the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 13 Aug 2026
Integrating Geodetic Constraints into Earthquake Source Characterization for Probabilistic Seismic Hazard Analysis: A Dual Statistical–Physical Framework
Abstract. Reliable earthquake source characterization is essential for probabilistic seismic hazard analysis (PSHA), yet remains particularly challenging in low-seismicity regions where sparse earthquake catalogs introduce substantial epistemic uncertainty. Although geodetic observations provide independent constraints on contemporary crustal deformation, existing hybrid earthquake source models have generally been selected solely on the basis of statistical forecasting performance without explicitly considering their physical consistency with regional deformation. This study presents a statistical–physical hybrid framework that integrates independently validated catalog-based and GNSS-derived geodetic earthquake source models for PSHA. The proposed framework combines retrospective earthquake forecast evaluation using the Collaboratory for the Study of Earthquake Predictability (CSEP) with independent physical screening based on the regional geodetic moment budget. A total of 126 candidate hybrid models were evaluated for Kalimantan, Indonesia, representing alternative catalog models, geodetic scenarios, and hybrid formulations. Although several candidates improved retrospective forecasting skill, only three satisfied both the statistical and physical selection criteria, with the preferred adaptive-smoothing hybrid model achieving the highest average retrospective pass rate (67.5 %). Physical screening rejected six of the seven evaluated geodetic scenarios because their implied seismic moment release exceeded the available geodetic moment budget. Incorporating the selected hybrid models into PSHA increased median peak ground acceleration by approximately 2–29 % for the 475-year return period and 2–23 % for the 2475-year return period. In contrast, equal-weight and performance-based logic-tree ensembles produced nearly identical hazard estimates, differing by less than 1.5 %. These results demonstrate that integrating statistical forecasting skill with independent geodetic constraints provides a physically consistent framework for earthquake source characterization and a transferable methodology for improving earthquake hazard assessment in low-seismicity regions.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2026-4242', Francesco Visini, 27 Oct 2026
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AC1: 'Reply on RC1', Yuliastuti Yuliastuti, 28 Oct 2026
Dear Referee,
Thank you for such a thorough and constructive review of our manuscript. The comments helped us clarify the physical meaning of the moment-budget criterion, document the geodetic scenarios, and improve the reproducibility of the PSHA. Referee comments are reproduced below, followed by our responses and the corresponding changes to the manuscript. Line numbers refer to the discussion paper.
Main comments
Role and interpretation of the geodetic moment-budget criterion
The hybrid models are normalized to preserve the regional earthquake occurrence rate, and Table 3 reports nearly the same implied seismic moment rate for all configurations. This suggests that the moment-budget test primarily compares the total moment rate implied by the catalog-based model with the different geodetic budgets, rather than testing whether each hybrid model’s spatial redistribution is physically plausible.
Could the authors clarify whether this is the intended interpretation? The CSEP S-test already evaluates the spatial consistency of the forecasts, whereas the moment-budget comparison appears to provide a complementary, region-wide physical constraint. I would like to suggest making this distinction explicit and describing the criterion as a test of regional moment-budget compatibility, unless the authors can demonstrate that it also assesses the physical plausibility of the spatial redistribution itself.
Author response:
We thank the Referee for pointing this out. The reviewer is correct that the moment-budget screening evaluates regional compatibility rather than the physical plausibility of the spatial redistribution. In our formulation, the geodetic covariate modifies the relative seismicity rates across grid cells, while normalization preserves the total occurrence rate within each magnitude–depth bin. As a result, the implied regional seismic moment rate remains unchanged from the catalog-based baseline, as reflected in Table 3. The moment-budget test therefore compares this regional seismic moment rate with the geodetic budget under each scenario, without evaluating the spatial redistribution itself.
We will revise the Methods (lines 225–228) to make this distinction explicit and refer to the criterion as a regional moment-budget compatibility test. We will also revise the Conclusions (line 511 onward) to distinguish regional moment-budget compatibility from physical validation of the spatial redistribution.
