the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 12 Sep 2025
Probabilistic and Deterministic Seismic Hazard Assessments of the area comprised between west Gulf of Cádiz and east Alboran Sea
Abstract. The increased deployment of subsea infrastructures and the exploration of marine resources have heightened the need to assess seismic hazard on the seabed, especially in tectonically active offshore regions. The area between the Gulf of Cádiz and the Alboran Sea, which is rich in coastal and submarine assets, is located within the Ibero-Maghrebian Region (IMR) a seismically active region. While previous research has addressed seismic hazard in adjacent inland areas using deterministic and probabilistic approaches, few studies have focused on offshore zones. Moreover, existing models often overlook the amplification effects introduced by bathymetry and seafloor conditions, and they rely on ground motion prediction equations (GMPEs) derived from inland data. Consequently, seismic hazard in marine environments remains poorly constrained. This study aims to evaluate the feasibility and applicability of both probabilistic (PSHA) and deterministic (DSHA) seismic hazard assessments for submarine areas, using updated seismogenic zonation, a high-resolution bathymetric model, and GMPEs suitable for soft marine soils. The objective is to produce reliable peak ground acceleration (PGA) estimates at the seabed and to examine the convergence of deterministic and probabilistic approaches in a complex tectonic context. The analysis was conducted using the OpenQuake (OQ) engine for PSHA and a custom MATLAB© script for DSHA. The seismogenic sources and parameters were taken from the ESHM20 model, and four GMPEs—IDR91, HZ23, NT24, and DKK24—were selected for their relevance to offshore or soft soil conditions. These GMPEs were validated against six regional offshore earthquakes recorded in the IMR. Hazard estimates were computed over a bathymetrically refined grid and expressed as PGA maps for various return periods (100, 475, 2475, and 5000 years). The results show that significant PGA values occur over key submarine fault systems such as the Gorringe Ridge, Horseshoe Plain, and Arzew Fault. Offshore PGA estimates for return periods of 2475 years using NT24 and DKK24 are close to those derived from DSHA, settling convergence between methodologies. The use of seabed-adapted GMPEs resulted in higher and more realistic PGA values compared to inland models. This study demonstrates the applicability of seismic hazard assessment methods to offshore environments and highlights the importance of incorporating seafloor conditions into hazard modelling. The findings offer a methodological basis for improving the seismic design of subsea infrastructure in tectonically complex marine regions such as the IMR.
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RC1: 'Comment on egusphere-2025-3248', Alexandra Carvalho, 07 Oct 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-3248/egusphere-2025-3248-RC1-supplement.pdfCitation: https://doi.org/
10.5194/egusphere-2025-3248-RC1 - AC1: 'Reply on RC1', Adrián José Rosario Beltré, 16 Oct 2025
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RC2: 'Comment on egusphere-2025-3248', João Fonseca, 22 Oct 2025
Beltré et al. (in the sequence, the manuscript) set out to discuss and evaluate the applicability of seismic hazard assessment to offshore regions, focusing on the Ibero-Maghreb Region (IMR). They argue, and rightly so, that with the increased occupation of the seabed by engineering infrastructures, the related seismic risk evaluation requires robust hazard assessment at its base. The authors correctly identify the specific geological conditions of the seabed as a differentiating factor. Reference is also made to the possible effect of water-column dynamics, but in a less clear manner.
While addressing the specific aspects of seabed ground motions, the manuscript engages on a comparison between probabilistic (PSHA) and deterministic (DSHA) seismic hazard assessment. For the latter, the manuscript proposes a “zone-based” (line 314) implementation for which no references are given in a clear way, leading me to assume that it was developed by the authors.
The key result of the paper, in my view, is a comparison (the manuscript's Figure 11) between the PGA values obtained in the manuscript using GMPEs derived for seabed conditions, and values obtained with a more standard approach. However, the way the comparison was conducted raises some issues:
- The selected seabed GMPEs are “evaluated” (Line 244) by comparing their predictions with recorded strong ground motion for six earthquakes with offshore epicenters (Lines 244-252). The manuscript does not specify the locations of the instrumental recordings, mentioning only that the accelerations were “sourced from IGN”. If the recording sites were not located on the seabed, these data are not suitable for validation of seabed-specific GMPEs;
- The PGA values proposed in the manuscript are compared to “those obtained using input data files containing the information of the seismogenic sources (…) and the OQ Engine configuration and input files. These were used to calculate the ESHM20 hazard mapping scheme”. Despite the obscure formulation, it seems that the comparison is between the new values proposed in the manuscript and the values that the ESHM20 model would have shown if it extended to the IMR seabed. If this is the case, this seems an unwarranted application of the ESHM20 input data to obtain results for an area that its (ESHM20’s) authors did not include in their model.
