SWIDP: Surface Wave Inversion Prep

• Surface Wave Inversion Dataset Preparation (SWIDP) is a modular workflow that converts raw geological and wavefield data into standardized inversion-ready inputs.
• It automates extraction, augmentation, forward modeling of dispersion curves, and uncertainty modeling to support various inversion methodologies.
• SWIDP integrates acquisition-aware curation, mode filtering, and precise parameterization to ensure accurate recovery of subsurface shear-wave velocity structures.

Surface Wave Inversion Dataset Preparation (SWIDP) denotes the organized preparation of raw geological models or measured wavefields into inversion-ready representations for recovering shear-wave velocity structure from surface waves. In the OpenSWI framework, SWIDP is a modular Python toolbox that automates collection and quality control of raw geological models, extraction and parameterization of 1-D velocity profiles, augmentation, forward modeling of fundamental-mode Rayleigh-wave phase and group velocity dispersion curves, and standardization and saving of profiles and dispersion curves in unified formats (Liu et al., 14 Aug 2025). Taken together, related studies suggest a broader usage in which SWIDP includes acquisition-aware curation of active-source, passive-noise, DAS, nodal, and site-response data; construction of dispersion curves and uncertainty models; and definition of layered or transdimensional parameterizations for deterministic, Bayesian, and learning-based inversion (Vantassel et al., 2020).

1. Conceptual scope

Surface-wave studies in this literature are consistently organized around an acquisition–processing–inversion chain. SWinvert explicitly separates acquisition, processing, and inversion, and treats dataset preparation as the transition from processed experimental dispersion data to inversion targets, parameter files, and uncertainty-aware post-processing products (Vantassel et al., 2020). A closely related decomposition appears in deterministic dispersion-curve inversion, where the data flow is divided into raw measurements, derived data, and inversion input: multichannel seismograms and survey geometry become dispersion curves $c^{\text{obs}}$ with uncertainties $\sigma_i$, which then become the weighted data vector and the layered subsurface parameterization used by the solver (Vignoli et al., 2021). In this sense, SWIDP is not a single inversion algorithm; it is the formal preparation layer that determines what an inversion is actually asked to fit.

A second defining feature is that SWIDP may begin either from measured wavefields or from pre-existing Earth models. Field-oriented workflows prepare active and passive records, filter wavefields, extract local or global dispersion information, and estimate uncertainty. Synthetic and benchmark-oriented workflows begin from 2-D or 3-D geological models, extract or standardize 1-D velocity profiles, compute forward dispersion, and save paired inputs and labels for inversion or machine learning (Liu et al., 14 Aug 2025).

Context	Prepared inputs	Prepared outputs
OpenSWI (Liu et al., 14 Aug 2025)	2-D OpenFWI subsets, 14 global/regional 3-D models, open-source real projects	standardized 1-D velocity profiles and Rayleigh phase/group dispersion pairs
Newberry site (Abbas et al., 2023)	DAS, nodal stations, T-Rex sweeps, impacts, ambient noise	subsets for dispersion analysis, MASW, surface-wave FWI, ambient-noise tomography
Uncertainty-consistent workflow (Vantassel et al., 2020)	experimental mean dispersion, standard deviation, correlation matrix	dispersion realizations and suites of Vs profiles
DAS tomography (Dalkhani et al., 2023)	filtered DAS shot gathers	local dispersion curves $c(f,x)$ and 2D $V_S(x,z)$ posterior summaries
Transformer/XGBoost workflows (Liu et al., 8 Jan 2025, Cheng et al., 29 Sep 2025, Mandal et al., 25 Sep 2025)	synthetic or observed dispersion curves	fixed-grid, standardized, or normalized $V_S(z)$ labels

