# Neural Machine Translation of Seismic Ambient Noise for Soil Nature and Water Saturation Characterization

José Cunha Teixeira, Ludovic Bodet, Agnès Rivière, Santiago Solazzi, Amélie Hallier, Alexandrine Gesret, Sanae El Janyani, Marine Dangeard, Amine Dhemaied, Joséphine Boisson Gaboriau

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José Cunha Teixeira, Ludovic Bodet, Agnès Rivière, Santiago Solazzi, Amélie Hallier, et al. Neural Machine Translation of Seismic Ambient Noise for Soil Nature and Water Saturation Characterization. Geophysical Research Letters, 2025, 52 (13), 10.1029/2025GL114852. hal-05145210

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Distributed under a Creative Commons Attribution 4.0 International License
# Geophysical Research Letters®

## RESEARCH LETTER

10.1029/2025GL114852

**Special Collection:**

Advancing Interpretable AI/ML
Methods for Deeper Insights and
Mechanistic Understanding in
Earth Sciences: Beyond
Predictive Capabilities

**Key Points:**

* Translating surface wave dispersion measurements into detailed petrophysical and hydrogeological descriptions using artificial intelligence

* Capturing dynamic changes in subsurface properties, such as water table levels and soil compositions

* Reducing the time required for inversion, enabling real-time monitoring by completing tasks 2,000 times faster than conventional methods

**Supporting Information:**

Supporting Information may be found in
the online version of this article.

**Correspondence to:**

J. Cunha Teixeira,
jose.teixeira@sorbonne-universite.fr

**Citation:**

Cunha Teixeira, J., Bodet, L., Rivière, A., Solazzi, S. G., Hallier, A., Gesret, A., et al. (2025). Neural machine translation of seismic ambient noise for soil nature and water saturation characterization. *Geophysical Research Letters*, *52*, e2025GL114852. https://doi.org/10.1029/2025GL114852

Received 15 JAN 2025

Accepted 17 JUN 2025

**Author Contributions:**

**Conceptualization:** José Cunha Teixeira,
Ludovic Bodet, Santiago G. Solazzi

**Funding acquisition:** Ludovic Bodet,
Amélie Hallier, Amine Dhemaied,
Joséphine Boisson Gaboriau

**Investigation:** José Cunha Teixeira

**Methodology:** José Cunha Teixeira,
Ludovic Bodet

© 2025. The Author(s).
This is an open access article under the
terms of the Creative Commons
Attribution License, which permits use,
distribution and reproduction in any
medium, provided the original work is
properly cited.

<figure><img src="image_2.png" /></figure>

## Neural Machine Translation of Seismic Ambient Noise for Soil Nature and Water Saturation Characterization

José Cunha Teixeira¹,² ID, Ludovic Bodet¹, Agnès Rivière³, Santiago G. Solazzi⁴ ID, Amélie Hallier², Alexandrine Gesret³, Sanae El Janyani², Marine Dangeard² ID, Amine Dhemaied², and Joséphine Boisson Gaboriau²

¹Sorbonne University, CNRS, EPHE, UMR 7619 METIS, Paris, France, ²SNCF Réseau, Saint-Denis, France, ³Geosciences Department, Mines Paris - PSL, PSL University, Paris, France, ⁴YPF Tecnología (Y-TEC) - CONICET, Buenos Aires, Argentina

**Abstract** Soil nature and water saturation of the near-surface directly influence land use resilience and sustainability in urban areas facing intense climate forcing and human activity. Seismic methods are widely applied in this context for subsurface characterization and monitoring, but often fall short in delivering joint geological, hydrogeological, and geomechanical descriptions. We explore the effectiveness of a passive seismic approach, coupled with artificial intelligence (AI), to characterize geological structures and capture groundwater dynamics. We present a deterministic inversion technique powered by a language model, to translates seismic wave velocity measurements into petrophysical parameters in the form of textual descriptions. Results successfully delineate subsurface structures with their respective composition and mechanical characteristics, while accurately predicting daily water table levels. Validation demonstrates high accuracy, with a normalized root-mean-square error of 8%, while delivering fast insights into subsurface conditions. This underscores the potential of AI to enhance subsurface characterization across multiple scales.

**Plain Language Summary** Understanding the ground beneath our feet is crucial for managing water resources, monitoring natural hazards like sinkholes, and ensuring the stability of infrastructure. Traditional methods for analyzing the subsurface are slow and often provide limited information. Our study introduces a novel approach that combines seismic waves, generated by passing trains, with artificial intelligence to quickly and accurately analyze the subsurface. We developed a model that acts like a translator, converting seismic wave measurements into detailed textual descriptions of soil types, mechanical properties, and water levels. This process, typically very time-intensive, can now be done in minutes, making it possible to monitor changes daily. Our results closely match field measurements and reveal important details about underground conditions, including how soil and water levels change over time. This new method provides a faster, more detailed way to study the subsurface, offering valuable insights for managing water resources, reducing natural hazard risks, and supporting sustainable infrastructure development.