Statements such as “the main input parameters in the classic DSHA (Reiter, 1990) are the maximum magnitude associated with the characteristic earthquake as the MCE for each seismic source area and a set of attenuation relationship or GMPEs” (lines 306-307) fail to capture, in my view, the essence of DSHA (standard DSHA doesn’t use source areas, identifying directly the capable geologic structure near the site whose rupture corresponds to the worst-case scenario). In terms of implementation, the manuscript refers that “For DSHA calculations, a MATLAB© code has been developed to calculate the seismic intensity with a selected GMPE, from different seismic source types” (lines 326-438), and later add “MATLAB code [available] from the corresponding author upon reasonable request” (line 680). In my view this is not acceptable: if the code is not public, the results cannot be reproduced independently and therefore cannot be regarded as scientific. Preferably, the code developed in-house should be validated through separate publication before being used in an applied study.
I found the extensive emphasis on PSHA/DSHA comparison a distracting tangent. As an example, statements to the effect that “the hazard maps obtained from deterministic and probabilistic estimations demonstrate a clear correlation: as the return period increases, PGA values calculated by PSHA increase and approach those obtained via DSHA” (line 548-550) are presented as a relevant conclusion of the study, whereas in my view they are a statement of what should be expected.
Occasionally, the manuscript suggests a lack of command of basic aspects of seismic hazard assessment that is concerning given the focus of the study, and the apparent objective of being didactic, as suggested by the extensive theoretical considerations (as opposed to simply referencing standard texts). As examples:
- in line 386 the manuscript states that the GR recurrence parameter l can be “adjusted from the seismic catalog of the project using statistical techniques of least squares or maximum likelihood”. It was well established 45 years ago that least-squares should not be used for this purpose;
- Figure 7 displays logic trees with nodes where the sum of the weights largely exceeds unity;
- While describing Cornell’s method line 363-364), the manuscript states “having established the
probability relationships that govern seismic events in a seismogenic area (point, fault plane, or spatial region) regarding the distribution of locations, sizes, and recurrence times, and knowing the past seismicity of the area”. The “probability relationships that govern seismic events” must be derived from the seismicity of the area, and therefore are not independent from it as the wording may suggest;
- The manuscript states (lines 455-459) that “the findings of this study demonstrate the effectiveness of using both DSHA and PSHA methodologies to generate seismic hazard maps within the IMR. These maps are based on the most recent GMPEs specifically tailored for offshore environments and show statistically robust compatibility with the available seismic data”. This passage seems to suggest that the compatibility of the maps with the seismicity comes from the selection of GMPEs, apparently ignoring the fact that the seismic data determines the choice of area-source geometry, which in turn is reflected on the hazard maps (in this particular case both PSHA and DSHA use area sources).
To conclude, reading the manuscript I got the impression that the research set out to address the very relevant issue of seismic hazard assessment in the seabed of the IMR region, but lost its focus by venturing excessively into a discussion of the relative merits and demerits of PSHA versus DSHA. The DSHA code, which is the basis of a substantial part of the manuscript, is not shared, defeating the possibility of scrutiny. I am forced to conclude that in its current form the manuscript is not fit for publication. Should the authors consider rewriting it to try a subsequent submission, the attached pdf includes extensive comments on the passages that need improvement.
LIsboa, October 22, 2025
João Fonseca
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AC2: 'Reply on RC2', Adrián José Rosario Beltré, 28 Nov 2025
Dear João Fonseca PhD,
Thank you very much for your detailed and constructive comments, and for helping once again as a reviewer of our work. We appreciate the care you took in examining our manuscript and we agree with many of your observations. We have addressed all comments and revised the manuscript accordingly. Please find below our detailed responses to each of your comments. We will implement your suggested changes in an updated version of the manuscript.
