The response spectrum is the central currency of earthquake engineering. It summarizes, for a range of vibration periods, the peak response a single-degree-of-freedom oscillator would experience when subjected to a particular accelerogram, and design codes around the world specify shaking demands in exactly these terms. A spectrum-compatible time history is therefore a record whose computed response spectrum matches a code spectrum or a scenario-specific prediction across the period range of interest. Classical approaches to this problem, including wavelet adjustment and frequency-domain optimization, iteratively tweak an existing record until its spectrum fits. Those methods work, but they can distort the phase characteristics, duration, and energy distribution of the original motion, sometimes producing signals that are mathematically compliant yet physically implausible, with unrealistic pulses or smeared energy that mislead nonlinear structural analyses.

The new framework attacks the problem in the time-frequency domain. The authors convert ground motion records into short-time Fourier transform, or STFT, representations, which describe how the amplitude content of the signal evolves across both time and frequency. This representation is crucial because earthquake shaking is inherently nonstationary: high-frequency P- and S-wave energy arrives first, lower-frequency surface waves dominate later, and the amplitude envelope rises and falls in ways that strongly affect structural response. By training a generative model on STFT amplitudes conditioned on a target response spectrum and a latent random variable, the model learns the conditional distribution of time-frequency amplitudes that real, spectrum-consistent accelerograms occupy. Once trained, it can sample that distribution, drawing an effectively unlimited family of distinct accelerograms for any given target spectrum, each with its own plausible waveform realization.

The architecture combines two of the most influential ideas in modern generative machine learning. A variational autoencoder provides a structured latent space from which diverse samples can be drawn, while a generative adversarial network, trained with the Wasserstein distance and a gradient penalty, sharpens the realism of the generated time-frequency amplitudes by forcing them to be statistically indistinguishable from those of genuine records. The Wasserstein formulation, introduced by Arjovsky and colleagues and refined by Gulrajani and colleagues, was chosen for its well-behaved gradients, and the authors report that training histories showed no numerical divergence and no abrupt collapse of sample diversity, a failure mode that plagues conventional adversarial training. The Griffin-Lim style signal reconstruction then maps the generated amplitude information back into the time domain to yield acceleration time histories.

The most distinctive component, however, is what the authors call the response spectrum consistency network, or RSCN. Rather than hoping that spectrum compatibility emerges implicitly from training on real records, the team embedded an explicit spectrum consistency loss directly into the training objective. The RSCN acts as a differentiable surrogate for the computation of the response spectrum, allowing gradients to flow from a period-weighted measure of spectral mismatch back into the generator. In ablation experiments on an event-independent test subset, adding the RSCN measurably reduced response spectrum residuals and improved period-specific calibration compared with an otherwise identical model trained without it. In other words, the network does not merely imitate the spectral statistics of its training data; it actively learns to hit the specific target spectrum handed to it at generation time.

Where do those target spectra come from? The study couples the generative model with a validation-derived, period-weighted ensemble ground motion model, or GMM, that supplies scenario-dependent targets. Ground motion models, the empirical equations that predict spectral accelerations as a function of magnitude, distance, and site conditions, have themselves been undergoing a machine-learning transformation, with neural networks, XGBoost, and hybrid recurrent architectures increasingly used to capture regional attenuation and site effects. By ensembling such predictions and weighting them across the period range, the framework produces a target spectrum tailored to a specific earthquake scenario, and the STFT-VAEGAN then fills in the missing physics: the full stochastic waveform structure that a spectrum alone cannot specify. This linkage between scenario-based spectrum prediction and stochastic time history generation is, according to the authors, the central contribution of the work.

The training and validation data were drawn from the NGA-West2 strong-motion database, the peer-maintained compilation of shallow crustal earthquake recordings curated at the Pacific Earthquake Engineering Research Center, which has become the de facto standard for empirical ground motion modeling worldwide. The authors evaluated the model on a test subset held out by event, a stricter protocol than holding out individual records, because it prevents the network from memorizing the characteristics of particular earthquakes. Test examples demonstrated that the generated accelerograms carry response spectra compatible with their targets while retaining nonstationary time-frequency structure. The team also applied the framework in a case study of the Chi-Chi earthquake, one of the most extensively recorded events in modern seismology, showing that the model can produce multiple distinct accelerograms appropriate to that scenario.

