Site-specific Ground Motion Research Articles

Site-specific seismic hazard and risk potential of Bengal Basin with emphasis on holistic seismic hazard microzonation and its structural impact assessment in the cities of Dhanbad and Mymensingh

The Bengal Basin located in the eastern part of the Indian subcontinent at the conjunction of the Eurasian, Indian, and Indo-Burma plates with two progressing deformation fronts viz. the Himalayas and the Indo-Burmese orogenic belts is one of the largest fluvio-deltaic to shallow marine sedimentary basin covered by alluvial plains of Holocene deposits extending from the Himalayas to the Bay of Bengal over thick younger alluvium comprising shallow layers of silt, clay, and sand that can have disastrous consequences due to site-specific ground motion amplification and liquefaction effects. The basin surrounded by Shillong and Assam plateaus in the Northeast is in the active tectonofabric of major active faults and lineaments triggering many devastating earthquakes in the past implicating the MM Intensity of VIII–XI in the near-source region causing widespread damage and destruction in the basin, thus bringing in the essence of assessing surface level seismic hazard and the risk imposed on the basin. Consideration of seismicity patterns, fault networks, and similarity in focal mechanisms yielded 49 areal seismogenic sources and additional active tectonic features in the 0–25 km, 25–70 km, and 70–180 km hypocentral depth ranges, which along with 14 ground motion prediction equations that include site-specific next generation spectral attenuation models pertaining to Northeast India, East-Central Himalaya, and Bengal Basin tectonic provinces yielded probabilistic peak ground acceleration (PGA) at engineering bedrock in the range of 0.08–0.58 g. Both the geophysical and geotechnical investigations at 6,000 sites provided effective shear wave velocity distribution in the range of 113–948 m/s on the geographical information system, thus classifying the basin into 11 site classes with “None” to “Severe” liquefaction hazard potential. A systematic non-linear/equivalent linear site response analysis and its spectral convolution with firm rock peak ground acceleration yielded surface-consistent hazard in the range of 0.09–1.17 g, thus opening up the issue of risk assessment and holistic seismic hazard microzonation of all the cities in the basin and their structural impact assessment using the SELENA-based capacity spectrum method on FEMA and BMTPC-regulated 11 model building types in the damage states of “none,” “slight,” “moderate,” “extensive,” and “complete” for all of those, however, in-depth studies carried out for Mymensingh and Dhanbad have been presented.

Correlation between SPT-N and shear wave velocity (VS) and seismic site classification for Amaravati city, India

The present study proposes a set of correlations between standard penetration number (SPT-N) and shear wave velocity (VS) using nonlinear regression analysis. These correlations have been developed for different categories of soil for Amaravati city. This study area is the current de facto seat of government of the Indian state of Andhra Pradesh, India. For this study, SPT-N data has been obtained from 400 boreholes distributed across the city of area 217.23 km2. Most of the boreholes considered for this study have a boring depth of 25 m to 45 m below the recorded ground surface. A comparison between the proposed correlations with existing worldwide accepted correlations has been performed to check the authenticity of this study. In addition to this, Vs obtained from the recommended correlations have been validated with the Vs obtained from 30 microtremor tests as well as established graphical methods. Furthermore, the seismic site classification of the study area has been conducted using the developed correlation for all soils. It is observed that the major part of Amaravati city falls under class D as per the National Earthquake Hazard Reduction Program (NEHRP) provisions. The average SPT-N and VS distribution across the city has also been generated at depths of 5, 10, 15, 20, 25, and 30 m. The outcomes of the study can be further used for the design of earthquake-resistant structures, seismic hazard studies, estimation of ground movements, and generation of site-specific synthetic ground motions.