Proposed revision in the Methods:
“Because the hybrid models preserve the total occurrence rate within each magnitude–depth bin, their implied regional seismic moment rates remain unchanged from the corresponding catalog-based baselines. The geodetic moment-budget test therefore evaluates regional moment-budget compatibility, rather than the physical plausibility of the spatial redistribution introduced by the geodetic covariates.”
Definition and variability of geodetic scenarios A–G
The geodetic moment budget can depend on several assumptions used to convert strain rate into moment rate, including the strain metric, seismogenic thickness, seismic coupling coefficient, elastic parameters, and GNSS network configuration. The manuscript presents substantially different budgets for scenarios A–G but does not clearly identify which assumptions distinguish each scenario.
Could the authors add a table listing, for each scenario, the relevant input choices and the resulting moment budget? This would help readers understand why the budgets vary and why Scenario F is retained. It would also be useful to report the uncertainty associated with each budget, rather than only a single value.
Author response:
We thank the Referee for this suggestion. The geodetic scenarios A–G were adopted from Yuliastuti et al. (2026b), where their parameter configurations and sensitivity analyses were originally described. We agree that these configurations should also be reported in the present manuscript to clarify the differences in regional moment budgets. Scenarios B and E intentionally share identical physical parameters (maximum shear strain, H = 8 km, and β = 0.10), serving as the common reference configuration for the thickness and coupling sensitivity groups, respectively. Consequently, these two scenarios yield identical regional geodetic moment budgets.
We will expand Table 3 to include the strain metric, seismogenic thickness (H), seismic coupling coefficient (χ), and regional moment budget for each scenario. All scenarios use the 46-station GNSS configuration, Young's modulus of 60 GPa, and a spatially varying Poisson's ratio. The budgets differ from those reported in Yuliastuti et al. (2026b), which used the 25-station configuration.
We also quantified the uncertainty in each regional moment budget using 100 GNSS bootstrap realizations. The resulting 5th–95th percentile intervals are included in the revised table. Scenario F satisfies the regional moment-budget compatibility criterion in 90–93% of bootstrap realizations across the three catalog-based baselines, compared with 43–48% for Scenario G and 0% for Scenarios A–E. These results support retaining Scenario F, while indicating that the screening outcome remains sensitive to GNSS-derived uncertainty. The bootstrap intervals do not include uncertainty in the assumed physical parameters.
Revised Table 3: Geodetic scenario configurations and regional moment-budget compatibility screening.
Geodetic scenario
Strain Metric
H (km)
χ
Geodetic moment budget (×1017 Nm/ yr)
Bootstrap P05–P95
Implied hybrid moment rate (×1017 Nm/ yr)
Hybrid/Budget
Decision
A
Max. shear
5
0.1
0.74
0.53–1.01
3.18–3.23
4.30–4.40
Rejected
B
Max. shear
8
0.1
1.18
0.84–1.61
3.18–3.23
2.70–2.80
Rejected
C
Max. shear
11
0.1
1.62
1.16–2.22
3.18–3.23
~2.00
Rejected
D
Max. shear
8
0.05
0.59
0.42–0.81
3.18–3.23
5.40–5.50
Rejected
E
Max. shear
8
0.1
1.18
0.84–1.61
3.18–3.23
2.70–2.80
Rejected
F
Max. principal
5
0.1
3.58
2.65–4.41
3.18–3.23
0.89–0.90
Selected
G
Max. principal
8
0.05
2.87
2.12–3.53
3.18–3.23
1.11–1.13
Rejected
Sensitivity of the Scenario F selection to the 10% tolerance
The physical criterion accepts models whose implied moment rate does not exceed 110% of the geodetic budget. Scenario G appears to exceed this threshold only slightly, whereas Scenarios A–E exceed it by much larger amounts.
