Fourier Amplitude Spectra Research Articles

Source Scaling and Ground-Motion Variability along the East Anatolian Fault

Abstract We investigate the source scaling and ground-motion variability of 1585 earthquakes with Mw>3 occurring along the East Anatolian fault since 2010. We compile a dataset of 17,691 Fourier amplitude spectra of S waves recorded by 186 stations. A spectral decomposition is applied to isolate the source contribution from propagation and site effects. Source spectra are fit with Brune’s model to estimate seismic moment and corner frequency and to compute the stress drop Δσ. The 10th, 50th, and 90th percentiles of the Δσ distribution are 0.18, 0.51, and 1.69 MPa, respectively, and the average Δσ increases with earthquake magnitude. For the two mainshocks of the 2023 sequence, the estimated Δσ is about 13 MPa, significantly larger than the Δσ of the smaller events. At intermediate and high frequencies, the interevent residuals are correlated with Δσ. When recorded peak ground accelerations and velocities for Mw<6 are compared with the predictions from ground-motion models proposed in the literature, the negative value of the average interevent residuals is consistent with low values of Δσ. Contrariwise, the average residuals for the peak parameter of the Mw 7.8 and 7.5 mainshocks of the 2023 sequence are almost zero, but with distance dependencies.

Transformation of reverse marketing model for electrical appliances based on Markov chain optimization with information technology support

Inverters are widely used in the military, industrial production and defense fields as current conversion devices that convert direct current to alternating current. If the inverter fails, it can cause damage to other equipment, resulting in financial losses and, in extreme cases, compromising the safety of users. In this study, by integrating neural networks, the input signals of inverters are quickly converted to Fourier spectrum amplitudes, and from fault signals (such as load phase voltage) to feature vectors. In order to realize automatic extraction and fault detection of inverters, an optimization method is used to determine the appropriate number of nodes in the hidden layer of complex neural networks. The ability to efficiently allocate limited computing, storage, and network resources to meet user demand for services; Continuously optimize quality of service (QoS), including reducing latency, improving bandwidth, and increasing reliability. These problems directly affect the performance and user experience of MEC systems. By studying these issues and proposing corresponding solutions, we aim to improve the performance of MEC systems and provide higher quality services. The accuracy of defect diagnosis can reach higher than 99%, and the method has a high remission rate, demonstrating its effectiveness and benefits.

SHINE_color: Controlling low-level properties of colorful images

Visual perception combines top-down processes arising from participants individual histories, such as expectations and goals, and bottom-up processes that arise from visual stimuli properties, such as luminance and contrast. The precise control of low-level visual stimuli properties is essential when investigating visual perception. Without it, for instance, investigations of bottom-up processes are virtually impossible and investigations of top-down processes risk major confounds when testing and formulating hypotheses. The SHINE (spectrum, histogram, and intensity normalization and equalization) toolbox for MATLAB [1] allows precise control of images’ Fourier amplitude spectra, the normalizing and scaling of luminance and contrast, and exact histogram specification optimized for perceptual visual quality. Following Willenbockel and Cols (2010) advices, here we present an adaptation of the SHINE toolbox, named SHINE_color, which extends SHINE functionalities by allowing the parametrical manipulation of low-level properties of both static and animated colorful images.•Parametric manipulation of low-level properties of colorful images•Spectrum, histogram, and intensity normalization and equalization

Simulation-based study of noise, vibration, and harness of BLDC motor for energy level variation with frequency

The energy spectrum measurements in noise, vibration, and harness analysis with power spectrum response is a very ancient concept. The work and energy approaches for analyzing Noise, Vibration, and Harmonics (NVH) features are increasing rapidly in recent years. The primary focus is on evaluating imparted energy due to the NVH using an FFT spectrum against the input energy in motors. The simulation depicts the input energy spectra of the kinetic energy, absorbed energy, and dissipated energy very clearly. Earlier the smoothed Fourier amplitude spectrum approach was used for plotting the energy dissipation due to the NVH effect. However, most of the part of accountable energy goes to waste with noise, vibration, and harmonics generated due to harness in motor design. This experiment is conducted in support of Sir Nikola Tesla’s statement “If you wish to understand the universe think in terms of energy, frequency, and vibration”. The ripples an induced in phase current because of the step change of the speed. The predominant frequency in phase current waveform creates the collapsing vibratory waves that create the sound. Sound frequencies above 20 dB are considered unwanted sound known as noise. The energy level variation with NVH influence in BLDCM is measurable for its performance analysis. This research can be further enhanced by designing NVH-free BLDC motors.

