New generalized ANN-based hybrid broadband response spectra generator using physics-based simulations

Estimation of the seismic risk associated with infrastructures requires site-specific seismic hazard studies. Further, for nonlinear time history analysis, one requires broadband ground motion. In modern times, physics-based simulations (PBS) for deriving the ground motion for future earthquakes have been considered. The PBS helps decrease the uncertainties related to hazard estimation compared to ground motion prediction equations. The PBS methods have a specific frequency threshold limit resulting from high computational demand. Hence, hybrid methods are required to attain broadband spectra for the simulated ground motion. This study uses a new artificial neural network (ANN)-based model to generate broadband ground motion spectra using the low-frequency spectral acceleration from PBS, source, path, and site parameters as input variables. A detailed parametric study and performance evaluation was made to identify the optimal input parameters in conjunction with the best-suited ANN architecture. The performance of the ANN model is demonstrated for Iwate (Mw\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_w$$\end{document} 6.9, 2008) earthquake. We found that the predicted values from the developed ANN model agree with the recorded data. Furthermore, time histories are generated using the spectral ordinate matching technique from the estimated broadband spectra.


Introduction
Several past earthquakes have caused huge societal and life damage to mankind. The evergrowing population, economic activities, and rising infrastructure demand escalate the seismic risk. In order to minimize the losses and to come up with better engineering solutions, seismic hazard analysis is required. Hazard estimation provides a basic framework for building codes, insurance companies, and mitigation strategies. In order to ensure public safety against a possible earthquake event, researchers are trying to develop earthquake forecasting capabilities equivalent to weather forecast (Maechling et al. 2007). Although the target is far from accomplished, incorporating physics laws in ground motion simulations is a step forward. Traditionally, the characterization of earthquake hazards is done using probabilistic seismic hazard analysis (PSHA) (McGuire and Arabasz 1990). The PSHA framework includes several empirical models typically subjected to source, site, and path modeling variability. The corresponding variability might result in significant uncertainties in the hazard model, reducing the predictions' accuracy. Ground motion prediction equations (GMPEs) are one of the key contributors to the seismic hazard framework's uncertainty. GMPEs represent the probability of exceedance of an intensity measure for an earthquake event at a particular site accounting for source, site, and path effects. Although GMPEs are easy to compute, these equations are regression-based. They do not entirely capture various physical phenomena like the source directivity and basin effect observed during an earthquake (Graves et al. 2011). With the computational advancements, researchers have proposed to replace the traditional GMPEs in PSHA with physics-based simulations (PBS) to minimize the aleatory uncertainty (Maechling et al. 2007;Graves et al. 2011;Cui et al. 2013;Paolucci et al. 2015;Shaw et al. 2018;Milner et al. 2021). Recently, Infantino et al. (2020) have performed 66 PBS on the Marmara segment of the North Anatolian Fault for a M w range varying from 7 to 7.4. They found that the PBS results were consistent with the ground motion models (GMMs). Likewise, Stupazzini et al. (2021) have found that the ground motion variability for PBS is comparable with the recorded data, showing the effectiveness of PBS in generating non-ergodic ground motion. Platforms like Cybershake (Graves et al. 2011) and Cybershake NZ (Tarbali et al. 2019) are also working in the field of PBS simulations and have generated PBS for over 415,000 and 11,362 rupture variations, respectively. With all the benefits of PBS, the computational requirement remains a major challenge. The available infrastructure for PBS involves a frequency threshold, i.e., 1-1.5 Hz of accuracy (Paolucci et al. 2018). Generally, earthquake ground motion comprises broadband frequencies (0-10 Hz), PBS of which requires a very fine mesh size and extensive detailing of topological and geological features that demand a huge computational cost. Recently, researchers are coming up with techniques to reduce these computational requirements by including various approximations (Cui et al. 2013;Shaw et al. 2018;Milner et al. 2021). However, a standard methodology is yet to be achieved. A suitable alternative would be to develop broadband ground motion using hybrid methodologies that combines low-frequency PBS with a suitable high-frequency generator. The effectiveness of the corresponding hybrid approaches is evident as many