Macroseismic intensity hazard maps for Italy based on a recent grid source model

Seismic hazard maps from probabilistic seismic hazard analysis or PSHA collect, at different sites, the values of the (site-specific) ground motion intensity measures of interest that, taken individually, have the same exceedance return period. For large-scale analyses, a widely used intensity measure is the macroseismic (MS) intensity, that provides an assessment of the earthquake effect based on the observed consequences in the hit area. Hazard maps can be developed in terms of MS intensity, and some examples exist in this respect. In the case of Italy, the last MS hazard map is based on the same seismic source model (known as MPS04) adopted to derive the design seismic actions of the current building code, a study dating more than ten years ago. It provides results in terms of countrywide Mercalli–Cancani–Sieberg (MCS) intensity level with 475 years return period. This short paper presents and discusses MCS probabilistic seismic hazard maps for Italy based on a recent grid-seismicity source model, herein named MPS19, synthetizing the large effort of a wide scientific community. The results, which are obtained by means of classical PSHA, are given in the form of maps referring to the 475 years return period, and also others of earthquake engineering interest. Moreover, it is discussed that the return period does not univocally identifies the MS intensity because, although MS is, by definition, a discrete random variable, it is modelled, in a given earthquake, by means of a normal distribution, that is, treated as continuous. Thus, the maps of the minimum return period causing the occurrence or exceedance of different MCS intensities are also provided. Finally, the comparison between the 475 years return period hazard map presented and the one which is currently the point of reference in Italy, that is, computed using MPS04, is briefly discussed. All the computed maps are made available to the reader as supplemental material.

Semi-empirical estimation of the Zagreb ML 5.5 earthquake (2020) ground motion amplification by 1D equivalent linear site response analysis

The 22 March 2020 Zagreb ML 5.5 earthquake ground shaking resulted in damage to buildings and infrastructure. The most affected buildings were older and cultural heritage buildings (built before 1963) in the old city centre with significant damage extent in the epicentral zone (southeastern foothills of Medvednica Mt.). This study presents site response analysis on the realistic site profiles from the epicentre towards the accelerometric stations QUHS and QARH and comparison with strong motion data recorded during the Zagreb 2020 earthquake. Semi-empirical estimation of the ground motion amplification (i.e., peak ground acceleration at surface) showed that modelled and recorded values are comparable. Moreover, we present 2D model of peak ground acceleration at surface (PGAsurf ) variation for the superimposed site profile from the epicentre towards two accelerometric stations. Ground motion amplification for the Zagreb ML 5.5 earthquake scenario showed that PGAsurf is larger by a factor of 2 than the bedrock value (approx. 0.35 g in the epicentre and 0.20 g on the 12 km distant accelerometric station). This study is a contribution to better understanding of the Zagreb ML 5.5 earthquake effects and significance of local site effects in the damage extent, something that combined with older and heritage buildings resulted in high economic consequences. Therefore, it is important that site-specific ground motion simulation and seismic microzonation of the Zagreb continues with installation of an accelerometric array. This is very important for earthquake retrofitting and resilience of the low, mid- and high-rise buildings with particular care of cultural and historical buildings as well for the further urban planning.

On the Development of Region and Site-Specific Ground Motion Prediction Model for the Region of I-Lan, Taiwan

On the Development of Region and Site-Specific Ground Motion Prediction Model for the Region of I-Lan, Taiwan

Broadband ground motion simulations for Northeast India

This study presents broadband (BB) ground motions for two historical earthquakes (Mw ≥ 8) in Northeast (NE) India. We apply a recently developed geology-based 3D velocity model of the Northeastern region (NER) to simulate low frequency (LF) ground motions (f < 1Hz). These synthetics are further combined with high frequency (HF) scattering wave-fields (f > 1Hz) using a hybrid approach, thus yielding BB ground motions (0.1–10Hz). First, we calibrate the 3D model and scattering parameters by comparing the simulated ground motions against recorded data available for four events (Mw 5.2, Mw 5.5, Mw 6.3, and Mw 7.2) in NE India. Our results indicate that the variability of the bias for spectral acceleration (SA) lies within limits [-1,1] for all four events. From the statistical analysis of the ground motion, we also observe that the hybrid approach gives a realistic estimation of site-specific BB ground motion and consistently reproduces the prominent features of the observed motions up to 10Hz at most of the stations. Next, we simulate a suite of BB ground motions to estimate ground motion intensities for two historical earthquakes (viz., 1897 Assam event, 1950 Assam event) in NE India. Our results indicate that the variations in the ground motion intensities at hard rock and soft soil sites are manifestations of the local geology and surface topography incorporated in the 3D regional velocity model. We also observe that the peak ground acceleration (PGA) for both events exceed 1 g in the epicentral region. The BB ground motions obtained from this approach will be useful to engineers in seismic design and site-specific hazard estimation.