## 1. Introduction

Climate change is anticipated to profoundly impact vulnerable regions worldwide in the coming decades (IPCC, 2023). While precipitation and groundwater recharge are expected to decrease in many regions, Western Europe is likely to experience a shift in seasonal rainfall patterns, with increased precipitation during winter and decreased precipitation in summer (Sauquet et al., 2025; Vergnes et al., 2023). This shift could strain human infrastructure, leading to higher flood risks during wetter winters and water shortages during drier summers, affecting agriculture, water supply systems, and urban drainage networks. Transportation infrastructure is already facing significant impacts from water-related challenges, such as flooding and waterlogging, which damage roads, weaken bridge foundations, disrupt rail networks, and compromise underground transport systems. Nevertheless, a shift toward low-carbon transportation systems is crucial to reduce greenhouse gas emissions and mitigate climate change. Achieving this requires designing resilient geoinfrastructure that can withstand evolving environmental conditions.

Seismic wave propagation analysis has been widely used for characterizing the Earth's subsurface (Aki & Richards, 1981) and providing essential insights into geological structures. Recent developments, leveraging continuous passive ambient seismic noise (Campillo & Paul, 2003; Shapiro et al., 2005; Snieder et al., 2002), have broadened its applications to include groundwater monitoring (Mao et al., 2022; Shen et al., 2024; Voisin
**Project administration:** Ludovic Bodet, Agnès Rivière, Amélie Hallier, Alexandrine Gesret, Marine Dangeard, Amine Dhemaied, Joséphine Boisson Gaboriau

**Software:** José Cunha Teixeira

**Supervision:** Ludovic Bodet, Agnès Rivière, Amélie Hallier, Alexandrine Gesret, Marine Dangeard, Amine Dhemaied, Joséphine Boisson Gaboriau

**Validation:** José Cunha Teixeira, Ludovic Bodet, Agnès Rivière, Santiago G. Solazzi, Amélie Hallier, Alexandrine Gesret, Sanae El Janyani, Marine Dangeard, Joséphine Boisson Gaboriau

**Visualization:** José Cunha Teixeira

**Writing – original draft:** José Cunha Teixeira, Ludovic Bodet

**Writing – review & editing:** José Cunha Teixeira, Ludovic Bodet, Agnès Rivière, Santiago G. Solazzi, Sanae El Janyani, Marine Dangeard, Joséphine Boisson Gaboriau

<figure><img src="image_3.png" /><figcaption>**Figure 1.** Conceptual schematic description. (a) Train-induced seismic waves are recorded along multiple geophone lines, with a focus on Rayleigh-waves. (b) These signals are analyzed through passive-MASW, estimating a dispersion curve (Rayleigh-wave phase velocity as a function of frequency) at each geophone location along the geophone lines. (c) Each dispersion curve is subsequently inverted via a trained language model to derive a petrophysical textual description of the subsurface. From these descriptions, a 3D image of the subsurface can be constructed for better analysis. This automated procedure operates on a daily basis, allowing for continuous monitoring of subsurface hydrogeological conditions and geomechanical states over time, with respect to environmental forcing.</figcaption></figure>

et al., 2016), and natural geohazard assessment at both large (Brenguier et al., 2008) and small scales (Le Breton et al., 2021; Rebert, Cai, et al., 2024), contributing significantly to environmental and geoengineering fields. Some of these methods leverage seismic waves generated by human activity, and offer a powerful approach for characterizing the subsurface beneath critical urban infrastructure, and monitoring its resilience over time (Figure 1a).

A key aspect of using seismic waves to characterize the subsurface is the need for solving inverse problems, which involves inferring subsurface properties, such as petrophysical and elastic parameters, from observed seismic data. Whereas seismic inversion specifically focuses on estimating elastic parameters from seismic records, petrophysical inversion estimates properties related to the composition and fluid content of subsurface formations based on these elastic parameters. Therefore, estimating petrophysical properties from seismic records involves solving two consecutive inverse problems: seismic inversion, followed by petrophysical inversion.

Inversion tasks are challenging due to the various sources of uncertainty and noise in the observed data, the nonlinearity of complex physical relationships, and the non-uniqueness of the solutions. Thus, most approaches rely on highly regularized or stochastic methods (Tarantola & Valette, 1982), which often require significant computational time and become increasingly challenging as the number of dimensions in the parameters increases. Additionally, with the advent of advanced sensor technology and the exponential growth of the amount of data collected during seismic surveys, these methods struggle to keep up with the increasing scale and complexity of modern seismic data sets, particularly for real-time or near real-time applications.

Artificial intelligence (AI) techniques, such as deep learning (LeCun et al., 2015), offer promising solutions to effectively handle non-linear and complex patterns in physical problems, and have been increasingly applied in inverse problems for subsurface characterization (Mousavi & Beroza, 2022). Multilayer Perceptrons (MLPs) were used to reconstruct elastic models from raw seismic records (Araya-Polo et al., 2018), to estimate water table (WT) level maps from seismic wave velocity measurements (Cunha Teixeira, Bodet, Rivière, et al., 2025), and to predict petrophysical parameters from elastic attributes (Weinzierl & Wiese, 2021). Convolutional Neural Networks (CNNs) were employed in Encoder–Decoder architectures for full-waveform inversion (Li et al., 2020;
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Study site description. (a and b) Location maps of the railway study site. (c) Experimental design of the study site showing the five geophone lines ($L_1$ to $L_5$), of 42 geophones (yellow dots $G_1$ to $G_{42}$) each, planted parallel to the railway tracks. Geophone lines are separated by 4.75 m, and geophones are regularly separated by 3 m. Rayleigh-wave dispersion curves are daily computed at each point of the geophone array by passive-MASW from seismic waves generated by train passages. Piezometers $PZ_1$ and $PZ_2$ were installed near geophone lines $L_1$ and $L_5$, respectively, to monitor water table levels. Additionally, two drillings, designated as DR$_1$ and DR$_2$, were conducted to investigate the soil formations at the site. (d) Example of Rayleigh-wave dispersion curves daily computed between 1 January 2023, and 30 September 2023, at the position of geophone 23 of line 1 ($L_1 - G_{23}$).</figcaption></figure>

