Seismic Wave Generator Overview

• Seismic Wave Generators are systems that create synthetic seismic observables or upstream Earth models using physics-based solvers, procedural methods, and data-driven techniques.
• They integrate various methodologies, such as finite-difference solvers, procedural model generators, and generative adversarial or diffusion frameworks, to simulate realistic wavefields and subsurface structures.
• Recent advancements focus on modular, integrated pipelines that enhance synthetic data realism and optimize simulation efficiency for applications like full-waveform inversion and hazard analysis.

Searching arXiv for the cited papers to ground the response in fresh sources. A seismic wave generator is not a single standardized device or algorithm but a family of systems that create, parameterize, or condition synthetic seismic phenomena. Across recent arXiv work, the term encompasses physics-based forward solvers that generate wavefields and receiver data, procedural generators of subsurface models that supply the material structure required by later forward modeling, conditional generative models that synthesize waveform records directly from data, and, in some metamaterial papers, passive structures that control rather than generate seismic waves (Wang et al., 1 Apr 2026, Fathizadeh et al., 13 Dec 2025, Duan et al., 21 Sep 2025, Kim et al., 2012). The common function is the production of synthetic seismic observables or the upstream physical state from which such observables are derived; the differences lie in whether the generator acts at the level of source, propagation, subsurface model, waveform statistics, or propagation control.

1. Terminology and conceptual scope

In the surveyed literature, “seismic wave generator” is used in at least four distinct senses. First, it may denote a numerical wave-equation engine that injects a source into a medium and computes synthetic receiver data, as in SWEEP, AstroSeis, marine microseismic forward modeling, and the Euler/SPH-based source-to-waveform frameworks (Wang et al., 1 Apr 2026, Tian et al., 2020, Das et al., 2017, Turner et al., 2023). Second, it may denote an upstream procedural model generator that produces the layered or field-scale Earth models required by later propagation codes, as in SoilGen and SubsurfaceGen (Fathizadeh et al., 13 Dec 2025, Stitt et al., 28 May 2026). Third, it may denote a data-driven waveform synthesizer or forecaster, such as SeismoGen, SWaG, SeismoGPT, high-resolution latent diffusion GWMs, or TimesNet-Gen (Wang et al., 2019, Duan et al., 21 Sep 2025, Esmail et al., 25 Sep 2025, Bergmeister et al., 2024, Yilmaz et al., 4 Dec 2025). Fourth, some papers use waveguide or shadow-zone language for seismic metamaterials that are in fact attenuators rather than generators (Kim et al., 2012, Kim et al., 2012).

Category	Representative systems	Primary output
Physics-based forward solvers	SWEEP, AstroSeis, PyAWD, marine GPU microseismic modeling	Wavefields, seismograms, shot gathers
Procedural Earth/site model generators	SoilGen, SubsurfaceGen	Soil profiles, velocity models, labeled earth models
Data-driven waveform generators	SeismoGen, SWaG, SeismoGPT, TimesNet-Gen, latent diffusion GWM	Synthetic waveform windows or continuations
Passive propagation-control systems	Seismic metamaterial barriers	Attenuation or shadow zones, not source generation

This breadth creates a recurrent misconception. A system may be central to synthetic seismic workflows without itself generating propagated waves. SoilGen is explicit on this point: it is “not a seismic wave generator in the narrow sense of producing source-time functions or waveforms,” but a synthetic subsurface model generator that supplies the layered earth models required by many forward-modeling workflows (Fathizadeh et al., 13 Dec 2025). Conversely, metamaterial barriers manipulate incident waves yet “do not really provide a seismic-wave generator design” (Kim et al., 2012).

