OpenSWI: Surface Wave Inversion Benchmark

• OpenSWI is a comprehensive benchmark for surface wave dispersion inversion, combining synthetic (shallow and deep) and real-world datasets for deep learning applications.
• The SWIDP pipeline automates data collection, quality control, and forward simulation to generate paired velocity profiles and dispersion curves for robust inversion.
• Baseline inversion using a DispFormer-style Transformer yields low RMSE values, demonstrating its effectiveness for transfer learning and real-time geophysical applications.

Searching arXiv for the provided OpenSWI-related papers and closely related work. I’m checking arXiv records for the cited OpenSWI materials. OpenSWI is a comprehensive benchmark dataset for surface wave dispersion curve inversion, introduced together with the Surface Wave Inversion Dataset Preparation (SWIDP) pipeline to address sensitivity to initial models, low computational efficiency, and the lack of large-scale, diverse benchmark datasets for data-driven inversion (Liu et al., 14 Aug 2025). The suite contains two synthetic datasets tailored to different research scales and scenarios—OpenSWI-shallow and OpenSWI-deep—and an AI-ready real-world dataset for generalization evaluation, OpenSWI-real. Its stated purpose is to support the development, evaluation, and extension of deep-learning approaches for intelligent surface wave inversion.

1. Scope and problem setting

Surface wave dispersion curve inversion plays a critical role in both shallow resource exploration and deep geological studies, yet it remains hindered by sensitivity to initial models and low computational efficiency (Liu et al., 14 Aug 2025). OpenSWI is positioned as a benchmark response to these constraints. Rather than defining a single corpus, it defines a suite: a shallow synthetic benchmark, a deep synthetic benchmark, and a real-world benchmark intended for zero-shot generalization testing.

A common misconception is to treat OpenSWI as only a synthetic training set. The source description is more specific: OpenSWI-real contains observed dispersion curves with corresponding reference models and serves as a benchmark for evaluating model generalization (Liu et al., 14 Aug 2025). Another misconception is to treat it as restricted to near-surface settings. The benchmark explicitly spans shallow geological structures and deep-Earth studies through distinct dataset components with different depth parameterizations and period ranges.

The naming can also be ambiguous in the broader literature. Separately, SWI-Prolog has been described as “neither a commercial Prolog system nor a purely academic enterprise, but increasingly a community project” (Wielemaker et al., 2010). That usage concerns a Prolog environment rather than geophysical inversion. In current geophysical usage, OpenSWI denotes the surface-wave benchmark suite.

2. SWIDP pipeline and forward-modeling workflow

SWIDP is a fully modular, end-to-end Python toolkit that automates the construction of paired 1-D velocity profiles and Rayleigh-wave dispersion curves (Liu et al., 14 Aug 2025). Its workflow is organized into collection and quality control, 1-D profile extraction and parameterization, data augmentation, and forward simulation.

In the collection and quality-control stage, SWIDP gathers 2-D and 3-D velocity models from open sources, standardizes formats such as .npz, .txt, and .nc, converts P-wave to S-wave velocities using Brocher 2005 empirical relations, fills missing values, and removes outliers (Liu et al., 14 Aug 2025). In the parameterization stage, it samples vertical profiles at every grid point or a subset, removes duplicates, smooths or merges very thin layers for numerical stability, and re-interpolates the models to uniform layer thickness. The reported parameterizations are 40 m thickness for shallow profiles, yielding about 70 layers over 0–2.8 km, and 1 km thickness for deep profiles, yielding 300 layers over 0–300 km. Physical parameters are completed by using Brocher’s formula for $\rho$ and $v_p$ above 120 km depth; below that threshold, a constant Poisson’s ratio is assumed to derive $v_p$ from $v_s$, followed by $\rho$ from $v_p$ (Liu et al., 14 Aug 2025).

The augmentation stage differs by regime. For shallow data, SWIDP applies random $\pm 10\%$ perturbations in layer thickness and $\pm 5\%$ perturbations in $v_s$, subject to plausibility checks. For deep data, it performs feature-aware perturbation by identifying the Moho, fitting crust and mantle segments with splines, perturbing spline nodes, and re-interpolating. For shallow data only, SWIDP also performs generative expansion by training a DDPM on 2-D OpenFWI cross sections and sampling new velocity maps via 1 000-step denoising before extracting 1-D profiles (Liu et al., 14 Aug 2025).

