Ground Motion Data Research Articles

Rapid mapping of seismic intensity assessment using ground motion data calculated from early aftershocks selected by GIS spatial analysis

Following a major earthquake, disaster information services must deliver accurate damage assessment results during the emergency ‘black box’ phase when data is scarce. Seismic intensity maps contain crucial information for determining the damage in the affected area. For earthquakes with Mw between 5.5 and 7, this study proposes using GIS analysis to mine aftershock events in early aftershock sequences that are closely related to the mainshock fault, and then using these events to generate seismic intensity assessment maps. Regression curves were first obtained using a nonparametric method (rLowess) to analyse the geographical coordinates of early aftershocks. Then, a buffer of 1 or 1.5 km radius was made for the curve, and the aftershocks in the buffer were used to calculate the predicted peak ground velocity (PGV) values over a specific km-grid range. Finally, rapid mapping of seismic intensity was assessed based on the intensity scale. This straightforward and repeatable method employs seismic station data obtained shortly after the mainshock. The assessed seismic intensity accurately reflects the location and extent of the hardest hit areas and can be cross-referenced with geophysical results to accurately assess the damage in the affected areas.

Quantification of amplitude modulation of wind turbine emissions from acoustic and ground motion recordings

Amplitude modulation (AM) is a common phenomenon associated with wind turbine (WT) related noise annoyance. Within the interdisciplinary project Inter-Wind, acoustic, ground motion, and meteorological data are captured to be evaluated with noise reports of residents living near a wind farm in Southern Germany. The recorded data builds a solid data base for the evaluation of AM. The occurrence of AM is detected within acoustic and ground motion data and set in relation to all available data, including WT operational parameters, meteorology, and noise reports. In this study, the origins of detected AM are tones at 57.8 Hz and 133 Hz, related to the generator and drive train, which are amplitude modulated by the blade passing frequency. AM detection was successful both with acoustic as well as ground motion data. A comparison of a method for AM detection developed by the Institute of Acoustics (IOA reference method) with a method specifically developed to detect AM in ground motion data showed that the reference method detected AM three to six times more often than the newly developed method. AM occurred most likely during stable atmospheric conditions, with a positive lapse rate, and was (albeit to a small degree) more likely to be detected when residents reported higher levels of annoyance.

Comparative study of the simulation ground motion by amplitude scale and spectral matching

Dynamic analysis is more accurate than static analysis in determining a response of structure due to earthquake loads. The limitation of this analysis is the lack of recorded ground motion data of an earthquake for the entire territory of Indonesia. Therefore, according to the Indonesian Code, it is permitted to use seismic data from other locations that have similar seismic characteristics. In application, ground motions need to be modified to match the Indonesia design code. There are two modification methods, which are amplitude scaling and spectral matching. Thus, the purpose of this study is to determine the reliability of these two methods. As the result, the response spectra of the ground motion modified by the spectral matching method present a similar pattern to the target response spectra compared to the amplitude scaling method. Ground motions modified by the spectral matching method generate Peak Ground Acceleration (PGA) values almost the same as the target PGA values. In contrast, the modified motions with amplitude scaling provide diverse PGA values that are not the same as the target PGA. From this study, the utilization of the spectral matching method is recommended in modifying ground motion data for dynamic analysis.

TFCGAN: Nonstationary Ground-Motion Simulation in the Time–Frequency Domain Using Conditional Generative Adversarial Network (CGAN) and Phase Retrieval Methods

ABSTRACTDespite the exponential growth of the amount of ground-motion data, ground-motion records are not always available for all distances, magnitudes, and site conditions cases. Given the importance of using time histories for earthquake engineering (e.g., nonlinear dynamic analysis), simulations of time histories are therefore required. In this study, we present a model for simulating nonstationary ground-motion recordings, which combines a conditional generative adversarial network to predict the amplitude part of the time–frequency representation (TFR) of ground-motion recordings and a phase retrieval method. This model simulates the amplitude and frequency contents of ground-motion data in the TFR as a function of earthquake moment magnitude, source to site distance, site average shear-wave velocity, and a random vector called a latent space. After generating the phaseless amplitude of the TFR, the phase of the TFR is estimated by minimizing all differences between the observed and reconstructed spectrograms. The simulated accelerograms produced by the proposed method show similar characteristics to conventional ground-motion models in terms of their mean values and standard deviations for peak ground accelerations and Fourier amplitude spectral values.