BASE-ROCK ELEVATION MEASUREMENT USING SINGLE AND ARRAY MICROTREMOR INVESTIGATION

Site-specific ground motion analysis is a method for developing surface ground motion and surface spectral acceleration models. The analysis is performed by conducting propagation analysis from base-rock to surface elevation. The important information needs for site-specific ground motion analysis is the position of base-rock or bedrock below the surface level. This paper presents the investigation results of base-rock elevation at the Diponegoro University Semarang, Indonesia. The background reason for the base-rock investigation of this university area is because this area is located close to three seismic sources (Semarang, Lasem and Demak shallow crustal faults). Seismic microzonation caused by all three seismic source scenarios are still on-going. One of the important analysis used for seismic microzonation at the study area is site-specific ground motion analysis. The base-rock elevation prediction in the study area was performed using a combination of single and array microtremor tests and soil boring investigations. The base-rock elevation prediction developed using microtremor tests was verified using the soil profile developed from soil boring investigation. Based on soil boring and microtremor investigations, the base-rock elevation at the university area was predicted at 30 to 60 m below the surface level.

Seismic fragility analysis of a coupled tank-piping system based on artificial ground motions and surrogate modeling

The catastrophic consequences of recent NaTech events triggered by earthquakes highlighted the inadequacy of standard approaches to seismic risk assessment of chemical process plants. To date, the risk assessment of such facilities mainly relies on historical data and focuses on uncoupled process components. As a consequence, the dynamic interaction between process equipment is neglected. In response to this gap, researchers started a progressive integration of the Pacific Earthquake Engineering Research Center (PEER) Performance-Based Earthquake Engineering (PBEE) risk assessment framework. However, a few limitations still prevent a systematic implementation of this framework to chemical process plants. The most significant are: (i) the computational cost of system-level simulations accounting for coupling between process equipment; (ii) the experimental cost for component-level model validation; (iii) a reduced number of hazard-consistent site-specific ground motion records for time history analyses.In response to these challenges, this paper proposes a recently developed uncertainty quantification-based framework to perform seismic fragility assessments of chemical process plants. The framework employs three key elements: (i) a stochastic ground-motion model to supplement scarcity of real records; (ii) surrogate modeling to reduce the computational cost of system-level simulations; (iii) a component-level model validation based on cost-effective hybrid simulation tests. In order to demonstrate the potential of the framework, two fragility functions are computed for a pipe elbow of a coupled tank-piping system.

Simulation of building damage distribution in downtown Mashiki, Kumamoto, Japan caused by the 2016 Kumamoto earthquake based on site-specific ground motions and nonlinear structural analyses

Most of the buildings damaged by the mainshock of the 2016 Kumamoto earthquake were concentrated in downtown Mashiki in Kumamoto Prefecture, Japan. We obtained 1D subsurface velocity structures at 535 grid points covering this area based on 57 identified velocity models, used the linear and equivalent linear analyses to obtain site-specific ground motions, and generated detailed distribution maps of the peak ground acceleration and velocity in Mashiki. We determined the construction period of every individual building in the target area corresponding to updates to the Japanese building codes. Finally, we estimated the damage probability by the nonlinear response model of wooden structures with different ages. The distribution map of the estimated damage probabilities was similar to the map of the damage ratios from a field survey, and moderate damage was estimated in the northwest where no damage survey was conducted. We found that both the detailed site amplification and the construction period of wooden houses are important factors for evaluating the seismic risk of wooden structures.

Dynamic tests of the collapse-prevention performance of a low-ductility low-rise steel concentrically braced frame

In past earthquakes, low-ductility steel concentrically braced frame (CBF) buildings have been observed to retain reserve capacity after brace fracture. The failure mechanisms and earthquake ground motion-sensitive characteristics of the reserve system of low-ductility CBFs are not understood due to limited dynamic experimental data. In this study, a series of shaking table tests is presented to examine the reserve capacity of a scaled two-bay, three-story, low-ductility CBF model in which a pair of square hollow section braces are arranged in a chevron pattern. The model structure was repeatedly subjected to two unidirectional ground motions with successively increasing magnitudes in a stiff soil site and a soft soil site. The experimental phenomena of elastic response, brace buckling behavior, brace reengagement behavior, reserve system response and collapse state were observed. The braces of the low-ductility CBFs were vulnerable to local buckling under dynamic loads and resulted in a soft story where braces failed, while braces and frames in the other stories had no further damage. The reserve stiffness, rather than energy dissipation or reserve strength, was the most important factor in the collapse-prevention capacity for the reserve system of the tested low-ductility CBF, and the lateral stiffness of the columns was the main source of reserve stiffness. Flexible reserve systems with small lateral stiffness were never significantly excited at their natural periods by hard soil site-specific ground motions, while with such systems, a greater risk of potential collapse appears to be posed due to earthquakes at soft soil sites than at hard soil sites for the test model.