Could the authors justify the choice of a 10% tolerance in relation to the uncertainty of the geodetic moment-rate estimates? I would like to suggest testing whether the classification of Scenario G changes when the uncertainty in the GNSS-derived budget is propagated. This would help establish whether the conclusion that only Scenario F passes is robust to the adopted threshold.
Author response:
The 10% tolerance was adopted as an operational margin for the nominal regional moment-budget screening, allowing the implied seismic moment rate to exceed the estimated geodetic budget by no more than 10%. It was not derived from GNSS measurement uncertainty and should not be interpreted as a confidence bound on the geodetic moment-rate estimates. We will clarify this definition in the Methods.
To assess the sensitivity of this criterion, we additionally evaluated tolerances from 0% to 20% and propagated the GNSS-derived variability using 100 bootstrap realizations. At the original 10% tolerance, Scenario F satisfies the criterion in 90–93% of realizations across the three catalog-based baselines, compared with 43–48% for Scenario G. Scenario G also passes the nominal criterion when the tolerance is increased to 15%.
Thus, Scenario F remains the only configuration passing the originally adopted nominal screening criterion, although the exclusion of Scenario G is sensitive to both the tolerance and the GNSS-derived budget uncertainty. We will report these results and qualify the interpretation of the screening outcome accordingly.
Revision in the Methods (line 217-219):
“A scenario was considered regionally compatible when the implied seismic moment rate did not exceed 110% of the corresponding geodetic moment budget. The 10% tolerance was adopted as an operational margin for nominal regional moment-budget screening, rather than as a quantitative estimate of uncertainty in the GNSS-derived moment budget. The bootstrap-derived P05–P95 intervals for Scenarios F and G extend approximately 26% below and 23% above their respective nominal budgets, indicating that GNSS-derived variability is appreciable relative to the adopted screening margin. We therefore examined the sensitivity of the screening outcome to tolerance values ranging from 0% to 20% and to 100 GNSS bootstrap realizations. At the original 10% tolerance, Scenario F satisfied the compatibility criterion in 90–93% of realizations across the three catalog-based baselines, compared with 43–48% for Scenario G. Scenario G also satisfied the nominal criterion when the tolerance was increased to 15%. These findings indicate that Scenario F is the only configuration accepted under the original nominal criterion, while the exclusion of Scenario G is sensitive to the adopted tolerance and GNSS-derived variability.”
Interpretation of the Type-2 model with (P=0)
The selected SF4 Type-2 model has (P=0). Under the formulation proposed, this gives a spatial weight of one in every cell, so the resulting model appears to be identical to the catalog-based baseline.
Could the authors confirm that this is the intended outcome? If so, it may be helpful to identify this configuration as a null or baseline case rather than as a hybrid model, and to explain how it is treated in the final model selection and PSHA comparisons.
Author response:
We thank the Referee for highlighting this important inconsistency and for suggesting clarification of the role of the SF4–F–P0 configuration. First, we confirm that the neutral outcome is intentional. In the Type-2 hybrid formulation, setting the rank-prior exponent to P = 0 produces a unity multiplicative factor. Consequently, SF4–F–P0 is mathematically equivalent to the original SF4 baseline and does not introduce any geodetic modification to the spatial seismicity distribution.
We verified this property through a direct numerical comparison of the original SF4 and SF4–F–P0 gridded seismicity forecasts. Both contain 243,936 spatial–magnitude–depth bins with identical bin definitions and annual occurrence rates. Their total annual seismicity rates are identical (1.670245 events/year), with zero differences across all compared bins.
Second, we agree that SF4–F–P0 is more appropriately identified as a null-hybrid or baseline-equivalent control configuration, rather than as an independently modified hybrid forecast. Its purpose is to represent the neutral limit of the Type-2 formulation and provide a consistency check on the hybridization procedure. We will clarify this distinction in the revised manuscript.