Ground motion prediction equations based on shallow crustal earthquakes in Georgia and the surrounding Caucasus

Strong ground motions caused by earthquakes with magnitudes ranging from 3.5 to 6.9 and hypocentral distances of up to 300 km were recorded by local broadband stations and three-component accelerograms within Georgia’s enhanced digital seismic network. Such data mixing is particularly effective in areas where strong ground motion data are lacking. The data were used to produce models based on ground-motion prediction equations (GMPEs), one benefit of which is that they take into consideration information from waveforms across a wide range of frequencies. In this study, models were developed to predict ground motions for peak ground acceleration and 5%-damped pseudo-absolute-acceleration spectra for periods between 0.01 and 10 s. Short-period ground motions decayed faster than long-period motions, though decay was still in the order of approximately 1/r. Faulting mechanisms and local soil conditions greatly influence GMPEs. The spectral acceleration (SA) of thrust faults was higher than that for either strike-slip or normal faults but the influence of strike-slip faulting on SA was slightly greater than that for normal faults. Soft soils also caused significantly more amplification than rocky sites.

In-situ shear-strain profile assessment in geotechnical array with ground motion data

In-situ shear-strain profile can be used to evaluate soil dynamic behavior with depth, but also safety of buried lifeline and structures due to seismic wave propagation in soil during an earthquake. Using 199 sets of ground-motion data recorded by six geotechnical arrays with 3–7 sensors in 43 earthquakes, the seismic interferometry by deconvolution method is employed to extract shear-wave velocity profile (Vs, sw) of seismic wave in each array; ratio of peak particle velocity (PPV) and Vs, sw between two successive sensors, PPV/Vs, sw, is computed in each array and assumed to be proxy of the in-situ shear strain. The characteristics of in-situ shear strain profiles in the arrays are studied under seismic loadings in various earthquakes. The relationships of evaluating both the in-situ shear strain profile and the largest in-situ shear strains of the upper soil near the surface are derived from the regression analysis for D and E class sites, respectively. Based on the linear and volumetric threshold shear strains and PGAs and PGVs, the variations of soil behaviors (i.e., linear elastic, nonlinear and plastic behaviors) with the increase of the shear strain or PGA or PGV are studied in the shear strain profiles. The results are as follows. (1) With the increase of PGA and/or PGV in various earthquakes, the in-situ shear strain profiles move towards the larger shear strains and the soil behavior will change to a higher stage or a higher level in the same stage. (2) In the shear strain profile, with the increase of depth, the in-situ shear strains decrease gradually and the soil behavior will change to a lower stage or a lower level in the same stage. (3) Among the shear strain profiles, upper soil has the largest shear strain (γmax) and the shallower the soil depth, the larger the shear strain. The relationships between the γmax and PGV and between the γmax and PGA and PGV combination can be used to evaluate the dynamic behavior of upper soil with less than 30 m at a strong motion array or station for D and E class sites. (4) The in-situ shear strains are highly correlated with the PPV and average shear wave velocity measured by the drilling-hole methods (Vs,dh) combination and with the PPV and Vs,dh and center depth between two successive sensors (Hcd) combination, and increase with the increase of the PPV and decrease with the increase of the Vs,dh and/or Hcd, respectively. The relationships are recommended to evaluate the in-situ shear strain profile with very high accuracy in the geotechnical array with more than two sensors for D and E class sites.

On the development of region and site-specific ground motion prediction model for the region of I-lan, Taiwan

this study presents the development of a region- and -site specific ground motion model (GMM) based on ground motion data obtained from the I-lan alluvial basin in northeastern Taiwan. The development was performed by calibrating the ergodic Phung et al. (2020) (Ph20) GMM developed for Taiwan. The source of strong ground motion data includes events from shallow crustal and subduction zones with magnitudes (MW) from 4.0 to 7.6, records from distances shorter than 200 km, and focal depths up to 150 km. The resulting regional model accounts for peculiarities that are not captured by the ergodic Ph20 GMMs, such as (1) the difference in source type effects, (2) VS30-scaling from the local site effects, and (3) enhancement of long period spectral ordinates due to the deep sedimentary basins. The standard deviations of the local model are much lower than those of the ergodic model, particularly the component of the standard deviation that corresponds to the site-to-site variability (ϕS2S), indicating that better site characterization can significantly reduce the overall uncertainty in ground motion estimation.

