Arias intensity and cumulative absolute velocity, often abbreviated as Ia and CAV, are not the household names of earthquake science that peak ground acceleration has become, but among engineers they are prized quantities. Arias intensity, introduced by the Chilean engineer Arturo Arias in 1970, measures the cumulative energy per unit weight absorbed by a simple oscillator subjected to a ground motion record, effectively capturing the total energy content of shaking over its entire duration. Cumulative absolute velocity, developed in the United States in the late 1980s as a criterion for judging whether a nuclear facility had experienced an earthquake exceeding its operating basis, sums the absolute acceleration over time and has proven a robust indicator of structural damage potential. Both measures are central to assessing landslide triggering, liquefaction, and the performance of buildings and infrastructure during prolonged shaking.

Despite their importance, most prediction equations for these intensity measures were built from onshore data. Offshore ground motions, recorded on the seafloor rather than on land, follow different propagation and site amplification rules, and treating them as interchangeable with onshore shaking can lead to serious misestimates of hazard for submarine cables, ports, coastal cities, and offshore infrastructure. The new study, led by Jingyang Tan and Xialei Zhu of China Three Gorges University together with Jinjun Hu and Yinan Zhao of the Institute of Engineering Mechanics, China Earthquake Administration, set out to close that gap for the Japan Trench region using data from the Seafloor Observation Network for Earthquakes and Tsunamis along the Japan Trench, known as S-net.

S-net, operated by the National Research Institute for Earth Science and Disaster Resilience, is the world’s largest cabled ocean-bottom monitoring network, spanning the trench that produced the devastating magnitude 9.0 Tohoku earthquake of 2011. The researchers assembled an exceptionally large dataset for offshore ground motion modeling: 28,950 three-component records from 150 ocean-bottom stations. These records captured 553 earthquakes across three tectonic families, including 130 subduction interface events, where the Pacific plate grinds beneath the Okhotsk plate; 243 slab earthquakes, occurring within the descending plate at depth; and 180 shallow crustal and upper mantle earthquakes. This breadth allowed the team to develop models covering the full range of earthquake mechanisms that threaten the region.

A central innovation of the study lies in how it characterizes the ground beneath each station. Rather than relying on geological maps, the team classified sites using the horizontal-to-vertical spectral ratio technique, or HVSR, which compares the amplitude of horizontal and vertical shaking at a site to reveal its resonant frequency, a fingerprint of soil stiffness and sediment thickness. This site classification scheme, applied uniformly across the ocean-bottom network, allowed the researchers to incorporate site effects directly into their prediction equations. The models account for the key explanatory variables that govern shaking: moment magnitude, rupture distance, focal depth, site class, and, uniquely for offshore settings, the installation condition of the seafloor instruments.

That last variable turned out to matter far more than anyone might have guessed. S-net stations come in different flavors: some instruments are buried in the sediment, while others sit unburied on the seafloor inside pressure vessels. The analysis revealed that the installation method significantly influences recorded Arias intensity and cumulative absolute velocity, with unburied stations exhibiting notably higher values. The likely culprit is the natural vibration of the instrument housing and its coupling with the soft seafloor, which can introduce amplification that is not representative of the true ground motion. For engineers using offshore records, this finding is a caution: ignoring installation conditions could inflate or deflate energy estimates and skew hazard calculations.

The site classification itself proved to be the study’s most valuable uncertainty-reducing tool. When site classes were explicitly included in the models, the model uncertainty, expressed statistically as the standard deviation of the residuals, dropped substantially compared with models that omitted site effects. By contrast, two other candidate explanatory variables, water depth and sedimentary thickness, had only negligible effects on model uncertainty. This is a practically important result, because it suggests that a relatively simple HVSR-based site classification captures most of the site-related variability in offshore energy measures, sparing modelers the difficulty of obtaining detailed sediment profiles from the deep ocean floor.

Comparing their offshore models with existing onshore equations revealed a systematic and physically meaningful difference. Offshore Arias intensity and cumulative absolute velocity exhibit a substantially greater energy accumulation effect than onshore ground motions at comparable distances and magnitudes. The researchers attribute this to amplification by soft seafloor sediments, the water-saturated, low-velocity materials that blanket much of the Japan Trench margin. Soft sediments lengthen the duration of shaking and concentrate seismic energy at low frequencies, inflating cumulative measures even when instantaneous peaks remain moderate. The finding echoes earlier comparisons of peak ground acceleration and response spectra between land and ocean-bottom stations in northeast Japan, but extends the picture to energy-based measures that are more directly tied to damage in flexible structures and to soil failure phenomena such as liquefaction.

Beyond the prediction equations themselves, the team developed spatial correlation models for offshore Arias intensity and cumulative absolute velocity. These geostatistical tools quantify how similar the shaking is at two sites separated by a given distance during the same earthquake, a quantity known as spatial correlation. In seismic risk analysis, spatial correlation governs whether damage concentrates in one neighborhood or spreads across an entire region, which is critical for estimating losses to distributed systems like power grids, pipelines, and transportation networks. By characterizing the spatial dependence of offshore energy measures for the first time in this region, the models enable more realistic simulations of earthquake scenarios that span both land and sea.

The practical reach of the new models extends across the earthquake engineering pipeline. Arias intensity feeds into empirical methods for predicting earthquake-induced landslide displacements through Newmark’s sliding block analysis, while cumulative absolute velocity underpins thresholds for structural damage and liquefaction assessment, including criteria originally developed for nuclear facilities and more recent applications to lateral spreading evaluation. With reliable offshore predictions of both measures, engineers can now assess hazards to submarine infrastructure, evaluate the seismic performance of coastal facilities, and refine probabilistic seismic hazard analyses for the densely populated Pacific coast of northern Japan. The researchers note that the models are applicable to the Japan Trench region and can serve as a reference for seismic hazard assessment in offshore areas more broadly, offering a template for other subduction zones, from Cascadia to Nankai, where ocean-bottom networks are expanding and the seafloor is no longer a blind spot in earthquake science.

Subject of Research: Development of offshore ground motion prediction models for Arias intensity and cumulative absolute velocity in the Japan Trench region using HVSR-based site classification

Article Title: A new ground motion prediction model for Arias intensity and cumulative absolute velocity in the Japan Trench region based on HVSR site classification

Article References: A new ground motion prediction model for Arias intensity and cumulative absolute velocity in the Japan Trench region based on HVSR site classification. (n.d.). https://doi.org/10.1007/s10518-026-02683-7

Image Credits: AI Generated

DOI: 10.1007/s10518-026-02683-7

Keywords: Arias intensity, cumulative absolute velocity, ground motion prediction, Japan Trench, S-net, ocean-bottom seismology, HVSR site classification, seismic hazard assessment, subduction earthquakes, site amplification, spatial correlation, offshore ground motion