2. Physics-based numerical generators

Physics-based seismic wave generators solve a governing PDE together with a source model, acquisition geometry, and boundary treatment. In SWEEP, the framework is organized around Propagator, Source, and Receiver modules, and supports acoustic, elastic, attenuative/viscoacoustic, VTI, TTI, Born approximations, acoustic-elastic coupled equations, and a pseudo-elastic pure-P formulation (Wang et al., 1 Apr 2026). The paper gives both first-order and second-order acoustic systems and illustrates the abstraction with the update

$$u^{n+1} = 2u^n - u^{n-1} + v_p^2 \Delta t^2 \nabla^2 u^n,$$

implemented through a user-supplied step function (Wang et al., 1 Apr 2026). In this usage, the generator is a conventional wave-equation time-marching engine with source injection into named wavefield components and receiver sampling at specified locations.

PyAWD occupies a narrower but practical position: it solves the damped forced acoustic wave equation

$$\frac{d^2u}{dt^2} = c\nabla^2 u - \alpha \frac{du}{dt}+ f$$

in 2D and 3D heterogeneous media, using Devito as a finite-difference backend, and can output both full wavefields and “interrogator” traces that function as virtual seismometers (Tribel et al., 2024). The paper is explicit that this is acoustic rather than full elastic physics, yet also explicit that it is intended as a synthetic data generator for earthquake-analysis and machine-learning workflows, including sparse-sensor epicenter retrieval (Tribel et al., 2024). This suggests an important distinction: some generators aim at physical completeness, others at scalable proxy realism.

AstroSeis is a numerical generator in the frequency domain rather than the time domain. It is a 3-D elastic Boundary Element Method code for arbitrarily shaped bodies such as asteroids, supports arbitrary surface topography and an optional liquid core, and uses either single-force or moment-tensor sources (Tian et al., 2020). Its boundary-integral formulation reconstructs the interior wavefield from boundary quantities, and the paper benchmarks the code against normal modes summation and DSM, reporting RMS error values of $0.88\%$, $0.48\%$, and $1.45\%$ for representative tests (Tian et al., 2020). Here the generator is defined by its source flexibility, geometry flexibility, and frequency-domain propagation.

A different physics-based strategy appears in the marine microseismic pipeline of 3D elastic GPU modeling. That work solves the 3D elastic wave equation in first-order stress–velocity form with heterogeneous $c_p(\mathbf{x})$, $c_s(\mathbf{x})$, and $\rho(\mathbf{x})$, using a Fourier-domain pseudo-spectral method in k-Wave, staggered-grid leapfrog updates, and PML boundaries (Das et al., 2017). The decisive efficiency trick is linear superposition of individually simulated event responses after amplitude scaling and origin-time shifts. Because the PDE is linear, complex source scenes are generated as

$$d_{\text{total}}(\mathbf{x}_r,t)=\sum_{m=1}^{N_e} a_m\, d_m(\mathbf{x}_r,t-\tau_m)$$

for pressure and each particle-velocity component (Das et al., 2017). In this sense, a seismic wave generator can be both a solver and a reusable library of Green’s-function-like responses.

Two specialized source-to-wave frameworks extend the concept further. The paper on waves generated by vertical seabed displacements solves the full nonlinear Euler equations with a time-dependent conformal map to simulate tsunami-generation physics from prescribed moving bottoms (Poletto et al., 2023). The cryoseismic SPH framework begins with smoothed particle hydrodynamics of water flow, converts detected water–ice collisions into damped vector force sources, propagates P and S body waves with geometric spreading, frequency-dependent attenuation, and weak dispersion, and sums all collisions to produce a synthetic three-component acceleration time series at any receiver (Turner et al., 2023). Both are generators in the strict source-to-observable sense, but they generate very specific classes of seismic or seismically relevant signals.