Seismic Performance of base isolated structure for Nepal Earthquake

Increased earthquakes have caused massive destruction and collapse of structures around the world in recent decades as a result of inadequate seismic design. In this way, creative work has received special attention with a focus on constructing the structure in such a way that harm to the structures is minimized. The goal is to construct structures that are safe, longlasting and durable for future generations. Active protective systems, hybrid protective systems and passive protective systems have all evolved as earthquake protection systems. The passive protection system keeps the structure elastic during large earthquakes and has a fundamental frequency that is lower than the predetermined base frequency of ground movement. The passive protective system includes base isolation as a component. Base isolation is currently the most innovative solution for seismic building protection in earthquake-prone areas. It has been successfully used for earthquake protection in a variety of buildings and other structures around the world. The purpose of this study is to investigate the performance of a G+8 building constructed of RCC and equipped with a high-damping rubber bearing and a lead rubber bearing isolation system. Two models are depicted in the work. The first model shows a conventional structure whereas the second model represents a base isolation structure. The goal is to use Time history in the ETABS-2017 software to compare the seismic response of a fixed base and base separated structure. The ground motion data from the Nepal earthquake of 2015 is used to do time history analysis.

A comparison of nonergodic ground-motion models based on geographically weighted regression and the integrated nested laplace approximation

Different nonergodic Ground-Motion Models based on spatially varying coefficient models are compared for ground-motion data in Italy. The models are based different methodologies: Multi-source geographically weighted regression (Caramenti et al. 2022), and Bayesian hierarchical models estimated with the integrated nested Laplace approximation (Rue et al. 2009). The different models are compared in terms of their predictive performance, their spatial coefficients, and their predictions. Models that include spatial terms perform slightly better than a simple base model that includes only event and station terms, in terms of out-of sample error based on cross-validation. The Bayesian spatial models have slightly lower generalization error, which can be attributed to the fact that they can include random effects for events and stations. The different methodologies give rise to different dependencies of the spatially varying terms on event and station locations, leading to between-model uncertainty in their predictions, which should be accommodated in a nonergodic seismic hazard assessment.

Testing the ShakeAlert Earthquake Early Warning System Using Synthesized Earthquake Sequences

Abstract We test the behavior of the United States (US) West Coast ShakeAlert earthquake early warning (EEW) system during temporally close earthquake pairs to understand current performance and limitations. We consider performance metrics based on source parameter and ground-motion forecast accuracy, as well as on alerting timeliness. We generate ground-motion times series for synthesized earthquake sequences from real data by combining the signals from pairs of well-recorded earthquakes (4.4≤M≤7.1) using time shifts ranging from −60 to +180 s. We examine fore- and aftershock sequences, near-simultaneous events in different source regions, and simulated out-of-network and offshore earthquakes. We find that the operational ShakeAlert algorithms Earthquake Point-source Integrated Code (EPIC) and Finite-Fault Rupture Detector (FinDer) and the Propagation of Local Undamped Motion (PLUM) method perform largely as expected: EPIC provides the best source location estimates and is often fastest but can underestimate magnitudes or, in extreme cases, miss large earthquakes; FinDer provides real-time line-source models and unsaturated magnitude estimates for large earthquakes but currently cannot process concurrent events and may mislocate offshore earthquakes; PLUM identifies pockets of strong ground motion, but can overestimate alert areas. Implications for system performance are: (1) spatially and temporally close events are difficult to identify separately; (2) challenging scenarios with foreshocks that are close in space and time can lead to missed alerts for large earthquakes; and (3) in these situations the algorithms can often estimate ground motion better than source parameters. To improve EEW, our work suggests revisiting the current algorithm weighting in ShakeAlert, to continue developments that focus on using ground-motion data to aggregate alerts from multiple algorithms, and to investigate methods to optimally leverage algorithm ground-motion estimates. For testing and certification of EEW performance in ShakeAlert and other EEW systems where applicable, we also suggest that 25 of our 73 scenarios become part of the baseline data set.

