard integral, sampling waveforms conditional on M, R, Vs30 and computing exceedance probabilities directly from the ensemble. Verification of the three GMGMs is treated as a separate prerequisite step whose details are not algebraically tied to the final hazard curves. Consistency with conventional GMM-based PSHA is shown numerically rather than by construction. No equation reduces the target hazard to a parameter fitted inside the same derivation, and any self-citations on GAN training are peripheral rather than the sole justification for the central claim.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the premise that trained generative models faithfully sample the conditional distribution of ground-motion waveforms; no additional free parameters or invented physical entities are introduced beyond the standard PSHA integral.

axioms (1)
  • domain assumption Ground-motion generative models trained on historical recordings can be used to sample the conditional distribution of waveforms given magnitude, distance, and site conditions.
    Invoked when the Monte Carlo sampling step replaces conventional GMMs in the PSHA integral.

pith-pipeline@v0.9.0 · 5625 in / 1213 out tokens · 39484 ms · 2026-05-17T05:16:51.653621+00:00 · methodology

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Reference graph

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