Forward simulation is framed through the Rayleigh-wave dispersion equation

$D(c,f,m)=0$

where $v_p$0 is frequency, $v_p$1 is phase velocity, and $v_p$2 are layer elastic parameters (Liu et al., 14 Aug 2025). Group velocity is computed from

$v_p$3

The implementation uses Disba, described as a Python port of CPS, in batch parallel mode to simulate fundamental-mode phase and group velocities. Period sampling is defined through a hybrid of uniform, random, and log sampling, with example ranges of 0.1–10 s for shallow settings and 1–100 s for deep settings (Liu et al., 14 Aug 2025).

3. Composition of the benchmark suite

OpenSWI consists of three datasets with distinct geological provenance, depth extent, and observables (Liu et al., 14 Aug 2025).

Dataset	Origin and scope	Key properties
OpenSWI-shallow	2-D geological models from OpenFWI in five categories: Flat, Flat+Fault, Fold, Fold+Fault, Field	22.08 million profiles after augmentation; 0–2.8 km; 40 m resolution; 70 layers; 0.1–10 s; 100 points; phase and group velocities
OpenSWI-deep	14 global and regional 3-D shear-wave velocity models including LITHO1.0, USTClitho1.0, Central & Western US, Continental China, US Upper Mantle, EUCrust, Alaska, and six CSEM regions	1 275 093 profiles after feature-aware spline perturbation; 0–300 km; 1 km resolution; 300 layers; 1–100 s; 300 points; phase and group velocities
OpenSWI-real	Open-source observed datasets from Long Beach and CSRM	Long Beach: 5 297 stations, 0.263–1.666 s, 0–1.4 km, 35 layers, phase only; CSRM: 12 901 grid points, 8–70 s, 0–120 km, 120 layers, phase and group

OpenSWI-shallow is derived from the 2-D OpenFWI geological model dataset and spans simple horizontal layers, faults, folds, and realistic stratigraphy learned via DDPM (Liu et al., 14 Aug 2025). The original model counts per category are reported as 30 k, 54 k, 30 k, 54 k, and 67 k. From these models, 3.49 million 1-D profiles were extracted, and augmentation through perturbation and DDPM expanded the set to 22.08 million profiles.

OpenSWI-deep is built from 14 global and regional 3-D geological models and is intended for crustal to upper-mantle structures across diverse tectonic provinces (Liu et al., 14 Aug 2025). The benchmark reports 212 508 extracted 1-D profiles, augmented by feature-aware spline perturbation by a factor of five to 1 275 093 profiles.

OpenSWI-real contains two observed datasets. The Long Beach component contains phase-velocity observations only, paired with traditional-inversion reference models. The CSRM component contains both phase and group velocities and pairs them with reference 1-D velocity profiles from Xiao et al. 2024 (Liu et al., 14 Aug 2025). This suggests that the benchmark is explicitly constructed to test cross-domain transfer from synthetic training distributions to field observations.

4. Statistical characteristics, file organization, and access

The benchmark reports distinct statistical summaries for its synthetic partitions. OpenSWI-shallow contains 22.08 M samples with input shaped as $v_p$4—period, phase velocity, and group velocity—and output over 70 depths; its synthetic test RMSE is reported as approximately 0.147 km/s (Liu et al., 14 Aug 2025). OpenSWI-deep contains 1.275 M samples with input shaped as $v_p$5 and output over 300 depths; its synthetic test RMSE is approximately 0.048 km/s. The source description further states that velocity distributions, expressed as mean $v_p$6, vary systematically with geology and region.

Training-time preprocessing adds 3% Gaussian noise and randomly masks 10% of dispersion points to boost robustness (Liu et al., 14 Aug 2025). Dataset partitioning uses stratified splits of 90%/5%/5% for train, validation, and test by geological category or region. A plausible implication is that evaluation is intended to preserve structural diversity rather than rely on random instance-level partitioning alone.

Data files are organized as arrays for 1-D velocity profiles and dispersion curves. Velocity profiles are stored as [depth, v_p, v_s, \rho] arrays in .npz or .npy format, together with metadata such as source, category, and augmentation flag (Liu et al., 14 Aug 2025). Dispersion curves are stored as [period, phase_velocity, group_velocity] in the same file formats. Metadata conventions include a JSON sidecar containing model ID, geographic or geological label, layer count, and period sampling indices.