researchers have successfully implemented them to simulate broadband ground motions (Smerzini and Villani 2012;Razafindrakoto et al. 2018;Gade and Raghukanth 2017;Jayalakshmi et al. 2021). With the recent advancements in the field of artificial intelligence (AI) and machine learning, researchers are including AI-based methods in the field of earthquake engineering (Ahmad et al. 2008;Derras et al. 2014;Dhanya and Raghukanth 2018;Gade et al. 2021;Mignan and Broccardo 2020;Dhanya and Raghukanth 2022;Derras et al. 2017). Recently, Paolucci et al. (2018) have proposed an ANN model that predicts broadband response spectra using PBS-based lowfrequency spectra. The ANN model was designed and trained by utilizing the SIM-BAD database, which consists of only 500 strong motion records corresponding to 130 earthquake events with a M w range of 5-7.3 and epicentral distance (R epi ) < 35 km. The methodology was demonstrated for a broadband ground motion for the 2012 Po Plain earthquake M w 6. Additionally, Paolucci et al. (2021) have developed a near source broadband strong ground motion dataset known as BB-SPEEDset, which contains 12,058 three-component earthquake waveforms by using the above methodology. The developed ground motions exhibit key ground motion features and directionality effects. However, the model is only applicable for specific events due to the limited range of M w and R epi . Further, the developed ANN model uses only spectral acceleration ( (S a ) ) values for T > T * (Period corresponding to threshold frequency) as the predictor variables. Applying the corresponding idea in a more general sense demands the inclusion of a more comprehensive dataset alongside source, path, and site parameters as predictor variables. Furthermore, an extensive parametric performance evaluation is needed to identify the best-suited ANN architecture.
The present study aims to develop a prediction model for high-frequency spectra using PBS-based low-frequency S a values, source, path, and site parameters as predictor variables. Further, a methodology is developed to generate broadband ground motion from the predicted ANN spectra. The comprehensive dataset available in the NGA-West2 database was utilized in developing the model. Here, moment magnitude ( M w ), rupture distance (R rup ) , shear wave velocity in top 30 m (V s30 ) , focal mechanism (FM) and S a for T ≥ T * are considered as input variables. The 2008 Iwate earthquake ( M w 6.9, 2008) is used as a case study to show the developed model's application. The model shows fairly good agreement with the recorded data.

Database
The present study utilizes spectral acceleration data available in NGA-West 2, which is a comprehensive global database for ground motion time histories (Taylor et al. 2007). Here, horizontal rotd50 response spectra available at https:// peer. berke ley. edu/ resea rch/ data-scien ces/ datab ases is used. The database constitutes 21,540 ground motion records from 600 events as on January 2015. The data is filtered (Dhanya and Raghukanth 2018) in order to avoid unsuitable records. The filtration led to the elimination of the spurious records and left with 13,552 records from 288 events. The distribution for the sorted data across various ranges of distance and magnitude among various focal mechanism classes is shown in Fig. 1. The range of magnitude ( M w ) and rupture distance ( R rup ) is 3-7.9 and 0.05-497 km, respectively, and V S30 ranges from 89 to 2016 m/s. The classification focal mechanism classes are based on rake angle, the ranges of which have been included in Fig. 1. The filtered database consists of 180 strike-slip, 38 normal and normal oblique, and 70 reverse and reverse-oblique events. The focal mechanisms (FM) are assigned with flags 1, 2, and 3 for strike-slip, normal and normal oblique, and reverse and reverse oblique. Additionally, the spectral acceleration values of 91 periods between 0 and 4 s are considered for the analysis.
1 3 3 ANN model for prediction of short-period spectra ANN models are generally used to develop nonlinear relationships between a large set of input and output variables. The methodology's inspiration is the human brain's functioning, which can work on several parallel networks of interconnected neurons in an instant. The methodology is simple to use and highly efficient for the generation of predictor models. The architecture of an ANN model consists of a layer of input neurons that is connected with the hidden layers that are further connected with a layer consisting of output neurons (Wang 2003). Each connection is assigned certain weights, and the weights are adjusted in such a manner that it matches the desired output. Other vital elements of an ANN network are the transfer and the error functions. The general representation of an ANN model is: where h i is the output parameters, is the transfer function, W ij is the weights, x j is the input parameters, and T hid is the threshold associated with hidden neurons.