Generating ground motions using the Fourier amplitude spectrum

AbstractIn this paper, a simplified method aimed at generating ground motions records using a Fourier amplitude spectrum model obtained by a response spectrum is presented. The use of white noise with specific conditions on the variance and inter‐frequency correlation allows to get a realistic variability of the Fourier amplitude spectrum. Moreover, a two‐corner frequency model is defined from empirical ground‐motion data and a filter is applied to capture the attenuation at high frequencies. The generated series of stochastic ground motions accurately match the mean value of the target response spectrum. The procedure was tested on an Italian site and results showed excellent matching in terms of mean and dispersion values with either the median obtained from ground motion prediction equations (GMPE) and conditional mean spectra (CMS). The advantage of the proposed methodology is that time‐histories can be generated with low computational effort, they do not need scaling or frequency content adjustments and are spectrum compatible with a given target spectrum.

Bayesian analysis-based ground motion prediction equations for earthquake input energy

Earthquake energy-based procedures offer a promising alternative for seismic evaluation and earthquake-resistant design of structures. Accurate determination of earthquake energy demand and the provision of an adequate energy supply to the structural system are crucial for this approach. This is where the utilization of ground motion prediction equations (GMPEs) becomes essential in achieving accurate assessment of seismic demands on structures. However, most GMPEs primarily focus on determining spectral accelerations. This study proposes a methodology to derive GMPEs by combining the Fourier amplitude spectrum, the elastic input energy spectrum, and Bayesian regression analysis. These GMPEs estimate energy-based spectral values for interplate and intraslab earthquakes recorded in the firm ground of Mexico City. Furthermore, a mathematical expression is devised to determine correlation coefficients between energy-based spectral values for interplate and intraslab earthquakes, expanding the GMPEs' applicability. Finally, a probabilistic seismic hazard analysis is conducted using the proposed GMPEs and the correlation model.

Simulating the strong ground motion of the 2022 MS6.8 Luding, Sichuan, China Earthquake

Stochastic finite-fault simulations are effective for simulating ground motions and are widely used in engineering to determine the impacts of ground motion and develop relevant predictive equations. In this study, the source, path, and site amplification coefficient of western Sichuan Province, China, and stochastic finite-fault simulations were used to simulate the acceleration time series, Fourier amplitude spectra, and 5% damped response spectra of 28 strong-motion stations with rupture distances within 300 km of the 2022 MS6.8 Luding earthquake. The simulation results of 14 stations at rupture distances of 45–185 km match the observation. However, the simulation results of 3 near- and 6 far-field stations at rupture distances of 12–36 km and 222–286 km, respectively, were obviously deviated from the observations. Simulation results of the near-field stations are larger than the observations at high frequencies (>6 Hz). The discrepancy likely comes from the nonlinear site effect of near-field stations, which reduced the site amplification at high frequencies. Simulation result of the far-field stations is smaller than the observation at frequencies above 1 Hz. As these stations are located close to the Longmenshan Fault Zone (LFZ), thus, we obtained a new quality factor (Q) from data of historical events and stations located around LFZ. Using the new Q value, the discrepancies of the high-frequency simulation results of the far-field stations were corrected. This result indicated that the laterally varying Q values can be used to address the impact of strong crustal lateral heterogeneity on simulation.

FX UMa: A New Heartbeat Binary System with Linear and Nonlinear Tidal Oscillations and δ Sct Pulsations

We present a detailed analysis of an eclipsing double-lined binary FX UMa based on TESS photometry and newly acquired spectroscopic observations. The radial velocities and atmospheric parameters for each component star are obtained from the SONG high-resolution spectra. Combined with the radial-velocity measurements, our light-curve modeling yields absolute masses and radii of the two components. The Fourier amplitude spectrum of the residual light curve reveals a total of 103 frequencies with signal-to-noise ratio (S/N) ≥ 4, including 12 independent frequencies, 17 multiples of the orbital frequency (Nf orb), and 74 combination frequencies. Ten Nf orb peaks with S/N > 10 have very high amplitudes and are likely due to tidally excited oscillations (TEOs). The remaining Nf orb peaks (4 ≤ S/N ≤ 10) may be originated from the imperfect removal, or they are actually real TEOs. Four anharmonic frequencies can pair up and sum to give exact harmonics of the orbital frequency, suggesting the existence of nonlinear tidal processes in the eccentric binary system FX UMa. Eight independent frequencies in the range of 20–32 day−1 are typical low-order pressure modes of δ Scuti pulsators.