Muller et al., 2023), petrophysical inversion (Das & Mukerji, 2020), soil nature classification (G. Zhang et al., 2018), and elastic model inference (Chen et al., 2022). Researches have also explored Recurrent Neural Networks (RNNs) for soil classification (Talarico et al., 2021), while Graph Neural Networks (GNNs) and Generative Adversarial Networks (GANs) were suggested for inferring elastic models from seismic velocities (Liu et al., 2024) and raw seismic records (Z. Zhang & Lin, 2020), respectively.

Nevertheless, the previous deep learning models demonstrate limited ability to capture long-range dependencies within structured data sequences, a challenge effectively addressed by the Transformer model (Vaswani et al., 2017), introduced in 2017, which exhibits remarkable efficiency in processing large data sets. Transformers leverage a mechanism previously applied with RNNs, known as *attention*, which assigns weights to elements within a sequence based on their relevance to each other, and allows for more accurate processing of long-range information. This architecture has led to significant improvements in generative AI and natural language processing tasks such as neural machine translation, text generation, and speech recognition. Well known Transformer-based language models (Brown et al., 2020) have demonstrated unprecedented capabilities in generating coherent and contextually relevant text and apprehending complex frameworks. The success of Transformers suggests a promising potential for AI in geoscience (Hadid et al., 2024), but their application in seismic and petrophysical inversion remains relatively unexplored (Dou & Li, 2024; Ning et al., 2023; Wang et al., 2023).

We leverage a challenging study site located along a railway line in the Grand-Est region of France (Figures 2a and 2b), at the eastern edge of the Paris Basin. Over the last decade, this railway site has encountered several instances of sinkhole dropouts, particularly impacting the integrity of the railway, which may be exacerbated by rapid hydrogeological condition variations. To effectively address and mitigate the risks associated with sinkholes, continuous subsurface monitoring using an ambient seismic noise based method passive-Multichannel Analysis of Surface Waves (passive-MASW) has been implemented since late 2020 (Bardaine & Rondeloux, 2018; Bardainne et al., 2023; Tarnus et al., 2022). This method uses seismic noise induced by train passages (Cunha Teixeira, Bodet, Dangeard, et al., 2025; Lavoué et al., 2020; Rebert, Bardainne, et al., 2024) to daily measure dispersion curves (DCs), showing Rayleigh-wave phase velocities ($V_R$) over frequencies (5–50 Hz), at each point of a seismic array (Figures 1a, 1b, 2c, 2d, and Section S1 in Supporting Information S1). Additionally, in late 2022, the site monitoring was enhanced with the addition of two piezometers, providing continuous recordings of WT levels (Figure 2c). The substantial volume of daily available seismic data presents challenges for conventional stochastic seismic inversion methods (Pasquet & Bodet, 2017; Sambridge, 1999), which are time-consuming and only provide a geomechanical description of the site by estimating shear-wave velocities ($V_S$) over
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Petrophysical inversion results. Section representation of the petrophysical inversion results using SILEX model, across the five geophone lines ($L_1$ to $L_5$), on July 2022 and 2023. (a and c) Sections of soil nature and smoothed water table (WT) level (dashed line). (b and d) Sections of the average number of contacts per particles (N) and smoothed water table level (dashed line). The soil natures identified from drillings at $DR_1$ and $DR_2$, as well as the measured water table levels at piezometers $PZ_1$ and $PZ_2$ (only in 2023), are shown for reference. Refer to Figure S14 in Supporting Information S1 for more detailed panel views.</figcaption></figure>

depth from DCs. This limitation can hinder efforts to obtain a comprehensive petrophysical and hydrogeological understanding, particularly needed when aiming to monitor both groundwater conditions and sinkhole hazards. To address these challenges, it is essential to integrate both elastic and petrophysical properties through a rock-physics model (Mavko et al., 2009), and to develop a frugal and fast direct petrophysical inversion method.

Taking inspiration from architectures used in neural machine translation and speech recognition (Baevski et al., 2020), we explore the use of AI for deterministic petrophysical inversion by implementing a language model to generate detailed descriptions of subsurface properties based on input seismic velocity measurements (Figure 1c). This inversion process is conceptualized as a translation task, where the seismic data is decoded into a structured textual sequence describing each soil layer in relation to the others, similar to the coherence found in language sentences. The model's ability to capture long-range dependencies is particularly crucial here, as the properties of any given soil layer are influenced not only by adjacent layers but also by more distant layers within the subsurface sequence. Similarly, phase velocities across frequencies in dispersion curves exhibit complex, non-local dependencies over depth that the model must account for to accurately decode the seismic data. The model, which we named SILEX for *Surface wave Inversion Lexicon*, is trained to translate DCs (numerical sequences of $V_R$) into textual descriptions of the subsurface's petrophysical parameters up to 20 m depth, within the framework of a rock-physics model (Solazzi et al., 2021).