In this study, a feed-forward neural network with a multi-layer of perceptron (MLP) is developed to predict short-period spectral ordinates ( T < T * ) based upon long-period spectral ordinates ( T ≥ T * ) and parameters representing source, path, and site. Here, T * is the threshold or cross-over period. The initial step in generating a neural network was deciding the functional form such that it captures the buried features within the data with minimal variance. For this purpose, several trials were performed using different where M w -moment magnitude, S a -spectral acceleration, R rup -rupture distance, V s30shear wave velocity in the top 30 m of soil and FM-focal mechanism.
The subsequent decision in the development of a neural network is selecting an optimal number of hidden layers and hidden neurons. However, there are no stringent criteria for selecting the number of hidden layers for a neural network. From past studies, it has been found that in most cases, a single layer of hidden neurons is sufficient to capture the model characteristics (Wang 2003). Therefore, this study also employs a single layer of hidden neurons. Several criteria exist for deciding the number of hidden neurons, and researchers have taken the number equal to twice the number of input neurons (Berry and Linoff 2004). Nevertheless, no improvement has been observed in the model performance when the hidden neurons are greater than the input variables. Therefore, to avoid the problem of over-fitting, we have taken the number of hidden neurons equal to the number of input neurons. Furthermore, an appropriate scaling function is used to bind the data between 0 and 1 or − 1 to 1 to maintain uniformity among the variables. Here, we scaled out parameters between the range − 1 to 1 using the scaling, such that where Y is the parameter value to be scaled, Y max and Y min are the corresponding maximum and minimum values. Further, the procedure includes training, validation, and testing of the ANN model. For this purpose, a random division of data is done into the training, validation, and testing sets in 70, 15, and 15%, respectively. This step ensures that the model does not show any trend/bias toward a particular input parameter. In the training phase, the error function between the predicted and actual values is minimized using different algorithms. This study utilizes Levenberg-Marquardt (LM) algorithm with the fitnet function available in the MATLAB deep learning toolbox (MATLAB 2019). Thus, we verified a total of 72 cases having varied combinations of input variables and transfer functions in arriving at the final prediction model. In all these cases, the cross-over period T * is taken as 0.75 s. The performance of each of the model architectures is assessed based on the following performance criteria: 3. Root mean squared error (RMSE) (2) log 10 S a (T < T * ) = f (log 10 S a (T ≥ T * ), M w , log 10 V (S30) , R rup , log 10 R rup , FM) where O = log 10 S a (T < T * ) is the output from the models, N is the number of data-points.
The best model will have R and PP values closer to unity and MSR and ( ) minimum. We observed that the best transfer function varies based on the form of input (Refer to Supplement material). Furthermore, the best performance was obtained for the model containing source, path, site characteristics, and long-period spectral accelerations. The corresponding model performed best with transfer functions as tan-sigmoidal between the input to hidden layers and pure-linear between hidden to output layers. It has been reported that the tansigmoidal function can capture the nonlinear effects efficiently (Derras et al. 2014). The related functional form of the model is shown further: where In Eq. 8 the X i is the input consisting of the parameters in Eq. 2, W ik,1 , bias k,1 are the unknowns between input-hidden layers and W k,2 , bias 2 are the unknown coefficients between the hidden-output layers. The best-performing network architecture for the crossover period of T * = 0.75 s consists of 21 input neurons and 17 output neurons, with 836 unknown weights and biases. The details of the network architecture can be understood from Fig. 2. Since physics-based simulators have different threshold frequencies, ANN models are also developed for additional periods of 0.5 and 1 s. The corresponding architecture for cross-over periods of 0.5 s and 1 s consists of 24 input neurons, 14 output neurons, 950 unknown weights and biases, and 18 input neurons, 20 output neurons, and 722 unknowns (weights and biases), respectively. The performance parameters corresponding to each cross-over period ( T * ) are compiled in Table 1. We obtained comparable performance at all cross-over periods. Further, we can observe from Table 1 that the value of the standard deviation of errors ( ) corresponding to all cross-over periods is bounded within 0.238 in log 10 scale, which is lesser than the reported value of Paolucci et al. (2018).