Beltré et al. (in the sequence, the manuscript) set out to discuss and evaluate the applicability of seismic hazard assessment to offshore regions, focusing on the Ibero-Maghreb Region (IMR). They argue, and rightly so, that with the increased occupation of the seabed by engineering infrastructures, the related seismic risk evaluation requires robust hazard assessment at its base. The authors correctly identify the specific geological conditions of the seabed as a differentiating factor. Reference is also made to the possible effect of water-column dynamics, but in a less clear manner.
Reply (R): Thanks for this comment. With respect to the effect of water-column dynamics, we agree that our treatment was brief. Sediment and deep-sea water characteristics significantly influence the Peak Ground Acceleration (PGA) experienced during seismic events. Sediment composition, water depth and seabed morphology play a significant role in determining how seismic waves propagate and interact with the underwater environment. We now synthesize what is known about how the water layer and soft seafloor alter impedance contrasts, incidence/refraction, and spectral content at the seabed. We make explicit how this motivates the use of seabed adapted GMPEs and a 3 D distance metric that includes bathymetric depth.
Although we support this with references already cited in the paper (e.g., Chen et al., 2023 and 2024; Dhakal et al., 2021; Diao et al., 2014; Lan et al., 2021; Hu et al., 2020; Tan and Hu, 2023), we also include additional studies. Nakamura et al. (2015) show that thick, low-velocity sediment layers and seawater significantly amplify long-period motions. This amplification leads to higher PGA in underwater environments and contributes to prolonged seismic waves, which differ from land-based attenuation patterns during seismic events. Dhakal and Kunugi (2023) and W. Chen et al. (2024) demonstrate, through numerical experiments with varying terrain and water depth conditions, that sediment characteristics, such as the strong nonlinearity of soft sediments, and deep-sea water dynamics significantly influence PGA by altering seismic wave propagation and amplification effects. Finally, Zhang et al. (2020) highlight that the temporal and spectral characteristics of seismic ground motions differ markedly between offshore and onshore environments. Offshore ground motions tend to exhibit higher spectral accelerations and peak ground velocities, particularly in low-frequency ranges, compared to their onshore counterparts.
So, the sentence in line 46 was rephrased and now read as follows:“In offshore settings, the water column, seabed morphology and compliant soft sediments rheology modify source to site path and site terms. The water layer alters impedance contrasts and incidence/refraction of P/SV waves at the seafloor, shifts spectral content, and can lengthen significant duration at the seabed relative to adjacent onshore sites (Nakamura et al., 2015; Zhang et al. 2020; Dhakal and Kunugi, 2023; W. Chen et al., 2024). These effects, together with basin geometry and bathymetric geography, motivate use of seabed adapted GMPEs and 3 D distance metrics that include depth (e.g., RRUP) when estimating seabed PGA (e.g., Chen et al., 2024; Hu et al., 2020; Dhakal et al., 2021; Tan and Hu, 2023; Diao et al., 2014; Lan et al., 2021).”
Chen, W., Lin, J., Zheng, Y., Su, L., Chen, G., & Huang, L. (2024). Nonlinear seismic response of seabed with terrain variation and seawater-seabed coupling. Soil Dynamics and Earthquake Engineering, 180, 108579. https://doi.org/10.1016/j.soildyn.2024.108579
Nakamura, T., Takenaka, H., Okamoto, T., Ohori, M., & Tsuboi, S. (2015). Long-period ocean-bottom motions in the source areas of large subduction earthquakes. Scientific reports, 5(1), 16648. https://doi.org/10.1038/srep16648
Dhakal, Y. P., & Kunugi, T. (2023). Preliminary analysis of nonlinear site response at the S-net seafloor sites during three Mw 7 class earthquakes. Frontiers in Earth Science, 11, 1180289. https://doi.org/10.3389/feart.2023.1180289
Zhang, Q., & Zheng, X. Y. (2020). Temporal and spectral characteristics of seismic ground motions: Offshore versus onshore. Marine Structures, 74, 102812. https://doi.org/10.1016/j.marstruc.2020.102812
While addressing the specific aspects of seabed ground motions, the manuscript engages on a comparison between probabilistic (PSHA) and deterministic (DSHA) seismic hazard assessment. For the latter, the manuscript proposes a “zone-based” (line 314) implementation for which no references are given in a clear way, leading me to assume that it was developed by the authors.