2. Measurement domains and acquisition-aware preparation

SWIDP in field applications is strongly conditioned by how the surface-wave field was acquired. The Newberry, Florida experiment is a representative example because it combines approximately two kilometers of distributed acoustic sensing fiber optic cable in a dense 2D array of 1920 channels with a 2D array of 144 three-component nodal stations, and it records both active-source and passive-wavefield stress waves (Abbas et al., 2023). The DAS cable has gauge length $g = 2.04\ \text{m}$, channel separation $1.02\ \text{m}$, and effective measurement as average normal strain $\epsilon_{xx}$ over $2.04\ \text{m}$; the nodal array is a 12×12 grid with 5 m spacing in $X$ and 10 m spacing in $\sigma_i$0. The active-source program combines a tri-axial vibroseis truck with 12-s linear chirps from 5–80 Hz at 260 locations and impact sources with 10–250 Hz content at 286 shot points. Passive records comprise 4 hours of DAS ambient noise and 48 hours of nodal ambient noise. These exact acquisition choices determine which subsets are best suited for 1D dispersion analysis, MASW, surface-wave FWI, or ambient-noise tomography (Abbas et al., 2023).

Straight-fiber DAS surveys impose their own preparation logic because DAS measures spatial derivatives of horizontal particle velocity. In the Groningen study, the DAS observable is written as

$\sigma_i$1

and a DAS channel over gauge length $\sigma_i$2 approximates the difference quotient of horizontal particle velocity across the gauge (Dalkhani et al., 2023). This dense spatial sampling is valuable for surface waves because phase velocity estimates remain geophysically meaningful when the gauge length is small relative to wavelength and spatial Nyquist conditions are respected. A plausible implication is that SWIDP for DAS must preserve gauge length, channel spacing, fiber orientation, and source geometry as first-class metadata rather than treating the records as interchangeable with point-receiver geophone traces.

The acquisition domain also determines whether effective-mode modeling is feasible. Predominant-mode inversion was introduced precisely for the common situation in which dispersion data are assembled from multiple active shots and passive arrays with unknown source locations; in that setting, effective-mode inversion cannot be applied because it requires precise source-receiver geometry (Bhaumik et al., 12 Dec 2025). This has direct SWIDP consequences: if the intended forward model is geometry dependent, the dataset must preserve exact acquisition geometry; if the workflow will rely on predominant-mode logic, the dataset can instead prioritize robust dispersion picks and uncertainties without explicit source-location recovery.

3. Dispersion representation, uncertainty, and quality control

The core SWIDP object in classical inversion is the dispersion dataset itself. In deterministic Rayleigh-wave inversion, the inversion input is a data vector of phase velocities, whose elements correspond to specific frequencies and modes, together with an uncertainty vector $\sigma_i$3 and a layered $\sigma_i$4 parameterization (Vignoli et al., 2021). In uncertainty-consistent workflows, the experimental dispersion dataset is elevated from a curve to a statistical object: per frequency $\sigma_i$5, one stores the mean $\sigma_i$6, the standard deviation $\sigma_i$7, the coefficient of variation $\sigma_i$8, and the correlation matrix $\sigma_i$9 across frequencies (Vantassel et al., 2020). This representation is then used to simulate multivariate-normal dispersion realizations, invert each realization independently, and test whether the implied theoretical dispersion statistics reproduce the experimental mean and variability (Vantassel et al., 2020).

Several papers treat the construction of $c(f,x)$0 or $c(f,x)$1 as an essential SWIDP step rather than a cosmetic add-on. In DAS-based transdimensional tomography, Multi Offset Phase Analysis (MOPA) is applied shot by shot, local phase velocities are estimated in moving windows, and the final local dispersion curves $c(f,x)$2 are averaged across shots; the standard deviation across shots becomes the uncertainty used in the likelihood (Dalkhani et al., 2023). In the predominant-mode workflow, SWprocess is used to extract peak-power dispersion picks and compute uncertainty, with a minimum coefficient of variation of 5% on phase velocity (Bhaumik et al., 12 Dec 2025). In joint inversion with downhole records, the covariance matrix is explicitly block diagonal,

$c(f,x)$3

where $c(f,x)$4 and $c(f,x)$5 weight acceleration time series and dispersion data, respectively (Seylabi et al., 2020).