The study builds on a rapidly growing body of work applying deep generative models to seismology. Earlier efforts include conditional GANs that synthesize nonstationary ground motion in the time-frequency domain, data-driven broadband synthesis of earthquake records, and adversarial neural operators for broadband ground-motion synthesis. Hu and colleagues had previously developed a conditional variational autoencoder with adversarial training for spectrum-compatible artificial accelerograms, published in Engineering Structures, and the new Bulletin of Earthquake Engineering paper extends that line by integrating the explicit spectrum consistency loss and the ensemble ground motion model into a single end-to-end pipeline. The distinction matters for practice: a generator that can accept an arbitrary, scenario-derived target spectrum and return a family of conforming, realistic time histories is precisely the tool that performance-based earthquake engineering workflows need for large ensembles of nonlinear structural analyses.

The practical implications extend across seismic hazard analysis, code-based design verification, and the growing field of physics-informed machine learning for earthquake engineering. Fragility curves, which estimate the probability of structural damage as a function of shaking intensity, depend on suites of ground motions that are both numerous and spectrally appropriate; generative sampling offers a way to build such suites without the record-scaling artifacts that contaminate many existing studies. The authors note that the codes developed in the work will be made publicly available on GitHub, and that the underlying records come from the openly accessible NGA-West2 database, lowering the barrier for other research groups to adopt and stress-test the approach. Funded by the National Natural Science Foundation of China under grants 52192675 and 52378541, the work signals a broader shift in which the stochastic simulation of earthquake shaking, once the province of hand-tuned spectral matching algorithms, is increasingly delegated to neural networks that learn the statistics of real ground motion directly from data, and then generate exactly the shaking scenarios engineers ask for.

Subject of Research: Generative AI-based simulation of spectrum-compatible earthquake ground motion time histories

Article Title: Generative AI for spectrum-compatible ground motion time history simulation

Article References: Hu, X., Chen, S., Ding, Y., Liu, X., Fu, L., Zhao, Q., & Li, X. (2026). Generative AI for spectrum-compatible ground motion time history simulation. Bulletin of Earthquake Engineering. https://doi.org/10.1007/s10518-026-02699-z

Image Credits: AI Generated

DOI: 10.1007/s10518-026-02699-z

Keywords: generative artificial intelligence, STFT-VAEGAN, ground motion simulation, response spectrum matching, earthquake engineering, variational autoencoder, generative adversarial network, Wasserstein GAN, NGA-West2 database, ground motion model, nonstationary waveforms, seismic hazard analysis

The study, led by Farhad Sedaghati of Aon Impact Forecasting together with Shahram Pezeshk and Mehran Davatgari-Tafreshi of the University of Memphis, focuses on a quantity called the Effective Amplitude Spectrum, or EAS. Unlike the response spectra most commonly used in building design, which describe how an idealized oscillator reacts to shaking, the EAS is derived directly from the Fourier amplitude spectrum of the recorded motion. That gives it a direct physical interpretation: it reflects how energy is distributed across frequencies by the earthquake source, modified by the path the waves travel and by the soil conditions beneath the recording station. Engineers can also feed EAS predictions into random vibration theory to estimate response spectra quickly, without running time-consuming simulations.

To train their model, the researchers drew on the NGA-West3 database, a large and uniformly processed collection of three-component accelerograms from shallow crustal earthquakes in active tectonic regions. The raw compilation contained 175,284 records, but the team applied a stringent sequence of quality-control filters before a single neuron was trained. Records were excluded if the earthquake was smaller than magnitude 3.0, if the hypocenter was deeper than 30 kilometers, if the rupture distance exceeded 300 kilometers, or if metadata such as fault dip or shear-wave velocity were missing or implausible. Sensors buried more than two meters below the ground surface were rejected, as were stations classified as non-free-field. After all screening steps, 50,639 high-quality records remained, roughly 90 percent of them from California, with the rest contributed by Alaska, Idaho, Nevada, Utah, Washington, and Wyoming.

The neural network itself is deliberately compact. It takes six explanatory variables as input: moment magnitude, rupture distance, fault dip, depth to the top of the rupture, the time-averaged shear-wave velocity in the upper 30 meters of the site, and the depth to a stiff 2.5 kilometers-per-second shear-wave velocity horizon that characterizes sedimentary basins. From these six numbers, the network predicts the natural logarithm of EAS at 22 discrete frequencies spanning 0.05 to about 33 hertz, all at once. This multi-output design proved crucial. When the researchers initially tried predicting each frequency with a separate single-output model, the resulting spectra were jagged and unstable. Predicting all frequencies simultaneously through shared hidden layers allowed the network to learn cross-frequency patterns directly from the data, producing smooth, physically plausible spectra.

One of the thorniest practical problems was missing data. A recording may contain reliable spectral information at some frequencies but not others, because signal-to-noise ratios degrade at both the lowest and highest frequencies. Rather than discarding every record with a single gap, the team used a masked loss function during training. Missing values, represented as not-a-number entries, simply do not contribute to the error that the network tries to minimize, so partially observed spectra still teach the model whatever they can. This masked approach substantially increased the effective amount of data available, particularly at the frequency extremes where coverage is thinnest.

