📄 earth science

An empirical vertical-to-horizontal (V/H) spectral ratio model for shallow-crustal and upper-mantle earthquakes: insights from the S-net seafloor stations in the Japan Trench region

This study presents an empirical vertical-to-horizontal (V/H) spectral ratio model for offshore ground motions in the Japan Trench region, derived from S-net seafloor stations, which reveals that offshore V/H ratios are significantly lower than onshore values due to water-layer attenuation and are strongly influenced by factors such as rupture distance, burial conditions, and site class.

Original authors: Shili Sheng, Jingyang Tan, Qinghui Lai, Qi Zhang

Published 2026-09-30

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CC BY 4.0

Original authors: Shili Sheng, Jingyang Tan, Qinghui Lai, Qi Zhang

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

When an earthquake strikes, the ground does not just shake side to side; it also jolts up and down. Engineers designing buildings, bridges, and offshore platforms must account for this vertical motion, as it can be just as destructive as the horizontal shaking. To understand how strong this upward force might be, scientists look at the ratio between the vertical and horizontal shaking. On land, this relationship is well understood, but the ocean presents a different story. Water is not solid ground; it is a fluid layer that sits between the earth's crust and the sensors placed on the seafloor. This layer changes how seismic waves travel, often dampening the vertical jolts in ways that land-based models cannot predict. For decades, engineers designing offshore structures have had to rely on land-based rules of thumb, a practice that might be either too conservative or dangerously inaccurate.

A team of researchers set out to replace these guesses with hard data, focusing on the vast network of sensors known as S-net, which lines the floor of the Japan Trench. This region is a hotspot for powerful earthquakes, where the oceanic crust dives beneath the continental plate. The researchers gathered thousands of recordings from these seafloor stations, capturing the shaking from both shallow crustal quakes and deeper events within the upper mantle. They carefully sorted this data, separating sensors that were buried in trenches dug into the seabed from those sitting directly on the ocean floor, and they categorized the seafloor itself based on how it vibrates. By analyzing the relationship between the up-and-down and side-to-side shaking across this massive dataset, they aimed to build a new, accurate model specifically for the ocean environment.

The results revealed a clear and significant difference between the ocean and the land. The vertical shaking measured on the seafloor was consistently much weaker than what is observed on land, particularly for the rapid, high-frequency jolts that occur in the first split second of an earthquake. The water layer acts as a filter, absorbing much of this vertical energy before it reaches the sensors. In fact, the vertical shaking offshore was often only half as strong as the vertical shaking recorded on land for the same earthquake. This finding suggests that using land-based models for offshore design could lead to overestimating the vertical forces, potentially resulting in unnecessarily expensive or overly heavy structures.

Beyond confirming that the ocean dampens vertical motion, the study uncovered how various factors change this relationship. The researchers found that the distance from the earthquake matters; as the seismic waves travel further across the ocean floor, the ratio of vertical to horizontal shaking tends to increase. The depth of the earthquake also plays a role, with deeper quakes showing a different pattern of vertical shaking compared to shallower ones. Perhaps most importantly, the study highlighted that the condition of the seafloor station itself changes the measurements. Sensors buried in the seabed recorded different vertical shaking patterns compared to those sitting on top of the sediment, especially during the initial, rapid jolts. The team also developed a way to classify the seafloor sites based on their natural vibration frequencies, allowing for more precise predictions of how different types of ocean floors will respond to an earthquake.

When the researchers compared their new ocean-specific model against existing models used for land, the differences were stark. The land-based models predicted much higher vertical shaking than what the ocean sensors actually recorded. This confirms that the physics of the ocean environment cannot be ignored. The new model provides a tailored tool for engineers and scientists, offering a realistic picture of how the seafloor moves during an earthquake. By understanding that the water layer significantly reduces the vertical jolt, and by accounting for the specific conditions of the seafloor and the distance from the quake, this work offers a more reliable foundation for designing safe and efficient offshore structures in one of the world's most seismically active regions.

Technical Summary: An Empirical Vertical-to-Horizontal (V/H) Spectral Ratio Model for Shallow-Crustal and Upper-Mantle Earthquakes in the Japan Trench Region

Problem Statement
While offshore seismic observation networks have expanded globally, there remains a pressing need for offshore-specific seismic design provisions. Significant discrepancies exist between offshore and onshore ground motions, particularly regarding vertical-component amplitude and the vertical-to-horizontal (V/H) spectral ratio. Previous studies indicate that offshore vertical ground motions are systematically attenuated relative to onshore motions, especially in the short-period range, due to the suppressive effect of the water column. However, existing V/H prediction models are predominantly derived from onshore strong-motion records. The applicability of these onshore models to offshore environments is questionable, and the specific influences of source, path, and site conditions on offshore V/H ratios—particularly using data from the extensive S-net (Seafloor Observation Network for Earthquakes and Tsunamis) along the Japan Trench—have not been sufficiently investigated.