A major methodological divergence concerns whether phase velocities should be picked at all. The traditional workflow constructs an $c(f,x)$6–$c(f,x)$7 spectrum and picks one phase velocity at each frequency, but the energy-likelihood method instead uses the spectrum itself as data because multimodal $c(f,x)$8–$c(f,x)$9 spectra can bias picks and therefore bias the recovered shear-velocity structure (Zhang et al., 2022). The proposed likelihood evaluates observed spectrum energy at the model-predicted dispersion point, thereby preserving multi-modality and removing the need to pick phase velocities explicitly (Zhang et al., 2022). This is not a rejection of curve-based SWIDP; it is a reminder that SWIDP may prepare either dispersion curves or whole spectral panels, depending on the inversion formalism.

A second recurrent quality-control issue is mode contamination. In the DAS tomography workflow, shot gathers are filtered in the $V_S(x,z)$0–$V_S(x,z)$1 domain to isolate the fundamental Rayleigh mode before local phase analysis; in the predominant-mode workflow, the low-frequency part of an apparently single Rayleigh curve may in fact be dominated by a higher mode, and frequencies with large relative dispersion misfit can be downweighted or excluded (Dalkhani et al., 2023, Bhaumik et al., 12 Dec 2025). This suggests that SWIDP should preserve the link between each accepted dispersion point and the filtering, stacking, or modal-assignment logic that produced it.

4. Parameterization and forward operators

Once the dispersion data are fixed, SWIDP must define how the Earth model is represented and how theoretical dispersion will be computed. In classical 1D inversion, the forward problem is the computation of Rayleigh-wave phase velocities $V_S(x,z)$2 in a layered elastic half-space given $V_S(x,z)$3, $V_S(x,z)$4 or Poisson’s ratio, and $V_S(x,z)$5 (Vignoli et al., 2021). Under the assumptions of constant density and constant Poisson’s ratio, the linearized relationship is

$V_S(x,z)$6

with Jacobian

$V_S(x,z)$7

and the iterative inversion is controlled by the data weighting matrix $V_S(x,z)$8 (Vignoli et al., 2021). This is the minimal analytical skeleton behind a large fraction of SWIDP workflows: dispersion vector, uncertainty vector, layered depth grid, and a forward solver for layered media.

The parameterization itself varies substantially. SWinvert emphasizes multiple layering parameterizations, especially Layering by Number (LN) and Layering Ratio (LR), because inversion uncertainty and non-uniqueness can be minimal for simple subsurface models characterized by broadband dispersion data but cannot be ignored for more complex models with band-limited dispersion data (Vantassel et al., 2020). In XGBoost-based inversion, a variable-layer soil profile is converted into a standardized 10-layer representation with geometrically increasing thicknesses, layering ratio $V_S(x,z)$9, and total thickness 30 m, allowing one regression model to predict standardized profiles even when the original soil contains 2–6 layers (Mandal et al., 25 Sep 2025). In DispFormer, all profiles are interpolated to 0.5 km layers and the target is $V_S(z)$0 at fixed depths, while $V_S(z)$1 and $V_S(z)$2 are derived from $V_S(z)$3 using Brocher’s empirical relationships or a fixed ratio $V_S(z)$4 below 120 km (Liu et al., 8 Jan 2025).

Forward solvers are equally diverse but remain tightly tied to SWIDP. OpenSWI uses the Disba Python library, a modern interface to Herrmann’s Computer Programs in Seismology, to compute fundamental-mode Rayleigh phase and group velocities for each 1-D layered model (Liu et al., 14 Aug 2025). Joint inversion of receiver functions and surface-wave dispersion uses Computer Programs in Seismology and the Thomson–Haskell propagator matrix method to compute synthetic Rayleigh phase velocities from layered 1D models (Wang, 2024). DAS tomography uses the reduced delta matrix method to compute theoretical local dispersion from extracted 1D profiles (Dalkhani et al., 2023). Predominant-mode inversion derives a geometry-independent forward model from the thin-layer method and defines, at each frequency, the modeled phase velocity as that of the mode with maximum vertical surface amplitude,

$V_S(z)$5

thereby avoiding explicit mode indexing in the observed data (Bhaumik et al., 12 Dec 2025).