This approach not only enhances the efficiency and accuracy of the inversion task but also provides unique insights into subsurface petrophysical characteristics that were previously unattainable using conventional methods due to the high number of parameters to invert and the time constraint of the study. The resulting inverted petrophysical parameters can ultimately be converted into water saturation or mechanical modulus profiles, and used for geological, hydrogeological, and geomechanical characterization at various scales.
## 2. Data and Methods

We adapted the original Transformer Encoder–Decoder architecture (Vaswani et al., 2017) to handle numerical input sequences, rather than textual data, allowing it to decode Rayleigh-wave phase velocities across frequencies as input and generate output sequences of variable length. To achieve this, we replaced the standard input embedding layer of the encoder part with a CNN that transforms the input sequence into a latent feature representation (Section S3 and Figure S3 in Supporting Information S1). The model was designed to generate a variable-length textual sequence describing the subsurface's petrophysical parameters based on an input DC. This process is grounded in a rock-physics model adapted from Solazzi et al. (2021), which extends the Hertz–Mindlin model (Mindlin, 1949) by incorporating Bishop's effective stress definition (Bishop & Blight, 1963) to account for stiffness variations caused by capillary stresses, and simulate the elastic properties of soils under varying saturation conditions (Section S2 and Figures S1 and S2 in Supporting Information S1). The structured output sentence includes parameters such as soil nature (clay, silt, loam, or sand), layer thickness, the average number of contacts per particle (N) which is linked to the soil compaction level, and the WT level. All four soil natures are defined with ratios of pure sand ($\gamma_{sand}$), clay ($\gamma_{clay}$), and silt ($\gamma_{silt}$), porosity ($\phi$), van Genuchten parameters ($\alpha_{vg}$, $n_{vg}$, and $\theta_{vg}$) (van Genuchten, 1980), a residual water saturation ($S_{wr}$), and a fraction of non-slipping grains ($f_{nsg}$) (Carsel & Parrish, 1988; Solazzi et al., 2021) (Table S1 in Supporting Information S1). The sequence length is dynamically adjusted to represent the inferred number of soil layers (ranging from 1 to 4), and a restrictive sampler ensures the coherence of the output sequence by selectively allowing or prohibiting specific tokens at each generation step of the sentence (Tables S4 and S5 in Supporting Information S1).

To train the model, synthetic data samples, consisting of pairs of soil descriptions and their corresponding modeled DC (15–50 Hz with a step of 1 Hz, and normalized between 0 and 1), were generated using the rock-physics model. The lower frequency bound was set at 15 Hz due to limitations of the rock-physics model, which is designed to parameterize unconsolidated soil layers but not rock formations. Indeed, at our study site, a deep gypsum bedrock significantly influences the dispersion curve below 15 Hz by introducing high phase velocities that cannot be accurately modeled and then learned by SILEX. Each synthetic sample was parameterized with a random number of 1–4 soil layers. Each layer was assigned a random thickness ranging from 1 to 20 m in increments of 1 m (constrained such that the total thickness of all layers is exactly 20 m), a random soil nature, and a random N value ranging from 6 to 10 in increments of 1. The WT level was also randomly defined with a value between 0.5 and 10 m in increments of 0.5 m. Note that the parameter space comprises a total of 1,323,654,400 different combinations. Initially, SILEX was trained on a data set of 1,166,446 synthetic sample pairs (covering 0.9% of the total possible soil models) for 100 epochs with a batch size of 64 samples, and using a validation set of 100,000 samples for early stopping as well as a test set of 50,000 samples to evaluate final performance. To ensure proper generalization assessment, identical soil profiles were excluded from appearing across the training, validation, and test data sets. A root-mean-square propagation (RMSProp) optimizer with a learning rate of $10^{-3}$, and a sparse categorical cross-entropy loss function were used for optimizing the model parameters during training. SILEX achieved an accuracy of 92.2% on the training data set, 91.7% on the validation data set, and 91% on the test data set. To enhance robustness on real data, SILEX was retrained for an additional five epochs using the same data set of 1,166,446 synthetic samples, but with Gaussian noise (centered in 0 and with a standard deviation of 1) added to the input normalized DCs to introduce variability. Although accuracy dropped to 83% on the training set and 82% on the test set, this approach aims to improve the model's generalization.

## 3. Results

### 3.1. Petrophysical and Mechanical Properties

SILEX was used to invert all subsequent DCs along the five geophone lines ($L_1$ to $L_5$), on a daily basis from 3 September 2020 to 4 September 2023. Since each DC depends on the soil properties beneath the surface point where it was measured (Section S1 in Supporting Information S1), the output petrophysical parameters are laterally concatenated along each geophone line (Figure S3 in Supporting Information S1) to build 2D sections that facilitate the visualization of complex subsurface structures and enhance the spatial understanding of geological formations and hydrogeological conditions.