Experimental study on longitudinal seismic damage progress and failure mode of a three-tower extradosed bridge

To understand the longitudinal seismic damage progress and failure mode of extradosed bridges, an experimental investigation was conducted on a 1/20 scaled shake table test model. Detailed design of the test model is firstly introduced. During the experimental investigation, the test model was longitudinally subjected to the site-specific artificial ground motion with the peak ground acceleration (PGA) ranging from 0.1 g to 1.5 g. Test results show that the seismic damage progress of the extradosed bridge could be categorized into four stages: (1) No damage (PGA = 0.1 g − 0.3 g); (2) Mild damage (PGA = 0.4 g − 0.6 g); (3) Moderate damage (PGA = 0.7 g − 1.2 g); (4) Severe damage (PGA = 1.3 g − 1.5 g). The bottom and top regions of four-column piers are earthquake-vulnerable regions, while short towers are not. The failure mode of the test model could be characterized by buckling of the rebar and crushing of the core concrete at the bottom region of four-column piers. Moreover, unlike conventional cable-stayed bridges, the longitudinal deformation of the short tower is quite small in each loading case, and the residual longitudinal displacement of the test model is negligible after the whole tests.

A database of seismic designs, nonlinear models, and seismic responses for steel moment-resisting frame buildings

A number of simplified methodologies have been developed and used to estimate seismic drift demands in buildings. However, none of them have been systematically tested against a large number of buildings subjected to a diverse set of ground motions. This is partly attributed to the lack of existing databases of building designs, nonlinear structural models, and simulated seismic responses. This article introduces the development of a comprehensive database, which includes 621 special steel moment-resisting frames designed in accordance with modern codes and standards and their corresponding nonlinear structural models and seismic responses (i.e. peak story drifts, peak floor accelerations, and residual story drifts). The seismic responses for a subgroup of 100 steel moment-resisting frames subjected to three groups of site-specific ground motions (with 40 records each), at the service-level, design-based, and maximum considered earthquakes, are also included. The database has been utilized by the authors (in a separate study) to evaluate the performance of existing methods and develop data-driven and hybrid (combination of mechanics-based and data-driven) models for estimating seismic structural drift demands. The database can also be utilized in the development and implementation of a performance-based analytics-driven seismic design methodology.

Seismic risk assessment of on-ground circular reinforced concrete and prestressed concrete water tanks using stochastic ground motion simulations

This case-study is dedicated to the seismic risk assessment of cylindrical fixed-based reinforced concrete and prestressed concrete water tanks situated in Romania. The fixed-based water tanks are designed according to the current seismic design prescriptions in Romania. The six selected sites are all under the influence of the Vrancea intermediate-depth seismic source. The seismic performance is evaluated using site-specific ground motion stochastic simulations and using the approach given in Eurocode 8-4 (2006). The largest mean annual failure probabilities are obtained for the two sites (Amara and Bucharest) with the highest long-period spectral amplifications. The study shows that from the strength point of view, the two types of tanks have very small corresponding failure probabilities and from the serviceability point of view, depending on the type of the tank and its position, sloshing or cracking due to bending are the prevalent failure modes.

Seismic Isolation Retrofitting of Typical Multi-Span Steel Girder Bridges in New York State

Many of the existing multi-span simply supported bridges in New York State, U.S., are susceptible to earthquake damage and need to be retrofitted to reduce their seismic risk. In this study, seismic retrofit of a five-span simply supported bridge with typical high-type fixed and expansion steel rocker bearings is conducted. A refined three-dimensional (3D) finite element model of the bridge is developed in ANSYS by considering foundation impedances. Multi-support time history analyses have been implemented in the seismic retrofit design for two levels of ground motions: 1,000- and 2,500-year return period earthquakes. The site-specific ground motions with consideration of the spatial variation are generated based on the geotechnical information. Seismic retrofit by replacing existing steel bearings with lead-rubber bearing (LRB) isolators has been adopted. The parameters of the isolators are determined by considering factors such as the seismic performance and translational resistance during normal service. The vulnerability of structural members and seismic retrofit effectiveness are quantified by the demand-to-capacity (D/C) ratio for the combined demands at the extreme limit state. The analyses show that after seismic isolation retrofit the pervasive vulnerabilities in pier columns and cap beams are eliminated. Comparing with strengthening the vunerable structural members, seismic isolation is proved a cost-effective retrofit solution. The overall seismic isolation design and analysis procedures presented in this study can help guide future seismic retrofit of similar types of bridges.