Predictive kappa (κ) models for Turkey: Regional effects and uncertainty analysis

High-frequency attenuation of ground motions is commonly characterized by the κ parameter. κ and its value at zero distance, [Formula: see text], are critical parameters for site characterization, ground motion simulations, and adjustment of ground motion models for different site conditions. In this study, we derive regional κ models for Eastern, Western, and Northwestern Turkey, using a ground motion data set of 3212 strong ground motion records with 9636 components from 1053 earthquakes, recorded at 178 stations with varying site conditions. Initially, models with linear functional forms are derived with distance and site conditions as predictor variables. Residual analyses showed that these models have non-normal residuals with heterogeneous variances (heteroscedasticity). Box–Cox transformations on κ values are performed to address these two issues. Models using these transformations resulted in normal residuals with homogeneous variances (homoscedasticity). Effects of earthquake magnitude on the κ value are also investigated, and a linear adjustment for magnitudes is proposed. A constant vertical-to-horizontal ratio of 0.78 is proposed to estimate the vertical κ values instead of deriving separate models for the vertical component. This approach does not result in significant decreases in accuracy and is preferred due to its simplicity. Next, the physical implications of logarithmic transformations for the κ values are discussed. Finally, regional differences in κ models are highlighted.

Strong ground motion data of the 2015 Gorkha Nepal earthquake sequence in the Kathmandu Valley

Strong-motion records of earthquakes are used not only to evaluate the source rupture process, seismic wave propagation and strong ground motion characteristics, but also to provide valuable data for earthquake disaster mitigation. The Kathmandu Valley, Nepal, which is characterised by having soft sediments that have been deposited in an earthquake-prone zone, has experienced numerous earthquakes. We have operated four strong-motion stations in the Kathmandu Valley since 2011. These stations recorded the 2015 magnitude 7.8 Gorkha Nepal earthquake that occurred in the Himalayan continental collision zone. For several months after the mainshock, we deployed four additional temporary stations. Here, we describe the seismic data for 18 earthquakes over magnitude 5.0 collected by this array, including the 2015 magnitude 7.3 Dolakha earthquake of maximum aftershock and three large aftershocks of magnitude 6-class. These data are essential for validating the sedimentary structure of the basin and for evaluating the hazard and risk of future earthquakes in the Kathmandu Valley.

A Nonergodic Ground Motion Model for Chile

ABSTRACTIn this study, we develop a new nonergodic ground motion model (GMM) for Chile, which better captures the trade-off between the aleatory variability and epistemic uncertainty on ground motion estimates compared with existing GMMs. The GMM is developed for peak ground acceleration and pseudospectral acceleration at a period of 1 s. Most existing GMMs for subduction earthquake zones were developed based on an ergodic assumption, and this is not the exception for the subduction zone in Chile. Under the ergodic assumption, the ground motion variability at a given single site–source combination is considered the same as the variability observed in a global database. However, recent efforts have highlighted significant location-specific systematic and repeatable effects for ground motions recorded within a particular region. These systematic effects promote the relaxation of the ergodic assumption and the transition to the development of nonergodic GMMs. The nonergodic GMM developed in this study uses an ergodic GMM as a backbone, the systematic source and site effects are modeled using Gaussian processes, and the path effects are modeled using the cell-specific attenuation approach enhanced with a computer graphics-based algorithm. The coefficients of the nonergodic GMM are estimated using Bayesian inference via Markov chain Monte Carlo (MCMC) methods, in which we use an integrated nested Laplace approximation approach to address the computational burden involved in MCMC. The developed nonergodic GMM reveals spatially varying and correlated location-specific source, path, and site effects in Chile, which cannot be captured by existing Chilean ergodic GMMs. Moreover, the developed nonergodic GMM shows a reduced aleatory variability compared to existing ergodic GMMs that are commonly used in Chile. In addition, the developed nonergodic GMM shows small epistemic uncertainty for regions with large ground motion data and large epistemic uncertainty for regions with few ground motion data. Finally, we provide guidelines on how to use the developed nonergodic GMM in the context of probabilistic seismic hazard analysis, which is important for performance-based earthquake engineering assessments in Chile.

Analysis of Multistorey RCC Frame subjected to Mainshock and Aftershock Earthquake