Third, regarding final model selection and PSHA comparisons, SF4–F–P0 was retained under its original configuration label during the retrospective CSEP evaluation and subsequent model-selection process. However, its P = 0 setting means that it should not be interpreted as evidence of an additional geodetic contribution or as an independent seismicity model relative to SF4. We will explicitly identify its baseline-equivalent status when presenting the selected models and discussing their implications for PSHA.
We also acknowledge the inconsistency in the previously reported PGA comparison between SF4 and SF4–F–P0. Because the underlying gridded forecasts are identical, the reported PGA differences cannot be attributed to the hybridization procedure. Our subsequent examination identified inconsistencies in the OpenQuake source-model representation that may explain this discrepancy. We will revise the affected hazard comparison and avoid interpreting the reported PGA increase as a physical effect of geodetic hybridization.
We appreciate the Referee's observation, which has helped us clarify the intended role of the neutral configuration and distinguish it from hybrid models that introduce non-uniform spatial modifications of seismicity rates.
CSEP evaluation and model selection
The study compares 126 candidate configurations and then reports results for selected models. If the same retrospective testing windows were used both to select the preferred configurations and to report their final performance, the reported pass rates may be optimistic.
Could the authors clarify whether model selection and final evaluation used independent data or testing windows? If the same windows were used, I would like to suggest acknowledging this limitation and, where possible, adding a separate validation exercise. Please also define passALL, specify how the individual CSEP tests are combined, and report the number of windows contributing to each pass rate.
There also appears to be an inconsistency (a typo?) in the forecasting horizons: the Methods section refers to 3-, 5-, and 10-year horizons, whereas the Results and Table 4 include a 1-year horizon. Could the authors reconcile these descriptions?
Author response:
We thank the Referee for highlighting this important distinction. The catalog used for model calibration (1967–2010) was independent of the ISC-GEM testing catalog (2011–2021). However, we acknowledge that the same retrospective CSEP testing windows were used both to select the preferred hybrid configurations and to report their forecasting performance. No additional testing period was reserved for independent post-selection validation. Consequently, the reported pass rates should be interpreted as retrospective selection performance rather than fully independent estimates of predictive skill, and some selection-induced optimism cannot be excluded.
We will clarify this limitation in the revised manuscript and identify independent temporal validation as a priority for future research. Such validation should separate model calibration, configuration selection, and final performance assessment, for example through temporally blocked or nested evaluation procedures in which the final assessment periods are excluded from all configuration-selection decisions.
We will also clarify the definition of passALL. A testing window passes the combined criterion only when all four CSEP consistency tests (N, S, M, and CL) pass simultaneously. The pass rate for each forecasting horizon is calculated as the proportion of windows satisfying this combined criterion. The respective numbers of sliding windows are 11, 9, 7, and 2 for the 1-, 3-, 5-, and 10-year horizons. We acknowledge that windows within and across horizons overlap and therefore do not represent independent observations.
Finally, we will correct the Methods section to consistently report all four forecasting horizons (1, 3, 5, and 10 years), in agreement with the Results and Table 4.
Uncertainty propagation and PSHA implementation
The manuscript describes both bootstrap-derived percentile source models (P05, P50, and P95) and a logic tree containing three selected hybrid models. Could the authors explain more explicitly how these two sources of epistemic uncertainty are combined in the hazard calculations, and how the reported PGA percentiles and error bars are derived?
In addition, the GMPEs and their logic-tree weights are not specified in Table 1. Since these choices are essential for reproducing and interpreting the PSHA results, could the authors provide them, together with the other important values used in the hazard calculations?
Author response:
We thank the Referee for this important comment. We agree that the original description did not sufficiently distinguish the uncertainty representations used in the individual-model PSHA calculations from those used in the multi-model ensemble calculations. We will revise Section 2.7 to clarify their implementation, the derivation of the reported PGA statistics, and the ground-motion modelling assumptions.