(R): We agree that the manuscript did not clearly cite the methodological precedent for the zone-based DSHA implementation. To clarify: this method was not originally scripted and programmed by the authors, but rather follows the algorithmic workflow used in prior works (i.e., Loi et al., 2018; Huang and Wang, 2012; Wang et al., 2012; Vipin, 2013; Candia et al., 2019; Ramkrishnan et al., 2021), who developed a deterministic seismic hazard maps using a zone-based framework implemented via Excel-based script, FORTRAN or Matlab codes, like ours. Their work demonstrates how deterministic hazard can be computed using areal source zones when fault-specific data are sparse or diffuse, particularly in offshore or complex tectonic regions.In our study, the zone-based DSHA approach is justified by the lack of well-constrained fault geometries in many offshore areas of the IMR, where seismicity is diffused and submarine structures are poorly resolved. In such contexts, using areal sources to represent seismogenic zones is a practical and accepted alternative, especially when the goal is to estimate maximum credible ground motions for infrastructure planning.
To further support this approach, we now cite additional relevant studies that have employed similar deterministic hazard frameworks using areal or zone-based sources:
Loi, D. W., Raghunandan, M. E., and Swamy, V.: Revisiting seismic hazard assessment for Peninsular Malaysia using deterministic and probabilistic approaches, Natural Hazards and Earth System Sciences, 18, 2387–2408, https://doi.org/10.5194/nhess-18-2387-2018 , 2018 .
Huang, D. and Wang, J.-P.: Seismic hazard map around Taiwan through a catalog-based deterministic approach, in: 15th World Conference on Earthquake Engineering, 2012.
Vipin, K. S.: Assessment Of Seismic Hazard With Local Site Effects : Deterministic And Probabilistic Approaches, Thesis, 2013.
Candia, G., Macedo, J., Jaimes, M. A., and Magna‐Verdugo, C.: A New State‐of‐the‐Art Platform for Probabilistic and Deterministic Seismic Hazard Assessment, Seismological Research Letters, 90, 2262–2275, https://doi.org/10.1785/0220190025 , 2019.
Ramkrishnan, R., Kolathayar, S., and Sitharam, T. G.: Probabilistic seismic hazard analysis of North and Central Himalayas using regional ground motion prediction equations, Bull Eng Geol Environ, 80, 8137–8157, https://doi.org/10.1007/s10064-021-02434-9 , 2021.
Wang, J. P., Huang, D., & Yang, Z. (2012). Deterministic seismic hazard map for Taiwan developed using an in-house Excel-based program. Computers & Geosciences, 48, 111–116. https://doi.org/10.1016/j.cageo.2012.05.014
Krinitzsky, E. L. (2002). How to combine probabilistic and deterministic methods for maximum credible earthquake ground motions for use in engineering design. Engineering Geology, 63(2), 149–158. https://doi.org/10.1016/S0013-7952(01)00074-5
Reiter, L. (1990). Earthquake Hazard Analysis: Issues and Insights. Columbia University Press.
Kramer, S. L. (1996). Geotechnical Earthquake Engineering. Prentice Hall.
K. Campbell, K. (2005). Overview of Seismic Hazard Approaches with Emphasis on the Management of Uncertainties. 2nd ICTP Workshop on Earthquake Engineering for Nuclear Facilities: Uncertainties in Seismic Hazard. Trieste, Italy. pp. 14-25. February 2005
These references are now explicitly included in the revised manuscript to clarify that our DSHA implementation is grounded in established practice and literature.
We will address this explicitly in the text, adding the following paragraph in section 4.1:
“This study adopts a zone-based DSHA approach, following the standard algorithmic workflow as used in Wang et al. (2012), Vipin (2013), Candia et al. (2019) and; Ramkrishnan et al., (2021) which implement the classical deterministic hazard assessment procedure (Reiter, 1990). Deterministic ground motions are computed for areal seismic sources in regions lacking well-defined fault geometries. This method has precedent in offshore hazard studies and is particularly suitable for submarine environments where seismicity is diffuse and fault structures are unresolved. Similar approaches have been discussed (i.e., Krinitzsky, 2002, Kramer, 1996, Campbell, 2005) and are widely used in engineering applications where deterministic estimates are required for preliminarily infrastructure design.”