3. Procedural subsurface and site-model generators

A second class of seismic wave generator acts upstream of propagation by synthesizing the medium rather than the waveform. SoilGen is the clearest example in the near-surface setting. It procedurally generates 1D layered soil columns, typically with 3 to 8 layers, including layer thickness $h_i$, shear-wave velocity $$\frac{d^2u}{dt^2} = c\nabla^2 u - \alpha \frac{du}{dt}+ f$$0, P-wave velocity $$\frac{d^2u}{dt^2} = c\nabla^2 u - \alpha \frac{du}{dt}+ f$$1, density $$\frac{d^2u}{dt^2} = c\nabla^2 u - \alpha \frac{du}{dt}+ f$$2, and Poisson’s ratio $$\frac{d^2u}{dt^2} = c\nabla^2 u - \alpha \frac{du}{dt}+ f$$3, while enforcing constraints such as $$\frac{d^2u}{dt^2} = c\nabla^2 u - \alpha \frac{du}{dt}+ f$$4, non-negative values, realistic geotechnical ranges, and $$\frac{d^2u}{dt^2} = c\nabla^2 u - \alpha \frac{du}{dt}+ f$$5 (Fathizadeh et al., 13 Dec 2025). It computes $$\frac{d^2u}{dt^2} = c\nabla^2 u - \alpha \frac{du}{dt}+ f$$6, attaches NEHRP and Eurocode 8 classes, estimates fundamental resonance frequency using

$$\frac{d^2u}{dt^2} = c\nabla^2 u - \alpha \frac{du}{dt}+ f$$7

and supports scenario logic such as “Gradual Increase,” “Sharp Contrast,” “Velocity Inversion,” “Shallow Bedrock,” “Thick Soft Deposit,” and “Thick Stiff Layer” (Fathizadeh et al., 13 Dec 2025). The paper repeatedly states that the framework can generate libraries with $$\frac{d^2u}{dt^2} = c\nabla^2 u - \alpha \frac{du}{dt}+ f$$8, which is decisive for ML-scale inversion and benchmark workflows (Fathizadeh et al., 13 Dec 2025).

The role of SoilGen is explicitly upstream. Once the layered column exists, it can be passed to site-response, HVSR, or dispersion solvers; the generator provides the material structure controlling impedance, resonance, and dispersion, but not the propagated wavefield itself (Fathizadeh et al., 13 Dec 2025). This suggests a broader conceptual definition: in seismic computation, wave generation often begins with the generation of a physically consistent Earth model.

SubsurfaceGen generalizes this idea to field scale. It procedurally builds 3D field-scale velocity models by composing geological modules such as deposit, squish, fault, saltsdt, saltwedge, carbonateplatform, deltaclinoformdeposit, and structuralsmoother, then extracts 2D slices and solves the acoustic wave equation on those slices to generate paired wavefields and shot gathers (Stitt et al., 28 May 2026). The released dataset contains 42 realistic, field-scale 3D velocity models, each spanning $$\frac{d^2u}{dt^2} = c\nabla^2 u - \alpha \frac{du}{dt}+ f$$9 laterally and $0.88\%$0 deep at $0.88\%$1 resolution; 4,276 2D velocity slices; and $0.88\%$2 wavefields plus $0.88\%$3 shot-gather cubes over five frequency bands (Stitt et al., 28 May 2026).

Its forward model is the constant-density isotropic acoustic equation

$0.88\%$4

with free-surface top boundary, Cerjan-style sponge damping on the other sides, 8th-order spatial finite differences, $0.88\%$5, and Ricker-based band-limited sources (Stitt et al., 28 May 2026). SubsurfaceGen therefore straddles two meanings of the term: it is both a procedural Earth-model generator and a synthetic seismic data generator. A plausible implication is that field-scale FWI datasets now increasingly depend on integrated geology-plus-wave-physics pipelines rather than on standalone forward solvers or standalone static benchmark models.

4. Data-driven waveform generators and forecasters

Data-driven seismic wave generators learn waveform distributions directly from labeled observations or synthetic corpora. SeismoGen is a station-specific conditional GAN that maps a 400-dimensional Gaussian latent vector plus a binary class label to a $0.88\%$6 waveform window, corresponding to 40 s at 40 Hz on three components, for earthquake/event versus non-earthquake/noise synthesis (Wang et al., 2019). Its discriminator performs adaptive low/high frequency decomposition with a learned cutoff and conditional convolutional scoring. The paper’s strongest validation is functional rather than visual: a classifier trained entirely on SeismoGen synthetics achieves $0.88\%$7 accuracy on V34A and $0.88\%$8 on V35A, and augmentation improves accuracy by over $0.88\%$9 on V35A and over $0.48\%$0 on V34A in the best limited-data cases (Wang et al., 2019).