Inferences from Surface Brightness Fluctuations of Zwicky 3146 via the Sunyaev–Zel’dovich Effect and X-Ray Observations

The galaxy cluster Zwicky 3146 is a sloshing cool-core cluster at z = 0.291 that in Sunyaev–Zel’dovich (SZ) imaging does not appear to exhibit significant pressure substructure in the intracluster medium. We perform a surface brightness fluctuation analysis via Fourier amplitude spectra on SZ (MUSTANG-2) and X-ray (XMM-Newton) images of this cluster. These surface brightness fluctuations can be deprojected to infer pressure and density fluctuations from the SZ and X-ray data, respectively. In the central region (Ring 1, r < 100″ = 440 kpc, in our analysis), we find fluctuation spectra that suggest injection scales around 200 kpc (∼140 kpc from pressure fluctuations and ∼250 kpc from density fluctuations). When comparing the pressure and density fluctuations in the central region, we observe a change in the effective thermodynamic state from large to small scales, from isobaric (likely due to the slow sloshing) to adiabatic (due to more vigorous motions). By leveraging scalings from hydrodynamical simulations, we find an average 3D Mach number ≈0.5. We further compare our results to other studies of Zwicky 3146 and, more broadly, to other studies of fluctuations in other clusters.

Shaking Table Test for Seismic Response of Nuclear Power Plant on Non-Rock Site

In order to compare and analyze the seismic response characteristics of a safety-related nuclear structure on a non-rock site in the condition of raft and pile group foundations under unidirectional and multidirectional seismic motion input, a large-scale shaking table test of the soil-nuclear structure system was carried out in this paper. In the test, the soil was uniform silted clay, and the shear wave velocity was 213 m/s. Considering the similarity of the superstructure natural frenquency, the actual nuclear power structure was simplified to a three-story frame shear wall structure model. The annular laminated shear model box was used to take the boundary effect of soil into consideration; the seismic motions = were input in only one horizontal direction or three directions at the same time for the shaking table test, and the results were analyzed. The results of the test show that the acceleration response of the safety-related nuclear plant is affected by the directions of input seismic motion and the forms of the foundation. When the seismic motion is input simultaneously in three directions, the acceleration responses of the horizontal motion and vertical rocking of the safety-related plant are larger than those of the single-direction input. The acceleration response of the horizontal motion and vertical rocking of the safety-related structure with the pile group foundation is smaller than that with the raft foundation. The values of most frequency bands in the horizontal acceleration Fourier amplitude spectrum at the top of the pile-foundation structure are smaller than that at the top of the raft-foundation structure, while the displacement is basically the same as that of the raft-foundation structure. This is related to the relation between the frequency component of input seismic motion and the natural frequency of the structure system. Therefore, it is more reasonable to use three-dimensional seismic input in the seismic response analysis of nuclear power plants. The seismic performance of nuclear power plants can be enhanced by using pile group foundations.

Use of Fourier phase characteristics and effective stress analyses for post-earthquake ground motion estimation: application to ESG6 blind prediction steps 2&3 dataset and JMA accelerometric data

After the occurrence of a large earthquake, engineering seismologists are often requested to estimate strong ground motions at a site where strong motion data were not obtained. The goal of this study was to test the ability of a class of methods that uses Fourier phase characteristics for the post-earthquake ground motion estimation, making use of the precious opportunity provide by the ESG6 Blind Prediction Steps 2&3. It was also part of the goal of this study to test the performance of the effective stress analyses to account for soil nonlinearity. In addition to the dataset provided by the organizer of the blind prediction, the author used additional accelerometric data from a nearby JMA site. To simulate ground motions for an M5.9 earthquake at the target site “KUMA”, the Fourier amplitude spectrum was estimated from the spectral ratio between KUMA and the nearby JMA site. The Fourier phase spectrum was approximated by the spectrum of another event at KUMA. Comparison between the estimated and recorded ground motions after the blind prediction revealed that the estimated ground motions were fairly consistent with the observed ground motions, indicating the effectiveness of the method when the rupture process of the target event is simple and the soil nonlinearity at the target site is not significant. To simulate ground motions at KUMA for the M6.5 foreshock and the M7.3 mainshock of the 2016 Kumamoto earthquake sequence, the author conducted effective stress analyses using a program called “FLIP” to account for soil nonlinearity. Comparison between the estimated and recorded ground motions after the blind prediction indicated that the low-frequency components were overestimated and the high-frequency components were underestimated. The strong soil nonlinearity considered in the effective stress analyses was the main cause of the discrepancy. One explanation for this result could be that the nonlinear soil behavior at KUMA during the foreshock and the mainshock was not a strong one. Another explanation could be that the effect of soil nonlinearity was already included in the records at JMA and the effect of soil nonlinearity was double counted in the results submitted by the author.Graphical