Residual analysis
Residual analysis helps investigate the model's prediction accuracy and tests for any pertinent biases. Residual is the difference between the actual and the model-predicted value; ideally, the residual's sum and mean should be zero. In this study, the logarithmic residual between the predicted and the recorded S a values and plots for three cross-over periods ( T * ) as presented in Fig. 3. The plot shows that the mean residuals do not contain any trend. Further, it can be concluded that the mean value of the residual value oscillates around zero, which depicts the method's accuracy and proves that there is no bias toward a particular period. Additionally, we observe that the residues are minimum at the cross-over period. The corresponding feature of the models will facilitate avoiding any jump that might arise in typical hybrid broadband methodologies (Paolucci et al. 2018). Hence, it can be stated that the statistical performance of the newly generated hybrid broadband spectra generator is acceptable when compared to the other hybrid models. After investigating the statistical performance of the developed model. The model is examined forward by verifying its ability to capture the physical trends related to earthquake processes. Furthermore, the model performance will be evaluated by comparing it with a recorded event. A detailed discussion of both aspects has been provided in the subsequent section.

Results and discussion
There exist several physical phenomena that impact the characteristics of ground shaking. Verifying the physical trends ensures that the model can account for the ground motion aleatory variability (GMAV) and does not suffer the problem of over-fitting (Derras et al. 2014). Further, the model's capability in dealing with a real-earthquake Fig. 2 The architecture of the artificial neural network (ANN) model to predict short-period spectra from long-period spectra, earthquake source, path, and site characteristics. The represented architecture corresponds to that for a cross-over period on 0.75 s ( M w = moment magnitude, R rup = closest distance to rupture, FM = focal mechanism, V S30 = average shear wave velocity of top 30 m, S a = spectral acceleration, T * (cross-over period) 1 3 scenario and evaluating the corresponding efficiency is also essential to assess its applicability toward a physics-based hazard framework. Therefore, this section provides a detailed investigation of model performance on the metrics of physical trends and a comparison with an actual earthquake.

Evaluation of physical trends in the model predictions
There always exists a debate on the usage of ANN in natural phenomena. Since several hidden layers exist in the network, verifying whether the developed model follows the physical laws is obligatory. The procedure consists of investigating the scaling of the predicted values against various input parameters that include M w , R rup , and V s30 . This investigation ascertains that the model can capture the nonlinear behavior of ground motion. Here, the model with a 0.75 s cross-over period is selected for the demonstration purpose. Further, the long-period spectral acceleration values (a primary input required for the present model) are taken from the mean prediction by Dhanya and Raghukanth (2018), which was developed using the same database. The variation of the predicted S a values with M w , R rup and V s30 for different focal mechanisms is shown in Figs. 4 and 5. From Fig. 4, it can be observed that the S a value decreases with an increase in R rup , and the peak period of the spectra is shifting toward long periods with the increase in magnitude. Further, from Fig. 5, it is observed that the spectral acceleration values increase with the decrease in V s30 , and the peak period gets shifted to long periods. Further, we attempted to understand the significance of the inclusion of V s30 by checking the trends followed by the model developed (refer to supplemental document) without the corresponding variable. It was noted that the corresponding predictions were not able to capture the trend as observed in Fig. 5. Furthermore, for the final model, it is also interesting to note that there are no jumps at the Fig. 4 Variation of spectral acceleration ( S a ) with respect to rupture distance ( R rup ) for different magnitude ( M w ) and focal mechanism (FM). Here the model with cross-over period T * = 0.75 s is considered and lowfrequency spectral acceleration is taken from the mean value of the prediction model developed by