The resulting petrophysical sections (Figure 3, or Figure S14 in Supporting Information S1 for a more detailed view), monthly-averaged over July 2022 and 2023, highlight a predominantly soft clayey soil (N at 6 and 7), as expected from geological drillings ($DR_1$ and $DR_2$ in Figures 2 and 3). Results also indicate the presence of
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Measured and inferred water table level, and rainfall over time. (a and b) Comparison between measured and inferred water table level variation over time at the positions of piezometers *PZ*₁ and *PZ*₂. (c) Daily measured rainfall, and 45-day running mean.</figcaption></figure>

compacted soil structures in the North-East, and to a lesser extent in the South-West regions of all geophone lines. These are located at depths ranging from −5 to −10 m and are predicted to be composed of a compact sandy soil (N value of 9 and 10). At both drilling locations, SILEX predicts a loam layer with a moderate N value of 7 where the drillings reveal a sandy clay soil, and a sand layer with a high N value of 10 at the depth corresponding to a gravelly sand layer.

However, the gypsum substratum remains undetected by our model as it does not qualify as soil. Nevertheless, a highly compacted sandy structure below −15 m was predicted around *x* = 42 m. This prediction may approximate the mechanical behavior of the substratum layer, but no drilling was conducted at this location to confirm the findings.

## 3.2. Temporal Stability

Drained shear modulus of the porous medium ($\mu_m$) sections were computed from the petrophysical inversion results, using a modified Hertz–Mindlin model (Mindlin, 1949) (Figures S15 and S16 in Supporting Information S1). Visualizing this parameter makes different geomechanical structures, more easily discernible. Subsurface structures above −15 m demonstrate consistent temporal stability over the study period, in terms of both inferred soil nature and $\mu_m$. This stability is crucial for understanding the long-term geological and hydrogeological conditions of the area, as well as for sinkhole risk assessment. However, below −15 m, the substratum imaging exhibits less stability (substratum at the North-East part of $L_1$ on Figures S15b and S15d in Supporting Information S1). This can be attributed to the frequency bandwidth limitations of the inverted DCs (15–50 Hz) rather to SILEX's inference capabilities, as the frequency lower limit may not sufficiently resolve the deeper substratum features. Typically, the maximum sensitivity depth is approximately half of the maximum wavelength $\lambda_{max} = \max[\frac{V_R(f)}{f}]$, where $V_R$ is the Rayleigh-wave phase velocity and $f$ is the frequency (Foti et al., 2018). In our case, the average $\lambda_{max}$ is 24 m, corresponding to a maximum investigation depth with good resolution of approximately −12 m.

Overall, the observed evolution of $\mu_m$ does not show a significant development of mechanical weaker zones (low $\mu_m$). This is coherent with the fact that no evidence of sinkhole development was observed at the surface of the site during the study period. The sandy zones should, however, be closely monitored, as suffusion phenomena could occur. Additionally, the uncertainty and reduced stability of the substratum at greater depths necessitate careful consideration.
### 3.3. Water Table Level

The WT levels were inferred with a depth step of 0.5 m. Thus, to obtain a smoother WT levels across the study area and period, a Savitzky-Golay filter (Savitzky & Golay, 1964) was applied, using a spatial window of 10.75 m along the x-axis and a temporal window of 137 days spanning (September 2020 to September 2023). The window lengths were selected empirically through visual inspection, as they yielded smoother and more coherent profiles without excessively smoothing important features. Nevertheless, the depth resolution could be enhanced by reducing the depth step during training data generation and accordingly adapting the model vocabulary (Tables S1 and S2 in Supporting Information S1).

The inferred levels align with the observed data at piezometers $PZ_1$ and $PZ_2$ (Figure 4), demonstrating SILEX's accuracy in capturing WT levels across time. However, sharp variations in the WT are not fully recovered, and a slight overestimation of approximately 0.5 m is observed in the inferred levels at $PZ_2$. This could be explained by the fact that $PZ_2$ is located over a relatively thick and laterally extensive gravely sandbank (Figure 3, or Figure S14 in Supporting Information S1 for a more detailed view). Since, gravely sand is not particularly sensitive to capillary suction, the corresponding mechanical properties are not expected to be particularly sensitive to saturation changes. These results are consistent with previous studies that used an MLP to directly convert DCs into WT levels, uniquely based on observed piezometric data (Cunha Teixeira, Bodet, Rivière, et al., 2025).

Additionally, the model accurately captures seasonal variations, with WT levels rising and falling in sync with low and high water periods. These fluctuations match the regional rainfall patterns, indicating the model's sensitivity to hydrological drivers.

### 3.4. Accuracy and Error

SILEX was evaluated on 50,000 synthetic samples outside the training data set, achieving a token accuracy of 81%. Additionally, using SILEX inference results, DCs were recomputed with the same rock-physics model used to generate the training data. Comparison between the input and recomputed DCs show a global low root-mean-square error (RMSE, Equation S22 in Supporting Information S1), estimated at 12 m/s (normalized RMSE of 8%), across all inversions from 4 September 2020 to 3 September 2023.

Yet, some discrepancies appear at few x positions (15 July 2022 and 2023 are shown as examples in Figures S4 to S13 in Supporting Information S1). These inconsistencies highlight the model's limitations in approximating DCs with abrupt variations, which is inherent to the rock-physics model used to generate the training data. At these specific locations, the input DCs tend to be of lower quality and may suffer from mode contamination, which occurs when a higher propagating mode is mistakenly identified as the fundamental mode (notably after 30 Hz in this example) during the automatic dispersion image picking process, resulting in a bump in the DC. Such contamination further complicates SILEX's ability to accurately capture the true subsurface characteristics at these points. It is interesting to note that SILEX seems to produce an average DC that attempts to balance the fit between the 15–30 Hz and 30–50 Hz frequency ranges.