In the individual-model calculations, each catalog-based baseline model (BF, SF4, and SA9) and its corresponding selected hybrid configuration was evaluated separately. Each calculation employed a single source-model representation combined with a GMPE logic tree containing five equally weighted branches (0.20 each). Consequently, the five realizations in each individual-model calculation represent alternative ground-motion models, rather than combinations of three source-rate percentile branches and five GMPE branches.
The bootstrap-derived P05, P50, and P95 seismicity-rate estimates represent a separate characterization of source-rate uncertainty. Their spatial characteristics are illustrated for the selected SA9-based hybrid configuration in Figure 3. We acknowledge that the original description could incorrectly suggest that all three source-rate percentiles were propagated as separate logic-tree branches in the individual-model hazard calculations. We will correct this description and distinguish the source-rate uncertainty analysis from the uncertainty represented in the reported PGA quantiles.
In the multi-model ensemble calculations, inter-model epistemic uncertainty was represented using a source-model logic tree comprising three selected source configurations. Two weighting schemes were considered: COMBO_EQ3, which assigned equal weights of 1/3 to the three source models, and COMBO_CSEP3, which assigned performance-based weights derived from the retrospective CSEP evaluation. The performance scores were calculated from the average combined CSEP pass rates (passALL) over the 3- and 5-year testing horizons and subsequently normalized to obtain the logic-tree weights. Both ensembles were combined with the five-branch GMPE logic tree.
Thus, the individual-model and multi-model ensemble calculations address different aspects of epistemic uncertainty. The individual-model results characterize the variation associated with the GMPE alternatives for a given source-model representation, whereas the ensemble calculations additionally account for differences among the selected source-model configurations. The bootstrap-derived source-rate uncertainty was examined separately and should not be interpreted as fully propagated through a nested source-rate and GMPE logic tree.
Second, regarding the PGA percentiles and error bars, the reported PGA P50 and P95 values were obtained from the corresponding OpenQuake hazard-curve quantiles, rather than directly from the percentile seismicity-rate inputs. PGA values for return periods of 475 and 2475 years were calculated by log–log interpolation of the hazard curves at annual exceedance probabilities of 0.002105 and 0.000404, respectively.
The upper error bars in Figure 4 represent PGA P95 minus PGA P50. For the individual-model calculations, these statistics describe the upper spread associated with the five GMPE realizations for the source-model representation used in each calculation. They are not symmetric standard deviations, conventional confidence intervals, or direct estimates of the bootstrap-derived source-rate uncertainty.
Third, regarding the GMPE configuration and reproducibility, we will expand Table 1 to identify the five GMPEs used for the active shallow crust tectonic region: Boore et al. (2014), Campbell and Bozorgnia (2014), Chiou and Youngs (2014), Cauzzi and Clinton (2014), and Zhao et al. (2006). Each GMPE was assigned an equal logic-tree weight of 0.20.
The revised table will also document the source-model logic-tree structure and weights, investigation time, intensity measure levels, ground-motion truncation level, maximum source distance, source discretization, magnitude-frequency distribution parameters, reference site conditions, and hazard-output statistics.
Finally, we will revise Section 3.5 and the Figure 4 caption to distinguish bootstrap-derived seismicity-rate uncertainty from the PGA variation represented by the GMPE and ensemble logic-tree calculations.
These revisions will clarify the scope of uncertainty propagation and improve the reproducibility and interpretation of the PSHA results.
Minor comments
- Please ensure that the equations and notation are complete and consistent. In particular, the moment–magnitude term in Eq. (3) appears to contain a typographical error.
Author response:
We thank the Referee for pointing out this typographical error. We will correct the moment–magnitude notation in Eq. (3) and ensure consistent notation and variable definitions throughout the manuscript.
- The transformation (x=log(1+M)) should specify the units or reference scale used for (M), since the logarithm is applied to a dimensional quantity.
Author response:
We thank the Referee for this observation. We agree that the logarithmic transformation should use a dimensionless argument. We will revise Line 175 to explicitly define the transformation as x = log(1 + Mdot/Mref), where Mdot denotes the geodetic seismic moment rate expressed in N·m/yr and Mref is a reference moment rate set to 1 N·m/yr. This ensures that the argument of the logarithm is dimensionless while remaining mathematically equivalent to the numerical implementation used in our calculations.