Dhanya and Raghukanth (2018) cross-over period. The model's ability to capture the scaling and the nonlinear site effects were also evaluated. The corresponding results are summarized from Figs. 6, 7 and 8. Figure 6 shows the variation of S a at T = 2 s with R rup for different magnitudes of earthquake (i.e., magnitude scaling effect). It can be observed from the figure that the response is highly nonlinear at near and intermediate values of R rup . Further, it can be observed that the value decreases with an increase in the rupture distance, which shows the anelastic attenuation (material damping) and geometrical spreading, similar to the trends observed in the parametric GMPEs. Furthermore, Fig. 7 shows the scaling of PGA predictions from the model against V s30 values. It can be observed that the PGA values decrease with an increase in V s30 , which supports the hypothesis that the intensity of ground motion decreases with the stiffening of the medium (Derras et al. 2017). Furthermore, Fig. 8 Derras et al. (2017). A key observation from Fig. 8a is the curvature of the plot that indicates the amplified site response in the case of soil site compared to rock site. The observation is consistent for all focal mechanisms; the convexity points toward the nonlinear site characteristics that the model is capturing successfully. Furthermore, Fig. 8b shows the nonlinear amplification of the ground motion. It can be observed from the plot that the amplification is more for lower PGA values, and for higher PGA ranges, the relationship becomes almost linear (Derras et al. 2014).

Fig. 5
Variation of spectral acceleration ( S a ) with respect to rupture distance ( V s30 ) for different magnitude ( M w ) and focal mechanism (FM). Here the model with cross-over period T * = 0.75 s is considered and lowfrequency spectral acceleration is taken from the mean value of the prediction model developed by Dhanya and Raghukanth (2018) Hence, based on these above observations, it can be concluded that the developed ANN model is physically sound and accounts for various scaling laws related to an earthquake process. Further, the spectra obtained from the model inherit the nonlinear site-specific effects. Similar observations were obtained for all the models listed in Table 1, and each can be applied suitably depending on the available computational infrastructure. Now, it would be interesting to observe the performance of the ANN model in case of a real earthquake; a detailed demonstration of the same has been presented in the following subsection.

Case study of Iwate Earthquake, 2008 M w 6.9
After analyzing the competency of the developed model on statistical performance and scaling law, the subsection includes the application of the methodology on a real-time earthquake. For this purpose Iwate Earthquake, 2008 M w 6.9 has been used.

Deterministic simulation of low-frequency ground motion
To generate low-frequency ground motions of the Iwate earthquake, we used rupture models of Asano and Iwata (2011) and Cultrera et al. (2013) have been used. The details of the source parameters for the rupture models are compiled in Table 2 (http:// equake-rc. info/ SRCMOD/ searc hmode ls/ viewm odel/ s2008 IWATE x01AS AN/). The corresponding slip and rupture time distributions for the models are shown in Fig. 9. The low-frequency simulations are performed using a discrete-wavenumber finite element method (Olson et al. 1984;Spudich and Xu 2002). To consider the slowest shear wave velocity, 2.7 km/s a grid resolutions of dz = 150 m is used to simulate ground motions up to a maximum frequency Fig. 6 Illustration of magnitude scaling and near field saturation effects: S a at T = 2 s versus R rup for V s30 = 760 m/s, R rup varies from 5 to 150 km and focal mechanism is reverse fault of 3 Hz. Adopting a 1D Earth structure (Table 3), synthetic waveforms at all recording stations (Joyner-Boore distance Rjb < 150 km) are computed. To capture nonlinear site effects, corrections are applied by removing the mean site residuals for each site class at selected natural periods. The low-frequency PBS simulations are performed for all 150 recording stations. However, for representation purpose three stations, AKT017, AKT012, and IWTH17 having R rup values 33.8, 58.1, and 73.7 km, respectively, has been chosen. The low-frequency time histories for the three stations are shown in Fig. 10. The Cultrera et al. (2013) model the peak amplitudes are larger, possibly due to the proximity of the stations to the largest asperity region of the source.