## 4. Discussion

### 4.1. Comparison With Conventional Inversion

The $V_s$ estimations, derived from SILEX's inference results, closely align with those obtained with a conventional seismic inversion (Section S6 and Figure S17 in Supporting Information S1). This confirms that the model reliably retrieves mechanical results that are comparable to established methods, despite the radical differences between the two approaches.

Beyond the additional detailed insights gained from a petrophysical inversion compared to a seismic inversion, SILEX also provides a significant computational advantage. On a single Intel Xeon central processing unit (CPU), the inversion of an entire daily geophone line is completed within 2 min, whereas the conventional seismic inversion requires approximately 65 hr, which is excessively time-consuming for daily monitoring. However, it is important to note that this extended time is primarily due to the stochastic nature of the conventional approach, which necessitates computing a large number of models when sampling the posterior probability distribution. Even though conventional seismic inversion can be optimized through parallel computing to reduce processing time, a conventional petrophysical inversion method of the rock-physics model we adapted (Solazzi et al., 2021),
yet to be fully developed, would still require significantly more time due to the high number of petrophysical parameters to retrieve.

However, the training data generation phase is highly time-consuming, requiring up to 20 hr for 1,316,446 samples on a single Intel Xeon CPU. Yet, it can be parallelized and is only necessary once per lifetime, as the data can be reused to train other models by selecting the desired frequencies. Similarly, the model's training phase is computationally intensive, requiring around 2 hr on an Nvidia Tesla T4 GPU, but it only needs to be performed once before deployment. Following this training, the model can be deployed for daily inversion tasks without any additional overhead, thereby demonstrating high efficiency for large-scale geophysical surveys. The lightweight architecture of SILEX (only 499,266 parameters, Section S3 and Figure S3 in Supporting Information S1) allows it to operate on standard hardware without requiring server infrastructure, thereby enhancing its practicality for field applications and effectively addressing technical limitations in geophysical monitoring.

## 4.2. Rock-Physics Model Limitation

The modified rock-physics model (Solazzi et al., 2021) used to generate the training data is primarily designed to model soil properties rather than consolidated rock formations. As a result, the inversion is accurate at shallow depths, where soils predominate, but may not accurately reflect the petrophysical properties of the rocky substratum, even though the mechanical properties of rocks are approximated with a high *N* (9 and 10 on Figures 3b and 3d). This limitation can lead to a lack of detailed information and perceived instability at greater depths, as certain geological features and variations may be overlooked or inadequately captured. Incorporating rock lithofacies could mitigate these issues but would require a redefinition of the rock-physics model. This is relatively straightforward for sandstones or sedimentary rocks, but implementing the full diversity of rock natures (igneous, sedimentary, and metamorphic) would necessitate a more complex rock-physics model.

## 4.3. Lack of Uncertainty Estimation

Additionally, the limitation of using a deterministic petrophysical inversion approach is the lack of inherent uncertainty quantification, which contrasts with stochastic methods commonly employed in seismic inversion. In fact, the Transformer-based language model used here provides a unique output per inversion, without representing the range of possible outcomes or associated uncertainties. While it is optimized for accuracy and efficiency, the absence of uncertainty quantification may limit its application in scenarios where risk assessment is critical.

Nevertheless, we estimate inference variability based on daily results over the studied months and show that the model's predictions, in terms of soil natures, *N* values and WT levels, are relatively uniform or concentrated around certain outcomes (Figures S28 and S29 in Supporting Information S1). However, future enhancements could integrate uncertainty estimation methods, such as ensemble modeling, or Bayesian inversion through posterior sampling with diffusion models (Moufad et al., 2024), to enhance the model's value in high-stakes geological and hydrogeological monitoring contexts.

## 5. Conclusions

In this study, we introduced a new approach for subsurface petrophysical inversion integrating a Transformer-based language model. This model effectively translates DCs derived from train-induced surface waves into detailed textual descriptions of subsurface properties, including soil natures, mechanical properties, and WT levels. These descriptions can be used for geological and hydrogeological interpretation or converted into soil elastic moduli for applications in civil engineering. The model effectively captured the spatial and temporal stability of subsurface structures above –15 m, correlating well with expected lithofacies and indicating the absence of sinkhole emergence at the surface during the study period. The inferred WT levels also closely match the measured data from piezometers, and accurately reflects seasonal variations induced by rainfall. Additionally, this technique demonstrated significant improvements in inversion speed, achieving a 2,000-fold increase compared to conventional stochastic methods.

Despite these successes, challenges remain in accurately imaging deeper substratum features below –15 m, largely due to limitations in the seismic data frequency bandwidth and the rock-physics model's design, used to
generate the training data. Future research should focus on expanding the inverted frequency range, and refining
the rock-physics model to also account for rock properties at greater depths.

The lack of uncertainty estimation inherent to our deterministic approach limits the reliability of predictions for critical decision-making. Addressing this limitation in future work, potentially through the integration of uncertainty quantification techniques, would enhance the model's trustworthiness, particularly for deeper and more complex geological features.

Overall, these findings underscore the potential of AI techniques in improving subsurface characterization and providing valuable insights for applications such as groundwater management, natural hazard monitoring, and structural health assessment. This approach represents a promising step forward in petrophysical inversion from surface wave analysis, offering a framework for future studies across various scales and contexts.

Conflict of Interest

The authors declare no conflicts of interest relevant to this study.