SWaG, explicitly titled a “Seismic Wave Generator,” moves to diffusion. It is a multi-conditional diffusion transformer that generates raw three-component waveforms of length 3000 samples, corresponding to 60 s at 50 Hz, conditioned on station ID, P-wave arrival time, S-wave arrival time, and magnitude (Duan et al., 21 Sep 2025). Its denoising objective is

$0.48\%$1

and its architecture uses four Conv1D encoders, 28 DiT blocks, and label/time embeddings into a 768-dimensional hidden space (Duan et al., 21 Sep 2025). The key downstream result is that phase-picking models trained entirely on 100,000 SWaG-generated waveforms achieve roughly $0.48\%$2 recall and precision on real labeled waveforms, while generated balanced datasets reduce systematic bias in magnitude estimation caused by uneven real-data magnitude distributions (Duan et al., 21 Sep 2025).

A different diffusion-based system targets strong-motion engineering rather than picking. The latent denoising diffusion GWM for Japanese strong-motion data generates three-component acceleration seismograms, 40 s long at 100 Hz, conditioned on magnitude, hypocentral distance, $0.48\%$3, and faulting type (Bergmeister et al., 2024). It operates on log-magnitude spectrograms compressed by an autoencoder and generates usable frequency content up to 50 Hz. The paper reports PGA bias of $0.48\%$4 log-units, PGV bias of $0.48\%$5 log-units, residual standard deviations matching real-data values almost exactly for PGA and PGV, and stable scenario statistics with around 60 realizations per conditioning vector (Bergmeister et al., 2024). In this formulation, the generator is not a deterministic forward model but an estimated conditional distribution $0.48\%$6.

SeismoGPT and TimesNet-Gen show two further directions. SeismoGPT is a transformer-based autoregressive forecaster for three-component seismic velocity waveforms in the Einstein Telescope context, using token length $0.48\%$7, 6 transformer layers, 8 attention heads, and either single-station temporal attention or array-based temporal-plus-spatial attention (Esmail et al., 25 Sep 2025). It generates future waveform tokens conditioned on past context and performs best in the immediate prediction window, with array-based predictions more stable later in the rollout (Esmail et al., 25 Sep 2025). TimesNet-Gen, by contrast, is a site-specific strong-motion generator in the time domain, using a station-specific latent bottleneck and evaluating realism through HVSR curves and $0.48\%$8 distributions; its station-specific alignment score is 0.93 versus 0.81 for a spectrogram-based conditional VAE baseline (Yilmaz et al., 4 Dec 2025). Together, these papers show that “generator” may refer either to stochastic synthesis of new records or to conditional continuation of an observed record.

5. Passive metamaterial systems often conflated with generators

Some seismic-wave literature uses terminology that can obscure the distinction between generating waves and suppressing them. The papers “Artificial Seismic Shadow Zone by Acoustic Metamaterials” and “Seismic Waveguide of Metamaterials” propose buried arrays of resonant cavities or meta-boxes that create a stop band through an effective negative shear modulus, making velocity, refractive index, impedance, and wavevector effectively imaginary over a target band (Kim et al., 2012, Kim et al., 2012). In the stop band, a propagating field becomes evanescent, with amplitude decay written as

$0.48\%$9

Both papers derive the barrier-thickness relation

$1.45\%$0

linking desired magnitude reduction to wavelength and effective refractive-index magnitude (Kim et al., 2012, Kim et al., 2012).

These systems are not active seismic sources. The papers themselves emphasize attenuation, shielding, or a seismic shadow zone rather than actuation, source-time functions, phased arrays, or launch efficiency into elastic modes (Kim et al., 2012, Kim et al., 2012). Their relevance to seismic-wave generation is indirect: they provide resonant-coupling principles, spectral filtering concepts, and a way to design the propagation environment. A plausible implication is that metamaterial control and waveform generation are complementary rather than interchangeable domains. A source engineer might use such structures to shape emitted wavefronts or suppress selected bands, but the cited papers do not provide a generator in the strict sense.