Abstract: Structure analysis and design are significantly influenced by earthquake. It is believed that seismic evaluation is required for the viability and serviceability of both present and future building structures. When a structure's base is subjected to a certain type of ground motion, a time history analysis is performed to examine the dynamic reaction of the structure at each time interval. The near-field earthquake ground motion verification may have specific impacts for both forward and backward directivity. The initial's velocity and displacement motions, respectively, exhibit pulse and fling-step characteristics. Therefore, it is crucial to assess how well structures built solely to withstand the primary shock would work through future aftershocks. Using modern seismic protection systems, such as base isolations or / and supplemental dampening devices, that significantly reduce building damages during main shocks and their related aftershocks is one of the appropriate solutions to this issue. Due to changes in both static and dynamic stress that take place during the earthquake process, aftershock events are set off by the primary shock. In order to better understand the ground motion features of a sizable collection of mainshock and subsequent aftershock ground motion data recorded in accelerograph stations around the region, this study reviews pertinent literature in the field. The G+9 RCC building will be used in this study to conduct a time history analysis of the mainshock and aftershock data of the Chamoli earthquake provided by the Centre for Engineering Strong Motion Research Ground Motion Database. For designing purposes, the IS 456-2000 code is taken into consideration. Live loads are measured in accordance with IS 875-part 1, and seismic zone IV is selected for analysis in accordance with IS 1893-2016. Storey drift, base shear, joint reactions, and storey displacement are just a few of the variables that can have an impact on how well a building performs. Since each of these variables has a significant impact on how a structure responds to seismic loads, they are also taken into account when evaluating the results.

Effect of Base Isolation using LRB on Stepped Building

Abstract: The base isolation design strategy uncouples the superstructure from the foundation, reducing the effects of earthquake ground motion. The structure is isolated from the ground motion by a flexible base. Installing base isolators in columns. The structural response accelerations are usually less than the ground motion acceleration. In general, base isolation reduces storey shear and acceleration while simultaneously increasing time period, and storey drift, allowing rigid buildings to be more flexible by dispersing energy to the foundation. The basic seismic isolation design provides a shielding technique, allowing the structure to function without harm even after significant earthquakes. The current study explores the seismic effects of a G+6 stepped building with an LRB isolator. An isolator with a lead rubber bearing was used. E-tabs is used to conduct the base isolation study and seismic analysis. The reaction of the structure, lateral shear force, time period, and base shear, was observed. This paper presents time-history analysis and performance assessment analyses on a base isolated stepped building using Bhuj Earthquake ground motion data.

Impact of Ergodic versus Nonergodic Seismic Hazard Estimation on the Risk Assessment of Liquefaction-Induced Ground Damage

ABSTRACT The seismic risk assessment of liquefaction-induced ground damage requires the hazard estimation of ground-motion intensity measures (IMs) through probabilistic seismic hazard analyses (PSHA). Current practice implements PSHA using ground-motion models (GMMs) developed under the ergodic assumption, which considers that the distribution of ground-motion IMs over time at a single site is the same as the distribution of ground-motion IMs over space. With the rapid growth of ground-motion databases, recent efforts have shown that ground-motion recordings are affected by location-specific systematic and repeatable effects favoring the transition to nonergodic approaches. However, the impact of using ergodic versus nonergodic PSHA (accounting for source, path, and site repeatable effects) on the risk assessment of liquefaction-induced damage has not been explored, which is the objective of this study. We consider three sites in California with different availability of ground-motion data to investigate the effects of the amount of available information on constraining repeatable effects and how this affects the final risk estimates within a nonergodic approach. In this context, the nonergodic-based estimates are compared against their ergodic counterparts, and insights are shared. The results from site-specific and regional assessments show important differences between ergodic and nonergodic estimates in terms of the mean risk and its uncertainty; the differences are dependent on the amount of data, and highlight the value of information (i.e., data) in nonergodic approaches.

EKSPLORASI REKAMAN GEMPA-GEMPA DI INDONESIA DAN KARAKTERISTIK DIRI YANG DINYATAKAN DALAM ACCELERATION BASED SEISMIC INTENSITY MEASURES (SIMs)

Indonesia is a prone country to earthquake hazards. This situation is indicated by the number of earthquakes ranging from small to significant events. However, digital earthquake ground motion data are not available, making it difficult for further research. This paper aims to explore recordings of earthquakes that occurred in Indonesia, which are then presented in digital data and used to identify their damage potential in the form of Seismic Intensity Measures (SIMs). After being traced, it turned out that there were only six earthquakes whose ground acceleration time history was found through the paPers published by researchers. The earthquakes were the Mw 6.2 Yogyakarta (2006), the Mw7.6 Padang (2009), the Mw6.1 Bener Meriah Central Aceh (2013), and the Mw6.5 Pidie Jaya Aceh (2016), the Mw7.5 Palu (2018) and the Mw6.1 Malang (2021) earthquakes. The manual digitization and processing to obtain ground acceleration data every 0.01s time step are required. Eight aspects based on acceleration and two aspects based on response spectrum have been used as parameters for Seismic Intensity Measures SIMs. The exploration results show that the source of the earthquake in Sumatra is still relatively shallow, getting more profound in the Java and Nusa Tenggara subduction. The P.G.A. of the Yogyakarta earthquake is 0.272g with a total duration of more than 50 seconds. In general, according to SNI 1726, 2019, the spectrum has been able to cover all ground acceleration time histories. The Yogyakarta earthquake has the highest Earthquake Power, Arias Intensity, and Potential Destructiveness values, namely PE = 0.255 and IA = 2.201, and P.D. = 0.166.