Data Availability Statement

All authors approved the final version of this article. The dispersion curves data set, used as input for SILEX model, as well as the output data are provided on Zenodo (Cunha Teixeira et al., 2024). All code that supports the claims in this manuscript are provided on Zenodo (Cunha Teixeira et al., 2024).

Acknowledgments

This research was made possible through funding from SNCF Réseau, CNRS, Sorbonne University, Mines Paris-PSL research contract, and ANRT/Cifre-SNCF Réseau convention No 2021/1552. This project is supported by the Europe's Rail Joint Undertaking and its members, and has received funding from the European Union's Horizon Europe research and innovation program under Grant Agreement No 101101966. We thank Thomas Bardainne, Renaud Tarnus, Thibaut Allemand, Ceifang Cai, Helene Toubiana Lille, Nicolas Deladrierriere, Lilas Vivin, and Loic Michel from the company Sercel for their contribution in acquiring and processing the geophysical passive-MASW data. We also express gratitude to the local teams from SNCF Réseau their invaluable assistance and support during field experiments. Finally, we thank Damien Jugnot, from UMR 7619 METIS, Sorbonne University, for the helpful discussions on rock-physics theory, and Maxime Gautier, from Mines Paris - PSL, for his detailed review before submission. The processing technique of the geophysical passive-MASW data used as input to our model, was performed by the company Sercel, and is under the patents No. FR3084473B1, BR112021000806B1, EP3827288B1, WO2020021177A1, CA3106292A1, US11971514B2, AU2019311797B2, and ZA202101057B, entitled "Method and device for monitoring the subsoil of the earth under a target zone".

References

Aki, K., & Richards, P. G. (1981). Quantitative seismology, theory and methods. *Geological Magazine*, 118(2), 208. https://doi.org/10.1017/S0016756800034439

Araya-Polo, M., Jennings, J., Adler, A., & Dahlke, T. (2018). Deep-learning tomography. *The Leading Edge*, 37(1), 58–66. https://doi.org/10.1190/tle37010058.1

Baevski, A., Zhou, H., Mohamed, A., & Auli, M. (2020). wav2vec 2.0: A framework for self-supervised learning of speech representations. https://doi.org/10.48550/arXiv.2006.11477

Bardaine, T., & Rondeleux, B. (2018). Method and device for monitoring the subsoil of the earth under a target zone. Patent No. FR3084473B1.

Bardainne, T., Cai, C., Rebert, T., Tarnus, R., & Allemand, T. (2023). Passive seismic monitoring using trains as sources to characterize near-surface and prevent sinkholes. In *84th EAGE annual conference & exhibition workshop programme, European association of Geoscientists and Engineers* (Vol. 2023, pp. 1–5). https://doi.org/10.3997/2214-4609.2023101262

Bishop, A. W., & Blight, G. E. (1963). Some aspects of effective stress in saturated and partly saturated soils. *Géotechnique*, 13(3), 177-197. https://doi.org/10.1680/geot.1963.13.3.177

Brenguier, F., Shapiro, N. M., Campillo, M., Ferrazzini, V., Duputel, Z., Coutant, O., & Nercessian, A. (2008). Towards forecasting volcanic eruptions using seismic noise. *Nature Geoscience*, 1(2), 126–130. https://doi.org/10.1038/ngeo104

Brown, T. B., Mann, B., Ryder, N., Subbiah, M., Kaplan, J., Dhariwal, P., et al. (2020). Language models are few-shot learners. *CoRR*, abs/2005.14165

Campillo, M., & Paul, A. (2003). Long-range correlations in the diffuse seismic coda. *Science*, 299(5606), 547–549. https://doi.org/10.1126/science.1078551

Carsel, R. F., & Parrish, R. S. (1988). Developing joint probability distributions of soil water retention characteristics. *Water Resources Research*, 24(5), 755–769. https://doi.org/10.1029/WR024i005p00755

Chen, X., Xia, J., Pang, J., Zhou, C., & Mi, B. (2022). Deep learning inversion of Rayleigh-wave dispersion curves with geological constraints for near-surface investigations. *Geophysical Journal International*, 231(1), 1–14. https://doi.org/10.1093/gji/ggac171

Cunha Teixeira, J., Bodet, L., Dangeard, M., Gesret, A., Hallier, A., Rivière, A., et al. (2025). Nondestructive testing of railway embankments by measuring multi-modal dispersion of surface waves induced by high-speed trains with linear geophone arrays. *Seismica, 4*(1). https://doi.org/10.26443/seismica.v4i1.1150

Cunha Teixeira, J., Bodet, L., Rivière, A., Hallier, A., Gesret, A., Dangeard, M., et al. (2025). Physics-guided deep learning model for daily groundwater table maps estimation using passive surface-wave dispersion. *Water Resources Research*, 61(1), e2024WR037706. https://doi.org/10.1029/2024WR037706

Cunha Teixeira, J., Bodet, L., Rivière, A., Solazzi, S. G., Hallier, A., Gesret, A., et al. (2024). *Neural machine translation of seismic waves for petrophysical inversion (Version 2) [Collection]*. Zenodo. https://doi.org/10.5281/zenodo.14192468

Das, V., & Mukerji, T. (2020). Petrophysical properties prediction from prestack seismic data using convolutional neural networks. *Geophysics*, 85(5), 1–85. https://doi.org/10.1190/geo2019-0650.1