Repeatable Source, Path, and Site Effects from the 2019 M 7.1 Ridgecrest Earthquake Sequence

ABSTRACTWe use a large instrumental dataset from the 2019 Ridgecrest earthquake sequence (Rekoske et al., 2019, 2020) to examine repeatable source-, path-, and site-specific ground motions. A mixed-effects analysis is used to partition total residuals relative to the Boore et al. (2014; hereafter, BSSA14) ground-motion model. We calculate the Arias intensity stress drop for the earthquakes and find strong correlation with our event terms, indicating that they are consistent with source processes. We look for physically meaningful trends in the partitioned residuals and test the ability of BSSA14 to capture the behavior we observe in the data.We find that BSSA14 is a good match to the median observations for M&amp;gt;4. However, we find bias for individual events, especially those with small magnitude and hypocentral depth≥7 km, for which peak ground acceleration is underpredicted by a factor of 2.5. Although the site amplification term captures the median site response when all sites are considered together, it does not capture variations at individual stations across a range of site conditions. We find strong basin amplification in the Los Angeles, Ventura, and San Gabriel basins. We find weak amplification in the San Bernardino basin, which is contrary to simulation-based findings showing a channeling effect from an event with a north–south azimuth. This and an additional set of ground motions from earthquakes southwest of Los Angeles suggest that there is an azimuth-dependent southern California basin response related to the orientation of regional structures when ground motion from waves traveling south–north are compared with those in the east–west direction. These findings exhibit the power of large, spatially dense ground-motion datasets and make clear that nonergodic models are a way to reduce bias and uncertainty in ground-motion estimation for applications like the U.S. Geological Survey National Seismic Hazard Model and the ShakeAlert earthquake early warning System.

A Generalization of the Stochastic Summation Scheme of Small Earthquakes to Simulate Strong Ground Motions

A generalization of the stochastic summation scheme of small earthquakes following a general form of the source spectrum (ω−n) model is developed to estimate the proper probability density functions for rupture propagation over the fault and to simulate site-specific strong ground motions in two independent stages. The probability density functions for rupture propagation are first developed for a single-corner-frequency source model, and then extended to multiplicative and additive double-corner-frequency source models to partially account for the effects of finite-fault rupture such as fault geometry, rise time, and rupture time on ground motions, and to better match observed Fourier amplitude spectra (FAS). The generalized two-stage stochastic summation scheme developed in this study can be used to simulate realistic strong-ground-motion time histories from small events, represented as empirical Green’s functions (EGFs), by specifying only two source parameters of the seismic moment and stress drop for a given site. The proposed two-stage stochastic summation schemes are tested using numerical examples following the theoretical source models as well as observed ground motions of the 2011 Mw 9.0 Tohoku earthquake in Japan and the 1994 Mw 6.7 Northridge earthquake in California to verify the applicability of the approach. Comparisons between the observed and simulated time histories for these two earthquakes, their response spectra, and FAS show satisfactory performance of the proposed approach for engineering purposes. The results of these comparisons indicate that the proposed stochastic summation of small events as EGFs can adequately replicate observed ground motions and evaluate uncertainties in ground motions with the generation of many time history realizations corresponding to a multitude of possible rupture processes . The proposed approach can also be used to generate multiple realistic acceleration time histories matched on average to the target response spectra for use in earthquake performance design, and to develop ground-motion models for low-seismicity regions, where there is a lack of recording of strong ground motions.