The reported repositories are the SWIDP toolkit and forward-modeling scripts at github.com/liufeng2317/OpenSWI, and the datasets, pretrained models, and training logs at https://huggingface.co/datasets/LiuFeng2317/OpenSWI (Liu et al., 14 Aug 2025). These access conventions position OpenSWI not only as a static benchmark, but as a regenerable pipeline.

5. Baseline inversion architecture and reported evaluation

The baseline inversion model is described as a DispFormer-style Transformer (Liu et al., 14 Aug 2025). Its input is a $v_p$7 dispersion matrix containing period, phase velocity, and group velocity. Embedding is performed through three separate $v_p$8 convolutions that produce features of size $v_p$9, with $v_p$0 for shallow models and $v_p$1 for deep models. The encoder contains 3 Transformer blocks with 8-head self-attention and feed-forward layers, followed by a linear output projection to a velocity profile of length $v_p$2, where $v_p$3 is 70 or 300 depending on the benchmark regime.

A notable modeling device is depth-aware masking, which dynamically suppresses outputs beyond the maximum resolvable depth, given as $v_p$4 (Liu et al., 14 Aug 2025). The training protocol uses Adam with warm-up and step decay. For shallow training, the learning rate rises from $v_p$5 to $v_p$6 in 2 epochs and decays every 20 epochs; for deep training, warm-up lasts 10 epochs and decay occurs every 200 epochs. Reported batch sizes are 2048 for shallow models and 512 for deep models. Epoch budgets are 100 for shallow models and up to 1000 for deep models, with early stopping triggered by no validation-loss improvement for 30 or 50 epochs, respectively. The loss is mean squared error over the effective depth range (Liu et al., 14 Aug 2025).

The reported synthetic test RMSE values are 0.147 km/s for shallow inversion and 0.048 km/s for deep inversion (Liu et al., 14 Aug 2025). Real-data evaluation is reported through phase-velocity misfits relative to observations. For Long Beach, the reference model has mean misfit $v_p$7 m/s and variance $v_p$8 $v_p$9, while the network has mean $v_s$0 m/s and variance $v_s$1 $v_s$2. For CSRM, the reference model has mean $v_s$3 m/s and variance $v_s$4 $v_s$5, while the network has mean $v_s$6 m/s and variance $v_s$7 $v_s$8 (Liu et al., 14 Aug 2025). The accompanying interpretation in the source text is that predictions show strong agreement between predictions and references, confirming the diversity and representativeness of the dataset.

6. Reproducibility, extensibility, and terminological context

OpenSWI is accompanied by usage guidelines that emphasize reproducibility and extensibility (Liu et al., 14 Aug 2025). The recommended reproducibility path is to follow SWIDP’s modular notebooks to regenerate data with custom layer thickness, depth ranges, or period bands. This makes the benchmark adaptable to alternative inversion scales without altering the overall quality-control, extraction, and simulation workflow.

Several extensions are explicitly proposed. Transfer learning is suggested through fine-tuning pretrained models on region-specific real data to further reduce misfit. Multi-mode and multi-physics extensions are described as adding higher-mode dispersion, ellipticity, or receiver functions by introducing additional forward simulators. Geological diversity can be enlarged by incorporating new 3-D models, including anisotropic media, fluid-saturated layers, and mid-ocean ridges. Generative modeling can be extended by adapting the DDPM module for deeper structures or by including variational autoencoders to sample novel velocity patterns. The source also mentions real-time field use through deployment of the trained network in field acquisition software for on-the-fly inversion of ambient noise or active-source data (Liu et al., 14 Aug 2025).

The broader term “OpenSWI” can, however, create cross-domain ambiguity because SWI-Prolog has also been presented as an integrating tool that supports a wide range of ideas developed in the Prolog community and acts as glue between foreign resources (Wielemaker et al., 2010). That software system includes a traditional copy-based abstract machine in C, a Quintus-style module system with extensions, a foreign-language interface, multi-threading, CLP libraries, and development tools such as PlDoc and PlUnit (Wielemaker et al., 2010). The overlap is nominal rather than substantive: one usage refers to a logic-programming environment, while the other refers to a benchmark suite for surface wave inversion. Recognizing that distinction is important in bibliographic and repository searches, especially because both are open, community-facing systems with associated tooling.