Methodology
This study develops an empirical V/H spectral ratio model for shallow-crustal and upper-mantle earthquakes in the Japan Trench region using 9,892 ground-motion records from 150 S-net ocean-bottom stations. The methodology involved the following steps:

Data Processing and Selection: Records were screened to exclude sensors with rotation angles >0.1°, those with waveform errors, or low signal-to-noise ratios (SNR < 3) in the 0.1–20 Hz range. Only events with $M_w \ge 4.0$ and at least three high-quality three-component records were retained.
Site Classification: Due to the unavailability of conventional $V_{S30}$ data for ocean-bottom stations, the study utilized a site classification scheme (SC1–SC4) based on the predominant frequency ( $T_n$ ) identified via the Horizontal-to-Vertical Spectral Ratio (HVSR) method. Stations were further categorized by burial condition (buried in trenches <1500m depth vs. unburied on the seafloor >1500m depth).
Model Formulation: An empirical model was constructed using a random-effects regression approach. The functional form includes:
- Source Term: Incorporates moment magnitude ( $M_w$ ), focal depth ( $h$ ), and fault mechanism (normal, reverse, strike-slip). A linear magnitude term was selected based on regression analysis.
- Path Term: Characterizes geometric spreading using rupture distance ( $R_{rup}$ ). The study investigated a magnitude-distance interaction term but excluded it from the final model due to inconsistent statistical significance across periods and to maintain model parsimony.
- Site Term: Three formulations were tested using the Akaike Information Criterion (AIC). The optimal formulation utilized site class indicators ( $SC_i$ ) and burial condition indicators ( $S_b, S_u$ ) multiplied by the natural logarithm of the site fundamental frequency.
Validation: Model performance was evaluated through between-event ( $\tau$ ) and within-event ( $\sigma$ ) residual analyses. The model was also benchmarked against established onshore V/H models (Bommer et al., 2011; Pezeshk et al., 2022; Tan and Hu, 2021).

Key Contributions and Results
The study yields a regionalized V/H prediction model and several key findings regarding offshore ground motion characteristics:

Offshore vs. Onshore Discrepancy: Offshore V/H spectral ratios are generally significantly lower than onshore ratios, particularly in the short-period range. Offshore V/H values typically range from 0.15 to 0.50, approximately half of onshore values. This supports the hypothesis that the water layer attenuates high-frequency vertical components.
Magnitude and Focal Depth Effects: The effect of moment magnitude exhibits clear period dependence. Focal depth shows an attenuating effect primarily in the intermediate- and long-period ranges ( $T > 0.12$ s), where V/H ratios decrease as depth increases.
Rupture Distance and Path Effects: Offshore V/H ratios tend to increase with increasing rupture distance. This distance dependence becomes more pronounced at longer periods ( $T > 1.0$ s).
Burial Conditions: Station burial conditions exert a significant influence. For periods $T < 0.7$ s, buried stations generally exhibit higher V/H ratios than unburied stations. Conversely, for $T > 1.0$ s, V/H ratios decrease progressively from site class SC1 to SC4 regardless of burial condition.
Fault Mechanism: Normal-faulting events generally produce higher V/H ratios compared to reverse- and strike-slip-faulting events.
Model Performance: The proposed model demonstrates low within-event and total standard deviations. Residual analysis confirms that the model is unbiased with respect to magnitude, focal depth, rupture distance, and the site classification parameters used.

Significance
The paper asserts that the proposed empirical model provides a necessary reference for offshore seismic hazard assessment and the seismic design of offshore structures, specifically addressing the vertical component of ground motion. The study demonstrates that onshore V/H prediction models systematically overestimate the vertical ground motion proportion in offshore environments, particularly for high-frequency measures like PGA. Consequently, the authors conclude that onshore models cannot be directly applied to offshore engineering without modification. The developed model, grounded in the extensive S-net dataset, offers a more accurate basis for predicting offshore V/H spectral ratios by explicitly accounting for the unique source, path, and site effects of the Japan Trench region.

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