The key result of the paper, in my view, is a comparison (the manuscript's Figure 11) between the PGA values obtained in the manuscript using GMPEs derived for seabed conditions, and values obtained with a more standard approach. However, the way the comparison was conducted raises some issues:
• The selected seabed GMPEs are “evaluated” (Line 244) by comparing their predictions with recorded strong ground motion for six earthquakes with offshore epicenters (Lines 244-252). The manuscript does not specify the locations of the instrumental recordings, mentioning only that the accelerations were “sourced from IGN”. If the recording sites were not located on the seabed, these data are not suitable for validation of seabed-specific GMPEs;
(R): We confirm that the earthquake database used in this work for lines 244-252 are form onshore/near coastal accelerogram recording IGN stations. We are carrying out a sanity‑check/benchmark using the best recent available regional strong‑motion data in overlapping Mw-R ranges. We are not validating seabed GMPEs. Offshore GMPEs are emerging from dense seafloor networks (S‑net, DONET, NEPTUNE) and explicitly include water depth, sediment properties, burial state and path corrections through marine layers; they show larger long‑period amplitudes and different attenuation than onshore models. So, unfortunately, current models remain regionally focused (Japan, Sagami Bay) where S‑net seafloor recordings or regional OBS arrays have been deployed. Current offshore GMPEs have been developed explicitly for seafloor recordings and subduction settings using this S‑net and other ocean‑bottom datasets (Hu et al., 2023; Li and Ji, 2023; Nakanishi and Takemura, 2024; Tan and Hu 2024; Dhakal et al., 2024). The rationale for including this benchmark is that, in the absence of offshore OBS networks in the IMR, these land-based records still offer insight into attenuation trends for nearby offshore events. This step provides context for the selected GMPEs and ensures their forecasts are not grossly inconsistent with observed trends for offshore events in the IMR. In our manuscript, Figure 4 compares observed onshore PGAs with predictions from selected seabed-specific GMPEs, showing that, for several offshore events, horizontal PGAs tend to be below the average predictions of seabed-calibrated models at short-to-moderate distances. This trend is consistent with the findings of Zhang and Zheng (2019), which show that offshore horizontal PGAs are systematically larger than onshore PGAs for earthquakes at similar epicentral distances (average amplification factor ≈1.8). They attribute this to the combined effects of soft seafloor sediments and high saturation, which enhance horizontal motion while vertical components are suppressed by the water column. Our results are consistent with this mechanism: the amplification observed in the predicted PGAs from the GMPEs relative to the observed onshore PGAs probably reflects this absence of local site effects.
This benchmark serves as a plausibility check to verify that the selected seabed GMPEs produce reasonable attenuation trends when applied to regional offshore events, even though the accelerograph recordings are from closest coastal stations, although we clearly recognize the limitations that must be reflected in the manuscript. This limitation reflects the current absence of offshore strong motion networks in the IMR, a gap repeatedly noted in previous studies (e.g., Molina Palacios, 1998; Vilanova and Fonseca, 2004; Terrinha et al., 2009; Martínez Loriente et al., 2013; Somoza et al., 2021; Perea et al., 2023; Olaiz et al., 2025). Our approach follows the precedent set by these works, which relied on inland proxies to characterize offshore hazard. We now explicitly state this limitation in our manuscript and frame the comparison as a diagnostic exercise, while emphasizing the urgent need for OBS networks to enable true seabed GMPE validation.
We will replace the term “validated/evaluated” with “benchmarked against nearby observed ground motions.” The diagnostic residual analysis will be qualified as illustrative, with methodological moved to the Supplementary Material. Finally, we will emphasize that the primary justification for using HZ23, NT24, and DKK24 GMPEs is their seabed calibration (S net/KiK net), complemented by literature evidence of systematic land–seafloor differences, rather than by our own validation in the IMR.