6. Applications, evaluation, and limitations

The surveyed generators serve markedly different applications. SoilGen supports site response analysis, HVSR simulation, dispersion curve modeling, and deep-learning inversion pipelines that require large labeled model libraries (Fathizadeh et al., 13 Dec 2025). SubsurfaceGen targets ML-based FWI, wavefield prediction, and end-to-end velocity inversion at field scale, with out-of-distribution evaluation across geological settings (Stitt et al., 28 May 2026). SWEEP is designed for wavefield modeling, FWI, LSRTM, and differentiable optimization (Wang et al., 1 Apr 2026). PyAWD emphasizes earthquake analysis and sparse-sensor ML problems such as epicenter retrieval (Tribel et al., 2024). SWaG, SeismoGen, the latent diffusion GWM, and TimesNet-Gen focus on labeled waveform generation for phase picking, magnitude estimation, hazard analysis, and site-specific strong-motion synthesis (Duan et al., 21 Sep 2025, Wang et al., 2019, Bergmeister et al., 2024, Yilmaz et al., 4 Dec 2025).

Evaluation criteria follow those application domains. Physics-based generators are judged by governing-equation fidelity, source representation, acquisition realism, and benchmarking against other numerical methods or known physical trends, as in AstroSeis and the full-Euler/SPH generators (Tian et al., 2020, Poletto et al., 2023, Turner et al., 2023). Data-driven generators are commonly evaluated by downstream transfer, distributional agreement, and task metrics rather than by one-to-one waveform matching, as in SeismoGen’s classifier transfer, SWaG’s phase-picking scores, the strong-motion GWM’s PGA/PGV/SA statistics, and TimesNet-Gen’s HVSR and $1.45\%$1-distribution alignment (Wang et al., 2019, Duan et al., 21 Sep 2025, Bergmeister et al., 2024, Yilmaz et al., 4 Dec 2025). This suggests that “realism” is increasingly operationalized through use-case-specific metrics rather than through a single universal waveform-quality score.

The principal limitations are equally heterogeneous. Many procedural generators do not model sources or propagated waves at all; SoilGen explicitly omits source-time functions, moment tensors, damping models, attenuation $1.45\%$2, nonlinear constitutive behavior, and numerical wavefield solvers (Fathizadeh et al., 13 Dec 2025). Many forward simulators simplify the physics: PyAWD uses acoustic rather than elastic propagation (Tribel et al., 2024), SubsurfaceGen uses 2D constant-density isotropic acoustics rather than elastic or 3D propagation (Stitt et al., 28 May 2026), and the strong-motion latent diffusion GWM is stochastic and data-driven rather than a deterministic wave-equation solution (Bergmeister et al., 2024). Data-driven models may be station-specific or region-specific, may inherit preprocessing constraints, and may not extrapolate reliably outside the training domain (Wang et al., 2019, Duan et al., 21 Sep 2025, Bergmeister et al., 2024, Yilmaz et al., 4 Dec 2025). Metamaterial papers, for their part, do not specify active source excitation at all (Kim et al., 2012, Kim et al., 2012).

A complete synthetic seismic wave generator, in the broadest engineering sense implied by the literature, therefore requires multiple coupled components: a source specification, a physically or statistically defined propagation model, a medium model, boundary conditions, receiver geometry, and a post-processing stage that delivers the target observable such as seismograms, HVSR curves, transfer functions, dispersion images, or shot gathers (Fathizadeh et al., 13 Dec 2025). Recent arXiv work does not converge on a single canonical architecture; instead, it maps out a modular ecosystem in which upstream Earth-model generators, PDE solvers, differentiable inversion platforms, and learned waveform generators can be assembled into end-to-end seismic simulation pipelines.