Avoiding inflated estimates of accuracy required equally careful design of the evaluation strategy. Recordings from the same earthquake share source characteristics, so splitting the data randomly would let the network effectively memorize events it was supposed to predict. The researchers therefore partitioned the dataset at the event level, keeping all recordings of a given earthquake together in the same fold. Hyperparameters were selected through ten-fold event-grouped cross-validation, and roughly five percent of events were held out entirely as an independent evaluation set, untouched during architecture selection, preprocessing, or training decisions. After that out-of-event assessment was complete, the final network was retrained on the full retained dataset so that every available earthquake contributed to the distributed model. The winning architecture turned out to be modest: two hidden layers with 32 and 16 neurons, a batch size of 64, and a learning rate of ten to the minus two.

The predictions that emerged show textbook seismological behavior, despite the fact that no functional form was ever imposed. Spectral amplitudes rise monotonically with magnitude and fall with distance, with high frequencies decaying faster than low ones as waves scatter and lose energy in the crust. At low frequencies the spectra steepen toward a corner frequency in a manner consistent with the classical omega-square source model, and at high frequencies they roll off in the way associated with near-surface damping. The team is careful to note that these are qualitative consistencies, not quantitative estimates of source parameters such as corner frequency or kappa, and that predictions above magnitude 7.36, the largest event in the training data, are extrapolations presented for illustration rather than validated forecasts.

Beyond median predictions, the researchers quantified aleatory variability, the irreducible randomness in ground motion that remains after source, path, and site effects are accounted for. Using a sequential mixed-effects decomposition, they separated total residuals into between-event, site-to-site, and event-site-corrected components at each of the 22 frequencies. The standard deviations show clear frequency dependence, increasing toward higher frequencies where ground motion is most sensitive to record-specific details, and they fall within the range reported by existing empirical EAS models. This decomposition matters for practice: in conventional probabilistic seismic hazard analysis the total variability is used directly, but for site-specific studies the explicit separation allows engineers to condition on measured site behavior and reduce uncertainty.

How does the machine stack up against the human-crafted equations it joins? The team compared their model against three established empirical EAS ground-motion models, Bora and colleagues from 2019, Bayless and Abrahamson from 2019, and Campbell and Bozorgnia from 2025, all built on the earlier NGA-West2 database. Across representative scenarios, the neural network’s median predictions track the empirical models closely in both spectral shape and scaling trends, and its variability estimates sit within the published range. The authors are candid that these comparisons demonstrate physical plausibility rather than superiority, since a rigorous head-to-head test would require fitting a parametric model to identical data with identical partitions, something they flag as important future work. Interestingly, the network also reproduced the observed cross-frequency correlation structure of the data with a Pearson correlation of 0.964 between observed and predicted correlation coefficients.

The researchers have released the trained model, its preprocessing scaler, and example code on GitHub, making the tool immediately usable by hazard analysts. Because the network produces broadband Fourier spectra in a fraction of a second, it is well suited to applications that demand thousands or millions of repeated ground-motion evaluations, such as probabilistic seismic hazard analysis and simulation-based risk studies. The model is strictly valid within the range of its training data, magnitudes from about 3.0 to 7.36, distances up to 300 kilometers, and sites from soft soil to hard rock, and it is calibrated specifically for western United States tectonics. Future directions include explainable artificial intelligence techniques to reveal which predictors matter most at each frequency, and physics-informed training that would embed source models such as Brune’s spectrum directly into the learning objective, potentially improving extrapolation to the largest, rarest earthquakes that engineers care about most.

Subject of Research: A data-driven neural network ground-motion model for Fourier amplitude spectra of shallow crustal earthquakes using the NGA-West3 database

Article Title: A data-driven ground-motion model for Fourier amplitude spectra of shallow crustal earthquakes using the NGA-West3 database

Article References: Sedaghati, F., Pezeshk, S., & Davatgari-Tafreshi, M. (2026). A data-driven ground-motion model for Fourier amplitude spectra of shallow crustal earthquakes using the NGA-West3 database. Bulletin of Earthquake Engineering. https://doi.org/10.1007/s10518-026-02708-1

Image Credits: AI Generated

DOI: 10.1007/s10518-026-02708-1

Keywords: ground-motion model, effective amplitude spectrum, NGA-West3, artificial neural network, machine learning, Fourier amplitude spectrum, seismic hazard analysis, shallow crustal earthquakes, aleatory variability, random vibration theory, western United States, earthquake engineering