We will address this explicitly in the text, adding the following paragraph in line 244:
“We benchmarked the selected GMPEs against observed horizontal PGAs for six regional offshore earthquakes using onshore/near‑coastal accelerograms from IGN (https://www.ign.es/web/siscatalogo-acelerogramas). This benchmark is a statistical plausibility check in overlapping Mw-R ranges. But it is not a validation nor recalibration of seabed GMPEs in the IMR. The primary evidence supporting seabed GMPEs (HZ23, NT24, DKK24) remains their calibration on ocean‑bottom data (S‑net/KiK‑net) and the documented land-seafloor differences reported in the literature (e.g., Dhakal et al., 2021; Hu et al., 2023; Chen et al., 2015, 2024). This approach follows previous IMR hazard studies (e.g., Molina Palacios, 1998; Vilanova & Fonseca, 2004; Terrinha et al., 2009; Martínez Loriente et al., 2013; Somoza et al., 2021; Perea et al., 2023; Olaiz et al., 2025), which also relied on inland proxies due to the absence of seabed recordings. Therefore, this comparison should be interpreted as an acceptability check within the GMPEs magnitude-distance validity ranges, rather than a direct GMPE re-calibration. The scarcity of offshore strong-motion data underscores the need for OBS deployments to enable future seabed-specific GMPE validation in the IMR.”
Martínez‐Loriente, S., Gracia, E., Bartolome, R., Sallarès, V., Connors, C., Perea, H., ... & Zitellini, N. (2013). Active deformation in old oceanic lithosphere and significance for earthquake hazard: Seismic imaging of the Coral Patch Ridge area and neighboring abyssal plains (SW Iberian Margin). Geochemistry, Geophysics, Geosystems, 14(7), 2206-2231. https://doi.org/10.1002/ggge.20173
Molina Palacios, S. (1998). Sismotectónica y peligrosidad sísmica del área de contacto entre Iberia y África (Doctoral dissertation, Universidad de Granada). http://hdl.handle.net/10481/53680
Olaiz, A., Álvarez Gómez, J. A., De Vicente, G., Muñoz-Martín, A., Cantavella, J. V., Custódio, S., ... & Heidbach, O. (2025). Onshore and offshore seismotectonics of Iberia: an updated review. Solid Earth, 16(10), 947-1024. https://doi.org/10.5194/se-16-947-2025
Perea, H., Jiménez, M. J., Lozano, L., Gómez Novell, O., Canari Bordoy, A., García-Fernández, M., & García Mayordomo, J. (2023). Reassessing seismicity and seismic hazard in offshore areas: The case of the Alboran Sea (western Mediterranean). http://hdl.handle.net/10261/338277
Somoza, L., Medialdea, T., Terrinha, P., Ramos, A., & Vázquez, J. T. (2021). Submarine active faults and Morpho-Tectonics around the Iberian margins: seismic and tsunamis hazards. Frontiers in Earth Science, 9, 653639. https://doi.org/10.3389/feart.2021.653639
Terrinha, P., Matias, L., Vicente, J., Duarte, J., Luis, J., Pinheiro, L., ... & Matespro Team. (2009). Morphotectonics and strain partitioning at the Iberia–Africa plate boundary from multibeam and seismic reflection data. Marine Geology, 267(3-4), 156-174. https://doi.org/10.1016/j.margeo.2009.09.012
Vilanova, S. P., & Fonseca, J. F. (2004). Seismic hazard impact of the Lower Tagus Valley fault zone (SW Iberia). Journal of Seismology, 8(3), 331-345. https://doi.org/10.1023/B:JOSE.0000038457.01879.b0
Zhang, Q., & Zheng, X. Y. (2019). Offshore earthquake ground motions: Distinct features and influence on the seismic design of marine structures. Marine Structures, 65, 291-307. https://doi.org/10.1016/j.marstruc.2019.02.003
• The PGA values proposed in the manuscript are compared to “those obtained using input data files containing the information of the seismogenic sources (…) and the OQ Engine configuration and input files. These were used to calculate the ESHM20 hazard mapping scheme”. Despite the obscure formulation, it seems that the comparison is between the new values proposed in the manuscript and the values that the ESHM20 model would have shown if it extended to the IMR seabed. If this is the case, this seems an unwarranted application of the ESHM20 input data to obtain results for an area that its (ESHM20’s) authors did not include in their model.