A relocated earthquake catalog and ground motion database for the southern East African rift system

The southern East African rift system (EARS) is geologically rare considering its early-stage continental rift setting combined with a deep seismogenic zone. Several seismically vulnerable communities are located within this tectonically active region, resulting in a significant seismic risk. However, the ground motion and seismic hazard analyzes necessary to increase the earthquake preparedness in the region have been limited due to the relatively short instrumentation history and scarce ground motion data available. Here, we present a newly compiled ground motion database for the southern EARS which is critically lacking and preventing local ground motion studies. This database includes a regional catalog of 882 earthquakes spanning 1994–2022 (magnitudes 3–6.5) with available waveform records within epicentral distances of 300 km. Three different velocity models were used to relocate 256, 255, and 252 events, respectively, to quantify depth sensitivity, relocating events down to depths of 35–40 km. The final database contains 10,725 time-series records from 353 stations along with P- and S-wave phase arrivals for each record. The ground motion database contains peak ground acceleration and velocity and 5% damped pseudo-spectral acceleration for 291 frequencies from 1.0 to 30 Hz for the horizontal components. In addition, a Fourier amplitude spectrum table for 212 frequencies from 0.1 to 30 Hz is included. The database is accessible through the ISC repository ( https://doi.org/10.31905/4GGVBFBE ).

3D physics-based ground motion simulation and topography effects of the 05 September 2022 MW6.6 Luding earthquake, China

On September 5, 2022, a MW6.6 earthquake occurred in Luding, Sichuan Province, which caused a large number of casualties and serious damage to infrastructures. To represent the strong ground motion of the destructive shock, the SPECFEM 3D code is adopted to model the wave propagation and a hybrid kinematic source to model the fault rupture. As for the hybrid fault source, spatial heterogeneities aimed to simulate the high-frequency radiation are added to a prescribed asperity model used to generate the low-frequency part. With a conforming mesh of the established 100 km × 100 km × 60 km numerical model and the developed hybrid fault source, the maximum resolved frequency of the simulation is 5 Hz. First, the numerical model is validated by comparing the simulated results with the six recorded waveforms as well as the corresponding Spectral acceleration and Fourier amplitude spectra. Then, the wave fields and Synthetic seismograms are presented to investigate the velocity pulse-like ground motion in the near-fault region. Finally, the topographic effect on the ground motions is identified by comparing the results from the numerical model with (Topo) and without topography (Flat). It is demonstrated that the simulated ground motion well reproduces the near-fault fling-step effect and the wave scattering effect caused by the surface topography. The hill-canyon topography significantly amplifies the surface motion, with the amplification factors (Topo/Flat) of PGV at the peak of Gonggashan mountain and at the bottom of Daduhe river reach 1.9 and 1.4, respectively. Moreover, the PGV amplification factor is in good correlation with the topography's elevation, indicating that the topographic amplification can be predicted by establishing the relationship between amplification factor and elevation.

The spatial properties of the site amplifications of S-waves by generalized spectral inversion technique and the correction method of the site amplifications considering the contribution of later arrivals after major S-waves

Site amplification is an important component of strong ground motion prediction as it differs among sites, reflecting its specific local subsurface geology. Here, we confirm that site amplifications are similar in a neighborhood area over a long period. However, few studies have investigated the spatial properties in a wide region (i.e., the whole of Japan). In this study, we explored the spatial properties of site amplifications based on the generalized inversion technique (GIT) using Fourier amplitude spectra (FAS) as well as pseudo-velocity response spectra (pSv) as the latter is an important index for engineering purposes and the most similar type of response spectra to FAS. The spatial distributions of S-wave site amplifications (SA-S), especially within large sediment basins (e.g., the Kanto and Osaka Basins in Japan), were found to be relatively similar in proximate areas for a long period ranging from 2 to 8 s. This suggests that we could easily predict the site amplifications using an empirical approach through spatial interpolation based on the properties obtained by the GIT. Furthermore, we propose a prediction procedure for site amplification for the whole duration from the SA-S at an arbitrary site. We used the correction function, which converts the SA-S to the site amplification for the whole duration (SA-W), including an S-wave portion and a subsequent portion. This function is called the whole-duration to S-wave spectral ratio (WSR) and is stable in terms of spatial properties. As we could estimate the SA-S either by theoretical transfer functions or observed microtremors, we can easily predict the SA-W based on the proposed WSR concept. We found that SA-S in pSv is more or less similar to SA-S in FAS, however, SA-W in pSv fails to capture the effects of the long duration of ground motions inside a large basin so that we cannot recommend to use pSv for the prediction of whole duration of ground motion.Graphical