Regularization is another part of parameterization, not merely of inversion. Standard Minimum Gradient Norm regularization favors smooth models, whereas Minimum Gradient Support introduces

$V_S(z)$6

so that the inversion minimizes the number of locations where significant gradients occur and yields blocky, sparse solutions with tunable sharpness (Vignoli et al., 2021). A plausible implication is that SWIDP should record not only the depth sampling and prior ranges but also whether the intended inversion assumes smoothness, sparsity, transdimensional complexity, or fixed standardized layers.

5. Workflow patterns: field datasets, synthetic benchmarks, and learning-oriented corpora

Open-access field datasets show one important SWIDP pattern: acquisition-aware subset selection. The Newberry dataset was documented explicitly as a “surface-wave-focused view” of how to turn a large active and passive DAS-plus-nodal experiment into a practical workflow. Straight DAS segments such as line Q can be selected as 1D arrays, while the full zigzag cable can be treated as a 2D strain array for 2D MASW or FWI; nodal DHZ channels are appropriate for Rayleigh dispersion, and DHN or DHE for Love or Rayleigh depending on source orientation (Abbas et al., 2023). In this pattern, SWIDP is less about generating synthetic labels than about making acquisition geometry, channel orientation, shot metadata, and ambient-noise segments explicit enough that later inversion choices remain reversible.

A second pattern is uncertainty-consistent dataset generation. The procedure in “A Procedure for Developing Uncertainty-Consistent Vs Profiles from Inversion of Surface Wave Dispersion Data” first builds a multivariate statistical representation of experimental dispersion, then draws $V_S(z)$7 dispersion realizations, inverts each realization independently, and retains one best model per realization (Vantassel et al., 2020). The paper reports that $V_S(z)$8 is effective, and it evaluates the resulting Vs ensemble by whether the implied theoretical dispersion reproduces the measured mean and coefficient of variation rather than by whether a few individual models achieve extremely low misfit (Vantassel et al., 2020). This pattern is explicitly designed to avoid under-dispersed suites of acceptable models.

A third pattern is large-scale synthetic benchmark generation for data-driven inversion. OpenSWI’s SWIDP workflow contains five steps: collection and quality control of raw geological models, extraction and parameterization of 1-D velocity profiles, augmentation, forward modeling of fundamental-mode Rayleigh-wave phase and group velocity dispersion curves, and standardization and saving in unified formats (Liu et al., 14 Aug 2025). The resulting benchmark datasets are large: OpenSWI-shallow contains 22,083,336 profiles, OpenSWI-deep contains 1,275,093 1-D velocity models, and OpenSWI-real standardizes observed dispersion curves and reference models from Long Beach and CSRM into the same AI-ready format (Liu et al., 14 Aug 2025). The workflow is implemented in the SWIModel class, with methods such as extract_velocity_profiles, perturb_vs_depth, augment_crust_moho_mantle, calculate_dispersion, and save_dispersion_curves (Liu et al., 14 Aug 2025).

A fourth pattern is normalization or standardization to reduce the burden of fixed-scale learning. DispFormer pretrains on 40,962 global synthetic profiles extracted from LITHO1.0, with all models interpolated to 0.5 km layers and dispersion curves computed over 1–100 s; synthetic curves are augmented with Gaussian noise of approximately 5%, random segment zeroing of about 10%, and random removal of phase or group curves (Liu et al., 8 Jan 2025). U-SWIFT instead uses a Normalized Dispersion Curve Space with fixed half-space depth $V_S(z)$9 and half-space shear velocity $g = 2.04\ \text{m}$0. Physical curves are mapped into normalized coordinates by

$g = 2.04\ \text{m}$1

with $g = 2.04\ \text{m}$2 and $g = 2.04\ \text{m}$3, and predicted normalized profiles are mapped back by

$g = 2.04\ \text{m}$4

This makes a single transformer applicable from $g = 2.04\ \text{m}$5 depth to crustal scales (Cheng et al., 29 Sep 2025).