(R): We have reframed this comparison. We now present a “baseline PSHA” computed with the published ESHM20 source model and GMPE logic tree as‑is (i.e., rock/onshore conditions), restricted to our study window, solely as a reference baseline to illustrate how seabed‑adapted GMPEs and bathymetry change PGA relative to a standard continental model. We explicitly state that these baseline maps are not ESHM20 products and should not be interpreted as an official extension of ESHM20 offshore. The text has been reworded to avoid any implication or misunderstanding of “extending” ESHM20 offshore or attributing the results to the ESHM20 consortium.
The title of section 5.4 will be changed to: “Distribution of PGA amplification relative to a baseline PSHA using the ESHM20 model (rock, onshore).”
The sentences on pages 583-587 will be replaced by:
“We computed a baseline PSHA using the published ESHM20 source model and GMPE logic tree exactly as released (rock/onshore site conditions), clipped to our study zone in the IMR, to provide a reference for how seabed-specific GMPEs and bathymetry alter PGA. These baseline results are not part of the official ESHM20 products and are used here strictly as a methodological contrast.”
In the legend for Figure 11, we will change “ESHM20” to “Baseline PSHA (ESHM20 model; rock)” and add the disclaimer sentence above in the caption.
Statements such as “the main input parameters in the classic DSHA (Reiter, 1990) are the maximum magnitude associated with the characteristic earthquake as the MCE for each seismic source area and a set of attenuation relationship or GMPEs” (lines 306-307) fail to capture, in my view, the essence of DSHA (standard DSHA doesn’t use source areas, identifying directly the capable geologic structure near the site whose rupture corresponds to the worst-case scenario).
(R): We agree our phrasing could misinform. Our deterministic implementation identifies the capable controlling source for each site (fault or areal zone) and computes the percentile of strong ground motion for the MCE of that source at the shortest distance under the selected distance metric (e.g., Rrup, Rjb). We revised Section 4.1 to remove the ambiguous “zone‑based” rephrasing and to state that DSHA can be performed with fault sources and, where appropriate, areal/background sources when faults are diffuse or unresolved, following Reiter (1990), Kramer (1996), and Krinitzsky (1995, 2002), already cited.
The sentence in lines 306-307 will be replaced with:
“In DSHA, the capable controlling source at a site (typically a mapped fault segment and, where faults are diffuse, an areal/background sources) identified. The maximum credible earthquake (MCE) for that source and an appropriate GMPE are then used to compute a chosen percentile (e.g., 50th or 84th) of ground motion at the shortest source‑to‑site distance under the adopted distance metric (Reiter, 1990; Kramer, 1996; Krinitzsky, 1995, 2002).”
Additionally, we will remove the term “zone based” in line 314 and rename Step (i) to “Build a catalogue of seismic sources (faults and, where needed, areal/background zones).”
In terms of implementation, the manuscript refers that “For DSHA calculations, a MATLAB© code has been developed to calculate the seismic intensity with a selected GMPE, from different seismic source types” (lines 326-438), and later add “MATLAB code [available] from the corresponding author upon reasonable request” (line 680). In my view this is not acceptable: if the code is not public, the results cannot be reproduced independently and therefore cannot be regarded as scientific. Preferably, the code developed in-house should be validated through separate publication before being used in an applied study.
(R): We agree that reproducibility is essential. We will (a) publish all DSHA MATLAB® scripts and configuration files used in this study as open source, and (b) include a minimal verification notebook that reproduces the example maps using a reduced grid. A permanent open DOI (via Zenodo) will be provided, and the link will be shared in the code availability section.
I found the extensive emphasis on PSHA/DSHA comparison a distracting tangent. As an example, statements to the effect that “the hazard maps obtained from deterministic and probabilistic estimations demonstrate a clear correlation: as the return period increases, PGA values calculated by PSHA increase and approach those obtained via DSHA” (line 548-550) are presented as a relevant conclusion of the study, whereas in my view they are a statement of what should be expected.
(R): Thanks for this comment. The comparison between DSHA and PSHA will be reduced largely and almost removed from the main text, retaining only what is necessary to motivate the specific seabed modeling choices.