ANN model predictions
After generating PBS for the earthquake, it is used as an input for the developed ANN model discussed in Sect. 3, to obtain broadband response spectra for all of the recording stations. To check the model performance, the residuals between the simulated and recorded S a values have been evaluated as shown in Fig. 11. The figure consists of bias for PBS and the developed ANN model (Model-1), indicated in blue and red, respectively. It is observed that, among the considered source models, Asano and Iwata (2011) model showed lesser residual and standard deviation compared to Cultrera et al. (2013) model. Such an observation can be attributed to the variability associated with the slip inversion techniques and the data. However, it was noted that the mean bias is very close to zero, pointing toward the efficiency of the developed model. Additionally, it was also noted that the standard deviation in the short-period range is lesser compared to the PBS period range.
We further compared the model-predicted values with an ANN model that considered only long-period spectral acceleration as input variables similar to Paolucci et al. (2018) by estimating the bias (Model-2, Refer Supplement Material no 2 for details). The corresponding bias is indicated as green color in Fig. 11. It can be observed that the prediction variability Here, M w is taken as 7 and V s30 for soft and stiff site is taken as 264 m/s (10 percentile) and 710 m/s (90 percentile), respectively. R rup varies from 20 to 200 km. b PGA soft ∕PGA stiff versus PGA stiff for various focal mechanism. Here, V s30 for soft and stiff site is taken as 264 m/s and 710 m/s, respectively, and focal mechanism is strike-slip fault. R rup varies from 20 to 200 km is more for Model-2, and the mean bias also significantly deviated from the zero-line in comparison with that of Model-1. These observations confirm that a better prediction of the short-period spectra can be made by including path and site characteristics in the prediction model. Furthermore, a comparison between the recorded and the predicted spectra corresponding to the two ANN models (i.e., Model-1 and Model-2) is made for the three stations (i.e., AKT017, AKT012, and IWTH17) and is shown in Fig. 12. It can be observed from the figure that the predicted spectra from Model-1 are comparable with the recorded spectra for all three stations. However, in the case of Model-2, the two spectra are not in good agreement with each other, similar to the observation from the bias plots (Fig. 11). It can be noted that Model-1 can generate comparable spectra at short periods, even if PBS spectra are not in line with the recorded values (generally occurs in PBS due to assumptions in fault rupture modeling), which is visible for station AKT017. A trend that was absent in the case of Model-2. All of the findings further boost the claim that the inclusion of source and site parameters as predictor variables in the ANN model leads to better prediction of short-period spectra.

Generation of broadband ground motion
For nonlinear structural analysis, however, one requires simulated time histories. In this study, we have used the spectral ordinate matching method for generating broadband time histories from the predicted spectra, which iteratively modifies the input seed ground motion until it matches the target spectra. The spectral ordinate matching is done in the frequency domain using the code of Ferreira et al. (2020), and PBS is used as input seed ground motion. Due to the deficiency of PBS waveform corresponding to higher frequencies, a broadband time history cannot be achieved directly. Therefore, we have modified the input seed ground motion so that it can cater to all frequency ranges. The methodology can be understood using Fig. 13. Here, the initial seed is modified by adding bandpass (1.33-15 Hz) filtered white noise. Here, the white noise signal is filtered using the Butterworth band-pass filter in MATLAB. Further, for generating a non-stationary ground motion, the filtered white noise is modified using an envelope function. The envelope function is the realistic exponential function (Takewaki 2004) given in the following equation: where = 0.13 and = 0.45. The added white noise is consistent with the stochastic nature of the earthquake ground motion and provides a complete waveform that can be spectrally matched to the target response spectra. In our case, we have used it because the methodology is simple, reproducible and robust, which makes the model useful for various source and site inputs. Smerzini and Villani (2012) suggested using either empirical or stochastic methods to generate high-frequency ground motion. The motivation behind using such Physics-based input low-frequency ground motion for Iwate earthquake ( M w − 6.9 , corresponding to different source models (Cultrera et al. 2013;Asano and Iwata 2011) techniques is to include source and site effects related to ground motion. However, the proposed ANN model has the ability to capture nonlinear source and site effects, as demonstrated in the Results and Discussion section (Sect. 4). The filtered white noise is then summed up with the PBS signals to generate a modified seed that is appropriate to be used as input for the spectral ordinate matching technique. The generated modified seed consists of intensity corresponding to all frequencies and can be spectrally matched to the ANNgenerated target spectra as shown in Fig. 14.