A fifth pattern is label standardization for variable layer counts. The XGBoost framework generates 10 million synthetic soil profiles with $g = 2.04\ \text{m}$6 in $g = 2.04\ \text{m}$7, converts each original 2–6-layer profile into a uniform 10-layer representation with geometric thickness increase and half-space at 30 m, and constrains both adjacent-layer contrasts and the ratio $g = 2.04\ \text{m}$8 to avoid unrealistic profiles (Mandal et al., 25 Sep 2025). This is a SWIDP strategy for making variable-layer geologies compatible with fixed-output regressors.

6. Joint inversion, scale extension, and methodological disputes

Many SWIDP designs are motivated by the fact that surface-wave dispersion alone is often non-unique. Joint inversion with downhole acceleration time series treats the combined data vector as

$g = 2.04\ \text{m}$9

and uses ensemble Kalman inversion together with inequality constraints on monotonic $1.02\ \text{m}$0 and damping bounds to recover $1.02\ \text{m}$1 profile and damping more robustly than dispersion-only or downhole-only inversion (Seylabi et al., 2020). Joint inversion of multi-frequency teleseismic P-wave reverberations, de-reverberation filtered receiver functions, and surface-wave dispersion defines a posterior

$1.02\ \text{m}$2

and uses Bayesian Unscented Kalman Inversion with RF and Der RF weights of approximately 0.01 and SWD weight of approximately 0.001 (Wang, 2024). These studies reinforce a persistent SWIDP lesson: dataset preparation includes the weighting and covariance structure by which heterogeneous observations are made commensurate.

At larger scales, the design question becomes whether SWIDP should feed a two-step or a direct inversion. In 3D surface-wave inversion beneath the British Isles, two-step methods first perform 2D tomography per period and then invert each local dispersion curve independently, whereas direct-3D inversion jointly uses all Love-wave travel times at all periods in a single 3D variational problem (Zhao et al., 21 Jul 2025). The direct-3D scheme preserved better lateral continuity and produced synthetic data simulations that align more closely with observed data, suggesting that SWIDP for regional tomography should preserve path-level data and spatial correlations when the intended inversion can exploit them (Zhao et al., 21 Jul 2025). By contrast, transdimensional DAS tomography shows that even when the data product is already local dispersion $1.02\ \text{m}$3, it can still be advantageous to invert all curves simultaneously using 2D Voronoi cells rather than independently (Dalkhani et al., 2023).

The literature also documents two persistent interpretive disputes. One concerns regularization: smoothing stabilizers remain common, but minimum support regularization was introduced for surface-wave data precisely because smoothing can be inconsistent with expected sharp boundaries (Vignoli et al., 2021). The other concerns modal interpretation. Fundamental-mode inversion can fail at sites with strong impedance contrasts because modal energy may transfer smoothly from the fundamental to higher modes at low frequencies; predominant-mode inversion addresses this by automatically selecting, at each frequency, the mode with maximum vertical surface amplitude and by working directly with combined active and passive dispersion datasets that lack a single source geometry (Bhaumik et al., 12 Dec 2025). This dispute is not merely algorithmic. It means that SWIDP must decide whether the prepared dataset will enforce explicit mode indexing, preserve only an apparent curve with uncertainty, or retain spectral images from which mode ambiguity can be handled later.

Taken together, these works indicate that SWIDP has evolved from a pre-inversion housekeeping step into a formal modeling layer. It now includes acquisition metadata, filtering decisions, uncertainty models, parameterization rules, benchmark generation, normalization or standardization strategies, and dataset organization for joint or transdimensional inversion. The recurring technical motive across these variants is the same: the success of surface-wave inversion depends at least as much on how the dataset is prepared as on the optimizer or neural network that is eventually applied.