Investigation of Site Amplification and Attenuation Effects in the Changjiang Delta

Abstract Site response in the Changjiang Delta in eastern China was studied using Lg Fourier amplitude spectra. We used broadband seismograms recorded at 70 stations from 62 earthquakes with magnitude (Ms) varying from 3.5 to 5.0 during 2009–2021. The crustal quality factor Q and site response in the Changjiang Delta were obtained simultaneously from regression of Lg Fourier acceleration amplitude versus frequency. The κ0 of each individual station was subsequently calculated from a regression of the high-frequency site terms versus frequency. The site terms exhibit obvious dependence on sediment thickness in the Changjiang Delta. The site amplification factor reaches ∼7–10 for stations overlying sediments ∼8–9 km thick in the northern Jiangsu basin. The site terms were found to behave consistently as a function of sediment thickness over the frequencies of 0.56–24.86 Hz. Site amplification shows a positive correlation with sediment thickness at lower frequencies (&amp;lt;7.26 Hz) but transitions to a negative correlation as frequency increases to 12.86 Hz and higher. Linear functions versus sediment thickness were used to model the site response terms at individual frequencies. We also showed that site terms calculated using the κ0 model as a function of sediment thickness fit the site response terms well at frequencies higher than 9.66 Hz. Results of this study can be incorporated in ground-motion prediction models for the Changjiang Delta. In addition, the site response estimates determined here can be used to reduce bias due to site effects in studies of earthquake source parameters.

Physics-based parametrization of a FAS nonergodic ground motion model for Central Italy

We propose a new fully nonergodic ground motion model for Central Italy, which is one of the most sampled areas in the world after the occurrence of the last seismic sequences of 2009 and 2016–2017. The model predicts 69 ordinates of the Fourier Amplitude Spectrum in the magnitude range 3.2–6.5 and is constrained on a dense set of seismological and geophysical parameters (i.e. stress-drop Delta sigma, shear-wave velocity in the uppermost 30 m, VS,30 and high-frequency attenuation parameter at source {kappa }_{source} and site {kappa }_{0}) made available from a non-parametric generalized inversion technique (GIT). The aim of this work is to capture the underlying physics of ground motion related to different source energy levels, as well as to the crustal and geological structure of the region, thus providing less uncertain predictions. Calibration is performed using a stepwise regression approach which has the advantage of taking a more complex functional form (advanced model) when all physical parameters are known while returning a simpler form (base model) when physical data are missing. As a result, the advanced model reproduces the reference rock motion of the region in case the site additional proxies are set to their average values (VS,30 = 1100 m/s, {kappa }_{0}=15 ms). We show that the inclusion of the set of physically-based explanatory variables in the regression has a beneficial effect in constraining the uncertainty, leading to a reduction of the high-frequency variability of about 70% on the between-event and 35% on the site-to-site. This reduction can be viewed as the result of the combination of a more effective physical description through the incorporation of the additional proxies and a calibration embedded in a completely nonergodic framework.

Fault Damage Zone Effects on Ground Motions during the 2019 Mw 7.1 Ridgecrest, California, Earthquake

ABSTRACT We have simulated 0–3 Hz deterministic wave propagation in the Southern California Earthquake Center Community Velocity Model (CVM) version CVM-S4.26-M01 for the 2019 Mw 7.1 Ridgecrest earthquake. A data-constrained high-resolution fault zone model (Zhou et al., 2022) is incorporated into the CVM to investigate the effects of the near-fault low-velocity zone (LVZ) on the resulting ground motions, constrained by strong-motion data recorded at 161 stations. The finite-fault source used for the simulation of the Ridgecrest event was obtained from the Liu et al. (2019) kinematic inversion, enriched by noise following a von Karman correlation function above ∼1 Hz with a f−2 high-frequency decay. Our results show that the heterogeneous near-fault LVZ inherent to the fault zone structure significantly perturbs the predicted wave field in the near-source region, in particular by more accurately generating Love waves at its boundaries. The fault zone decreases the 0.1–0.5 Hz mean absolute Fourier amplitude spectrum bias to seismic recordings for all sites in the model and in the Los Angeles basin area (∼200 km from the source) by 16% and 26%, respectively. The fault zone structure generally improves modeling of the long-period features in the data and lengthens the coda-wave trains, in better agreement with observations. The favorable fit to data was obtained with a model including high-resolution surface topography, a 700-m-thick geotechnical layer and frequency-dependent anelastic attenuation in the model domain, with QS=0.1VS and QS(f)=0.1VSf0.5 (VS in m/s) for frequencies lower and higher than 1 Hz, respectively. We recommend that a data-constrained fault zone velocity structure, where available, be included in ground-motion modeling to obtain the least-biased fit to observed seismic data.