- The regional PGA maps would be easier to interpret alongside maps of the difference or ratio between the hybrid and baseline hazard estimates. This would help distinguish localized increases from broader regional changes.
Author response:
We thank the Referee for this helpful suggestion. We agree that maps showing the spatial differences or ratios between hybrid and baseline PGA estimates would provide valuable additional insight. However, the regional-scale PSHA calculations were performed for the hybrid models, whereas the baseline–hybrid comparisons were conducted at five representative sites. Producing regional difference maps would therefore require additional full-domain PSHA calculations for the baseline models, which are computationally demanding.
To address the Referee's concern within the scope of the present study, we will strengthen the discussion of the baseline–hybrid PGA comparisons at the five evaluation sites and explicitly acknowledge that the regional maps illustrate the spatial distribution of hybrid hazard rather than the spatial extent of changes relative to the baseline. A comprehensive regional comparison will be identified as a direction for future work.
Overall, the proposed revisions will provide a clearer distinction between the statistical evaluation of seismicity forecasts, regional geodetic moment-budget compatibility, and the treatment of epistemic uncertainty in PSHA. They will also clarify the scope and limitations of the proposed framework, allowing its results and implications for seismic hazard assessment to be interpreted more appropriately. We look forward to incorporating these improvements into the revised manuscript.
Yours respectfully,
Corresponding Author.Citation: https://doi.org/10.5194/egusphere-2026-4242-AC1
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AC1: 'Reply on RC1', Yuliastuti Yuliastuti, 28 Oct 2026
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RC2: 'Comment on egusphere-2026-4242', Anonymous Referee #2, 31 Oct 2026
The authors of this manuscript discussed a strategy to integrate two different seismicity rate models, one catalog-based using a smoothing approach, and another geodetic-based using data from continuous GNSS observations. These two models were recently published, and this work focuses only on how to integrate the two models into a hybrid model.
Some ideas and some parts of the process to merge the models seem interesting; however, there is an important lack of information (descriptions, data, and figures) that prevents a proper understanding of the results.
Although they refer to the two other papers, in this work there are no figures referring to the two different seismicity rate models. There are no magnitude-frequency distribution plots, and no catalog maps or tables to help understand the CSEP tests they made. Thus, it is not possible to properly understand where the hybrid models come from and how they are selected.
There is also a lack of clear explanations of what is the rational behind their choice of the physical constraint. They say “ moment release was then compared with the independent geodetic moment budget derived from the GNSS-based strain model”, and then “Hybrid models whose implied moment release exceeded this threshold were classified as over-injected and excluded from further analysis”. While the CSEP test description in the previous section is accompanied by several quotations from other research papers, in the physical constraint section there are no quotations at all (apart from the one related to the magnitude-moment relation). And this physical constraint seems central to their work.
The few figures in this manuscript are poor: in both Figures 3 and 5, the Kalimantan island is not fully covered, whereas in the two papers by the same first author published in 2026, the models cover the same island completely, as expected.
In its current form, the manuscript is not understandable, and some important sections of this work are neither justified nor sufficiently analyzed.
To conclude, given all these flaws in the manuscript, I suggest rejection.
Citation: https://doi.org/10.5194/egusphere-2026-4242-RC2
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- 1
This manuscript addresses an important problem in seismic source characterization for low-seismicity regions: how to combine the statistical information provided by earthquake catalogs with the physical constraints provided by geodetic observations. The proposed framework, which combines CSEP evaluation with a regional geodetic moment-budget check and then propagates the selected models into PSHA, is potentially valuable. I particularly welcome the effort to examine whether models that perform well retrospectively are also compatible with independent constraints on tectonic deformation.