Occasionally, the manuscript suggests a lack of command of basic aspects of seismic hazard assessment that is concerning given the focus of the study, and the apparent objective of being didactic, as suggested by the extensive theoretical considerations (as opposed to simply referencing standard texts). As examples:
• in line 386 the manuscript states that the GR recurrence parameter I can be “adjusted from the seismic catalog of the project using statistical techniques of least squares or maximum likelihood”. It was well established 45 years ago that least-squares should not be used for this purpose;
(R): We agree with the reviewer. We have removed the term “least squares” from the sentence and now indicate that we use maximum likelihood (with completeness assessment) for the GR parameters, in line with standard practice (e.g., McGuire, 2004; Kijko, 2019).
• Figure 7 displays logic trees with nodes where the sum of the weights largely exceeds unity;
(R): Thank you for this comment. We will implement a logic tree within the SHA using weighted GMPEs, based on statistical performance and regional relevance, in order to properly address epistemic uncertainty. We will rebuild the figure with weights summing to 1.0 at every node. The text will be updated accordingly.
• While describing Cornell’s method line 363-364), the manuscript states “having established the probability relationships that govern seismic events in a seismogenic area (point, fault plane, or spatial region) regarding the distribution of locations, sizes, and recurrence times, and knowing the past seismicity of the area”. The “probability relationships that govern seismic events” must be derived from the seismicity of the area, and therefore are not independent from it as the wording may suggest;
(R): Thanks for this comment. We rephrased the paragraph to reflect that those relationships are derived from regional seismicity and source characterization. Now, the paragraph reads as follows:
“The principles of PSHA find their roots in the seminal works of Cornell (1968), Cornell et al. (1971), and McGuire (1976). Cornell uses the total probability theorem (Kramer, 1996) to consolidate information on various variables (magnitude, distance, source location) into a single measure of seismic hazard for a specific site. Once established the probability relationships that govern independent seismic events in a seismogenic area it is possible to quantify the probability of exceeding a specific level of ground motion (Kijko, 2019). It takes into consideration the seismicity of the area from the distribution of locations, sizes, recurrence times and energy attenuation (Benito and Jiménez, 1999), to integrate the probabilities of exceeding a certain level of ground motion from various seismic sources, at different distances and with different magnitudes, that may occur at a site.”
• The manuscript states (lines 455-459) that “the findings of this study demonstrate the effectiveness of using both DSHA and PSHA methodologies to generate seismic hazard maps within the IMR. These maps are based on the most recent GMPEs specifically tailored for offshore environments and show statistically robust compatibility with the available seismic data”. This passage seems to suggest that the compatibility of the maps with the seismicity comes from the selection of GMPEs, apparently ignoring the fact that the seismic data determines the choice of area-source geometry, which in turn is reflected on the hazard maps (in this particular case both PSHA and DSHA use area sources).
(R): We agree with the reviewer. Therefore, we will revise that paragraph to make clear that compatibility with observed seismicity primarily reflects the source spatial model and its seismic parameters, while GMPEs govern the source-to-site attenuation term. Therefore, both are necessary.
To conclude, reading the manuscript I got the impression that the research set out to address the very relevant issue of seismic hazard assessment in the seabed of the IMR region, but lost its focus by venturing excessively into a discussion of the relative merits and demerits of PSHA versus DSHA. The DSHA code, which is the basis of a substantial part of the manuscript, is not shared, defeating the possibility of scrutiny. I am forced to conclude that in its current form the manuscript is not fit for publication. Should the authors consider rewriting it to try a subsequent submission, the attached pdf includes extensive comments on the passages that need improvement.
(R): Thank you for your comprehensive feedback. We acknowledge your concerns regarding focus and reproducibility, and we will take steps to address them in the revised manuscript:
We will substantially reduce discussion on the relative merits of PSHA versus DSHA, moving explanatory content to the Supplement. The main text will now focus on the core objective: seismic hazard assessment for seabed conditions in the IMR, emphasizing bathymetry, seabed-specific GMPEs, and implications for subsea infrastructure. The DSHA MATLAB© scripts and all configuration files will be open sourced in a repository.
Regarding the attached PDF, we reviewed the file and found that it pertains to a different manuscript. It appears this was included inadvertently. Therefore, we have relied exclusively on your comments provided in the current review and have addressed each point in our detail response. If there are specific passages in our paper that you intended to highlight for improvement, we would be grateful if you could confirm or resend the correct annotated document.
Thank you very much.
The authors
Citation: https://doi.org/10.5194/egusphere-2025-3248-AC2
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