Empirical Green’s Function Simulations Toward Site-Specific Ground Motion Prediction in Vietnam

Vietnam has a low-to-moderate seismicity, but the currently available strong ground motion data used as a basis for a seismic-resistant design are insufficient. Generally, to overcome this issue, strong ground motions recorded at other places around the world are used, which have similar seismic, tectonic and physical earthquake characteristics, such as earthquake magnitude, source model, distance to the source, tectonic geological conditions, and soil conditions. However due to different path effects and site effect, if applied to the site-specific studies in Vietnam, the above approach would generate certain errors. Therefore, it is important to obtain strong ground motion data that are applicable for seismic design of constructions in a particular region. Especially, it is important to adhere to strict seismic design requirements for facilities, such as hydropower, thermal, and nuclear power plants. One of the most interesting solutions is the theory of simulating the waveforms of strong earthquakes commonly known as the empirical Green’s function. The empirical Green’s function is a useful tool for estimating the ground motions produced by large earthquakes using small earthquake records. The basic idea of the method is that these small events data already incorporate the information of the propagation path and the local site effects. Ground-motion simulations essentially use these small events as an empirical Green’s function and add them following the scaling law based on the omega-square model. In this article, we simulate design basis ground motion for the Song Tranh 2 hydropower dam as an example. We have applied the empirical Green’s function method to predict broadband ground-motion time histories for several M5.5, one M5.7, and one M5.9 earthquake scenarios at the dam site based on M4.6 observed ground motions without/with considering radiation pattern corrections. The results confirm that strong ground-motion simulations are applicable to seismic hazard assessment in Vietnam. Once we obtain accurate source parameters, the site-specific synthetic ground motions of the earthquake scenarios can be used for seismic design safety in Vietnam.

Modeling nonlinear site effects in physics-based ground motion simulations of the 2010–2011 Canterbury earthquake sequence

This study examines the performance of nonlinear total stress one-dimensional (1D) wave propagation site response analysis for modeling site effects in physics-based ground motion simulations of the 2010–2011 Canterbury, New Zealand earthquake sequence. This approach explicitly models three-dimensional (3D) ground motion phenomena at the regional scale, and detailed site effects at the local scale. The approach is compared with a more commonly used empirical VS30-based method of computing site amplification for simulated ground motions, as well as prediction via an empirical ground motion model. Site-specific ground response analysis is performed at 20 strong motion stations in Christchurch for 11 earthquakes with 4.7≤ MW≤7.1. When compared with the VS30-based approach, the wave propagation analysis reduces both overall model bias and uncertainty in site-to-site residuals at the fundamental period, and significantly reduces systematic residuals for soft or “atypical” sites that exhibit strong site amplification. The comparable performance in ground motion prediction between the physics-based simulation method and empirical ground motion models suggests the former is a viable approach for generating site-specific ground motions for geotechnical and structural response history analyses.

Site-specific ground motion modeling for a historical Cairo site as a step towards computation of seismic input at cultural heritage sites

Throughout time, the area of historical Cairo has been affected by several earthquakes from near and distant seismogenic zones. The maximum earthquake intensity reported in Cairo is VII, on the Modified Mercalli Intensity scale, due to the 1992 Cairo earthquake (Mw=5.9). About 212 Coptic and Islamic monuments were damaged. The spatial distribution of damage, suggests the occurrence of strong local site effects in combination with high vulnerability of the cultural heritage buildings. This study presents the application of a novel seismic hazard analysis approach at a local scale based on physics-based ground motion simulations. A site-specific multi-scenario seismic input (ground motion time histories and response spectra) is computed at a heritage building in Cairo, considering the local site effect. The seismic input is calculated in three steps: a regional scale analysis followed by a site-specific analysis and the combinations of the computed scenarios ground motion. In the regional scale analysis synthetic accelerograms are computed at the site bedrock. Then, the site-specific analysis is performed to calculate the site surface ground motions or response spectra considering the local site effect. Three earthquake scenarios have been considered, characterized by different locations, magnitudes, and fault configurations. The last step consists in the combination of the computed scenario ground motion into one single multi-scenario seismic input specific for the site of interest. This input is represented by spectral ordinates and their variability. For the engineering purpose of time history analysis, the method allows also to extract the computed site specific physics-based accelerograms, requiring no amplitude scaling nor filtering by magnitudes, distances, or site classifications, as usually done with real ground motion records.

Point to Note of Site-Specific Ground Motion Prediction Using a Revised Empirical Relation Formula for the Hypothetical Nankai Trough Earthquake

Point to Note of Site-Specific Ground Motion Prediction Using a Revised Empirical Relation Formula for the Hypothetical Nankai Trough Earthquake