The manuscript is generally well structured, and the application to Kalimantan is relevant. My comments are intended to help clarify the physical meaning of the proposed selection procedure, improve the description of the geodetic scenarios, and make the analysis easier to reproduce.
Main comments
Role and interpretation of the geodetic moment-budget criterion
The hybrid models are normalized to preserve the regional earthquake occurrence rate, and Table 3 reports nearly the same implied seismic moment rate for all configurations. This suggests that the moment-budget test primarily compares the total moment rate implied by the catalog-based model with the different geodetic budgets, rather than testing whether each hybrid model’s spatial redistribution is physically plausible.
Could the authors clarify whether this is the intended interpretation? The CSEP S-test already evaluates the spatial consistency of the forecasts, whereas the moment-budget comparison appears to provide a complementary, region-wide physical constraint. I would like to suggest making this distinction explicit and describing the criterion as a test of regional moment-budget compatibility, unless the authors can demonstrate that it also assesses the physical plausibility of the spatial redistribution itself.
Definition and variability of geodetic scenarios A–G
The geodetic moment budget can depend on several assumptions used to convert strain rate into moment rate, including the strain metric, seismogenic thickness, seismic coupling coefficient, elastic parameters, and GNSS network configuration. The manuscript presents substantially different budgets for scenarios A–G but does not clearly identify which assumptions distinguish each scenario.
Could the authors add a table listing, for each scenario, the relevant input choices and the resulting moment budget? This would help readers understand why the budgets vary and why Scenario F is retained. It would also be useful to report the uncertainty associated with each budget, rather than only a single value.
Sensitivity of the Scenario F selection to the 10% tolerance
The physical criterion accepts models whose implied moment rate does not exceed 110% of the geodetic budget. Scenario G appears to exceed this threshold only slightly, whereas Scenarios A–E exceed it by much larger amounts.
Could the authors justify the choice of a 10% tolerance in relation to the uncertainty of the geodetic moment-rate estimates? I would like to suggest testing whether the classification of Scenario G changes when the uncertainty in the GNSS-derived budget is propagated. This would help establish whether the conclusion that only Scenario F passes is robust to the adopted threshold.
Interpretation of the Type-2 model with (P=0)
The selected SF4 Type-2 model has (P=0). Under the formulation proposed, this gives a spatial weight of one in every cell, so the resulting model appears to be identical to the catalog-based baseline.
Could the authors confirm that this is the intended outcome? If so, it may be helpful to identify this configuration as a null or baseline case rather than as a hybrid model, and to explain how it is treated in the final model selection and PSHA comparisons.
CSEP evaluation and model selection
The study compares 126 candidate configurations and then reports results for selected models. If the same retrospective testing windows were used both to select the preferred configurations and to report their final performance, the reported pass rates may be optimistic.
Could the authors clarify whether model selection and final evaluation used independent data or testing windows? If the same windows were used, I would like to suggest acknowledging this limitation and, where possible, adding a separate validation exercise. Please also define passALL, specify how the individual CSEP tests are combined, and report the number of windows contributing to each pass rate.
There also appears to be an inconsistency (a typo?) in the forecasting horizons: the Methods section refers to 3-, 5-, and 10-year horizons, whereas the Results and Table 4 include a 1-year horizon. Could the authors reconcile these descriptions?
Uncertainty propagation and PSHA implementation
The manuscript describes both bootstrap-derived percentile source models (P05, P50, and P95) and a logic tree containing three selected hybrid models. Could the authors explain more explicitly how these two sources of epistemic uncertainty are combined in the hazard calculations, and how the reported PGA percentiles and error bars are derived?
In addition, the GMPEs and their logic-tree weights are not specified in Table 1. Since these choices are essential for reproducing and interpreting the PSHA results, could the authors provide them, together with the other important values used in the hazard calculations?
Minor comments
Addressing these points would make the proposed framework clearer and strengthen the interpretation of its main result: that statistical forecast performance and physical moment-budget compatibility provide complementary information for selecting source models for PSHA.