Seismological and engineering characteristics of strong motion data from 24 and 26 September 2019 Marmara Sea earthquakes

An MW 4.5 earthquake took place on September 24, 2019 in the Marmara Sea. Two days after, on September 26, 2019, Marmara region was rattled by an MW5.7 earthquake. With the intention of compiling an ample strong ground motion data set of recordings, we have utilized the stations of Istanbul Earthquake Rapid Response and Early Warning System operated by the Department of Earthquake Engineering of Boğaziçi University and of the National Strong Motion Network operated by AFAD. Altogether 438 individual records are used to calculate the source parameters of events; namely, corner frequency, radius, rupture area, average source dislocation, source duration and stress drop. Some of these parameters are compared with empirical relationships and discussed extensively. Duration characteristics are analysed in two steps; first, by making use of the time difference between P-wave and S-wave onsets and then, by considering S-wave durations and significant durations. It is observed that they yield similar trends with global models. PGA, PGV and SA values are compared with three commonly used ground motion prediction models. At distances closer than about 60 km, observed intensity measures mostly conform with the GMPE predictions. Beyond 60 km, their attenuation is clearly faster than those of GMPEs. A frequency-dependent Q model is developed by using both events. Its consistency with existing regional models is confirmed.

Supershear shock front contribution to the tsunami from the 2018 Mw 7.5 Palu, Indonesia earthquake

SUMMARY Hazardous tsunamis are known to be generated predominantly at subduction zones. However, the 2018 Mw 7.5 Palu (Indonesia) earthquake on a strike-slip fault generated a tsunami that devastated the city of Palu. The mechanism by which this tsunami originated from such an earthquake is being debated. Here we present near-field ground motion (GPS) data confirming that the earthquake attained supershear speed, i.e. a rupture speed greater than the shear wave speed of the host medium. We subsequently study the effect of this supershear rupture on tsunami generation by coupling the ground motion to a 1-D non-linear shallow-water wave model accounting for both time-dependent bathymetric displacement and velocity. With the local bathymetric profile of Palu bay around a tidal station, our simulations reproduce the tsunami arrival and motions observed by CCTV cameras. We conclude that Mach (shock) fronts, generated by the supershear speed, interacted with the bathymetry and contributed to the tsunami.

GMPE-consistent hard-rock site adjustment factors for Western North America

Empirical ground-motion prediction equations (GMPEs) such as the Next Generation Attenuation-West2 (NGA-West2) GMPEs are limited in the number of recordings on hard-rock stations used to develop the models. Therefore, the site response scaling in the GMPEs cannot be reliably extrapolated to hard-rock conditions. The state of practice for the development of hard-rock adjustment factors involves the use of analytical methods that typically assign small values to the small-strain damping parameter ([Formula: see text]) for hard-rock sites resulting in large scaling factors at short periods. Alternatively, the hard-rock scaling factors developed in Ktenidou and Abrahamson (KA16) based on empirical ground-motion data are used. These empirical factors, developed for a broad rock site category, show that the average hard-rock scaling factors observed in ground-motion data are small in amplitude contrary to the large factors typically obtained from analytical studies. The empirically derived KA16 factors also suffer from limitations due to the relatively small number of rock sites in the data set and do not distinguish between different hard-rock conditions. To address the shortcomings in the current state of practice, we present a methodology to develop linear site adjustment factors to adjust the NGA-West2 GMPEs from V S30 of 760 m/s to target hard-rock site conditions with V S30 ranging from 1000 to 2200 m/s. These factors are analytically derived using the inverse random vibration theory (IRVT) approach of Al Atik et al. but with inputs constrained using the empirical KA16 factors and normalized to the scaling of the NGA-West2 GMPEs for V S30 of 1000 m/s. The proposed factors merge the results of the NGA-West2 site response scaling for V S30 ≤ 1000 m/s with the KA16 hard-rock category factors to produce a site factor model that is a continuous function of V S30. The epistemic uncertainty of these factors is evaluated.