Relationship between SDOF-Input-Energy and Fourier Amplitude Spectral Amplification Ratios

ABSTRACT This article presents the theoretical relationship between the site amplification ratio of the input energy spectrum for a single-degree-of-freedom system (SDOF) and that of the Fourier amplitude spectrum (FAS). The relationship indicates that the input energy spectral ratio is the result of smoothing the square of the Fourier amplitude spectral ratio. The spectral window for smoothing is determined by the bedrock-motion FAS and the oscillator transfer function for the relative velocity. The characteristics of the input energy spectral ratio were derived based on the idea of smoothing and confirmed based on real seismic records. The findings of this study contribute to a better understanding of site effects on the input energy spectrum.

Engineering-oriented ground-motion model for Israel

This study presents a response-spectral Ground Motion Model (GMM) for Israel, called KYB22 herein and derived with practical applications in mind. This model is based on the former work by Maiti et al. (Bull Seismol Soc Am 111: 2177–2194, 2021), who derived a suite of nine Fourier amplitude spectra GMMs, using both empirical data and calibrated point-source simulations. In this study, a weighted average of the Maiti et al. (Bull Seismol Soc Am 111: 2177–2194, 2021) FAS models is computed and a synthetic database is created. Next, this database is converted to the Response spectral domain using the random vibration theory and a new GMM is regressed, constraining the magnitude and distance scaling on the synthetic response-spectral data. Site scaling is represented by VS30 and is a combination of empirical scaling with other considerations which are discussed in the text. Nonlinear site response is constrained from a global model, as are finite-fault effects, such as hanging-wall, mechanism and top of rupture—which cannot be constrained from the data because it does not contain enough large magnitude data. State-wide hazard is then computed using KYB22, comparing results with other GMM combinations. It is found that the hazard results obtained by using KYB22 as a backbone model are comparable to results obtained using other popular combinations of GMMs in the logic tree. Therefore, we recommend using the new GMM as one of the branches within the ground-motion logic tree when conducting seismic hazard calculations for Israel.

Including Radiation-Pattern Effects in Ground-Motion Models for Taiwan

ABSTRACT Most ground-motion models (GMMs) parameterize the earthquake source by magnitude, style of faulting, and source depth. GMMs are isotropic in terms of the source scaling for these three parameters. The radiation pattern, which leads to azimuthally varying source effects, is not included in most GMMs. As a result, any systematic radiation-pattern effects are treated as aleatory variability in the path terms in the GMMs, which does not make physical sense. We incorporate the far-field radiation pattern into GMMs for pseudospectral acceleration and Fourier amplitude spectra for the Taiwan region. A key issue is how to combine the radiation pattern from the SH and SV components for predicting the RotD50 amplitudes of ground motions used in GMMs. A suite of point-source simulations was generated for a range of focal mechanisms and site azimuths. Empirical models for the phase differences between the radial and transverse components were developed to constrain the between-component phase differences in simulations. The results show that the vector sum of the SH and SV far-field radiation patterns, FS, has a higher correlation with the RotD50 amplitudes of the ground motion than the arithmetic mean or the geometric mean. The radiation-pattern term is modeled by S0(M)+S1(M)ln(Fs+S2), in which S0(M) and S1(M) are linear functions of magnitude between M 4 and 6; they equal 0 for M &amp;gt; 6. The magnitude dependence reflects that, for large magnitudes and short distances, ground motions are more affected by the slip distribution and rupture timing than by the average radiation pattern from the subevents along the rupture, but the radiation pattern has a significant effect on the long-period ground-motion amplitude for small-magnitude events. Including radiation patterns into GMMs will improve estimates of 3D path effects from small-magnitude events by removing radiation-pattern effects from combined radiation-pattern and path terms used in current GMMs.