The recorded and the simulated time histories, along with the Fourier amplitude spectra, is represented in Figs. 15 and 16. It can be inferred from the figure that the generated time histories are in reasonable comparison with the recorded ones, having comparable peaks and duration. The Fourier amplitude spectra of the simulated time histories match reasonably well with the recorded values at higher frequencies, even if lower-frequency values are not comparable, similar to what was observed before in the response spectra plots. The study for the Iwate earthquake shows that the model can accurately predict response spectra for earthquakes in active shallow crustal regions. Additionally, broadband time histories can be obtained from the developed model. Fig. 11 Bias plots between recorded and simulated spectra for the ANN prediction models corresponding to fault normal and fault parallel components for Iwate earthquake using the slip fields reported by Asano and Iwata (2011) and Cultrera et al. (2013), respectively. Here, spectral acceleration corresponds to the PBS is in the higher period part ( T * = 0.75-4 s) and from the ANN models with the corresponding LF inputs for high-frequency part ( T * < 0.75 s). [Note: input variable for Model-1 were ( M w , FM, R rup , log 10 (R rup ) , log 10 (V s30 ) , log 10 (S a ≥ T * ) ) and Model-2 were ( log 10 (Sa ≥ T * ))] In short, from the detailed evaluation of the results and the corresponding discussion, the model was observed to be unbiased, having an acceptable variability during the predictions. Further, the present model could capture the physical trends typically exhibited by the ground motions as discussed in GMPE-related literature. The efficiency in modeling an earthquake scenario was also demonstrated, projecting the corresponding potential toward Fig. 12 Comparison plots between recorded, physics-based simulation (PBS), and ANN models predicted response spectra at stations AKT017, AKT012, and IWT017 corresponding to Asano and Iwata (2011) and Cultrera et al. (2013) rupture models Fig. 13 Procedure for generation of modified seed from seed obtained from physics-based simulations (PBS) by addition of filtered white noise broadband physics-based hazard analysis. A fine-tuning of the corresponding hybrid modeling using a more extensive database or different approaches that could further reduce the aleatory variability can be thought off.

Conclusions
This study proposes a new ANN model that can predict a broadband spectrum using the physics-based low-frequency simulation, source, and site parameters as the predictor variables. The ANN model is developed using the NGA-West2 database. The generated model gives better performance both on statistical and physical trend metrics. Further, including the source and site parameters make the model more robust and accurate. The spectra obtained from the new model are self-sufficient in capturing all the earthquake source and site effects. The Iwate earthquake of 2008, M w − 6.9 , was used as a case study to display the model efficiency. The results show that the model-predicted spectra values are comparable with the recorded ones. Also, the model can predict the short-period S a values when PBS S a values are not in line with the recorded values. The model-generated spectra can be used for seismic hazard studies, leading to better mitigation strategies.
Further, the time histories are obtained from the generated spectra using the spectral ordinate matching method. The simulated time histories are compared with recorded ones for several stations. The results show that generated time histories are in agreement with the recorded ones. Since the source and site effects were included at the response spectra level, we have found that the input seed ground motion, i.e., required for generating broadband time histories, can be developed by simplified approaches (i.e., white noise . The simulated ground motions are helpful while performing nonlinear structural analysis for the earthquake forces. Although the model performs well in predicting a real earthquake, a model based on advanced machine-learning techniques will be interesting to explore. Further, the NGA-West2 database consists of only shallow crustal earthquakes in active regions. A similar model can be developed for broader applicability using other regional/global databases. Furthermore, the model can be made more robust by including more input variables for training and validation purposes.