Dou, Y., & Li, K. (2024). 3d seismic mask auto encoder: Seismic inversion using transformer-based reconstruction representation learning. *Computers and Geotechnics*, 169, 106194. https://doi.org/10.1016/j.compgeo.2024.106194

Foti, S., Hollender, F., Garofalo, F., Albarello, D., Asten, M., Bard, P.-Y., et al. (2018). Guidelines for the good practice of surface wave analysis: A product of the interpacific project. *Bulletin of Earthquake Engineering*, 16(6), 2367–2420. https://doi.org/10.1007/s10518-017-0206-7

Hadid, A., Chakraborty, T., & Busby, D. (2024). When geoscience meets generative ai and large language models: Foundations, trends, and future challenges. *Expert Systems*, 41(10), e13654. https://doi.org/10.1111/exsy.13654

IPCC. (2023). *Climate change 2023: Synthesis report. Contribution of working groups I, II and III to the sixth assessment report of the inter-governmental panel on climate change*. (Core Writing Team, H. Lee, & J. Romero (eds.)) https://doi.org/10.59327/IPCC/AR6-9789291691647
Lavoué, F., Coutant, O., Boué, P., Pinzon-Rincon, L., Brenguier, F., Brossier, R., et al. (2020). Understanding seismic waves generated by train traffic via modeling: Implications for seismic imaging and monitoring. *Seismological Research Letters*, 92(1), 287–300. https://doi.org/10.1785/0220200133

Le Breton, M., Bontemps, N., Guillemot, A., Baillet, L., & Éric, L. (2021). Landslide monitoring using seismic ambient noise correlation: Challenges and applications. *Earth-Science Reviews*, 216, 103518. https://doi.org/10.1016/j.earscirev.2021.103518

LeCun, Y., Bengio, Y., & Hinton, G. (2015). Deep learning. *Nature*, 521(7553), 436–444. https://doi.org/10.1038/nature14539

Li, S., Liu, B., Ren, Y., Chen, Y., Yang, S., Wang, Y., & Jiang, P. (2020). Deep-learning inversion of seismic data. *IEEE Transactions on Geoscience and Remote Sensing*, 58(3), 2135–2149. https://doi.org/10.1109/TGRS.2019.2953473

Liu, F., Li, J., Fu, L., & Lu, L. (2024). Multimodal surface wave inversion with automatic differentiation. *Geophysical Journal International*, 238(1), 290–312. https://doi.org/10.1093/gji/ggae155

Mao, S., Lecointre, A., van der Hilst, R., & Campillo, M. (2022). Space-time monitoring of groundwater fluctuations with passive seismic interferometry. *Nature Communications*, 13(1), 4643. https://doi.org/10.1038/s41467-022-32194-3

Mavko, G., Mukerji, T., & Dvorkin, J. (2009). *The rock physics handbook: Tools for seismic analysis of porous media* (2nd ed.). Cambridge University Press. Hardcover.

Mindlin, R. D. (1949). Compliance of elastic bodies in contact. *Journal of Applied Mechanics*, 16(3), 259–268. https://doi.org/10.1115/1.4009973

Moufad, B., Janati, Y., Bedin, L., Durmus, A., Douc, R., Moulines, E., & Olsson, J. (2024). Variational diffusion posterior sampling with midpoint guidance. https://doi.org/10.48550/arXiv.2410.09945

Mousavi, S., & Beroza, G. (2022). Deep-learning seismology. *Science*, 377(6607). https://doi.org/10.1126/science.abm4470

Muller, A. P. O., Costa, J. C., Bom, C. R., Klatt, M., Faria, E. L., de Albuquerque, M. P., & de Albuquerque, M. P. (2023). Deep pre-trained FWI: Where supervised learning meets the physics-informed neural networks. *Geophysical Journal International*, 235(1), 119–134. https://doi.org/10.1093/gji/ggad215

Ning, C., Wu, B., & Zhu, Z. (2023). Transformer and CNN hybrid neural network for seismic impedance inversion. In *IGARSS 2023 - 2023 IEEE international geoscience and remote sensing symposium* (pp. 5543–5546). https://doi.org/10.1109/IGARSS52108.2023.10281611

Pasquet, S., & Bodet, L. (2017). SWIP: An integrated workflow for surface-wave dispersion inversion and profiling (Version 2.3) [Software]. *Geophysics*, 82(6), WB47-WB61. https://doi.org/10.1190/geo2016-0625.1

Rebert, T., Bardainne, T., Allemand, T., Cai, C., & Chauris, H. (2024). Characterization of train kinematics and source wavelets from near-field seismic data. *Geophysical Journal International*, 237(2), 697–715. https://doi.org/10.1093/gji/ggae067

Rebert, T., Cai, C., Hallier, A., & Bardainne, T. (2024). Rockfall alarm system for railway monitoring: Integrating seismic detection, localization, and characterization. *Geophysics*, 89(1), KS13-KS23. https://doi.org/10.1190/geo2023-0058.1

Sambridge, M. (1999). Geophysical inversion with a neighbourhood algorithm—I. Searching a parameter space. *Geophysical Journal International*, 138(2), 479–494. https://doi.org/10.1046/j.1365-246X.1999.00876.x

Sauquet, E., Evin, G., Siauve, S., Aissat, R., Arnaud, P., Bérel, M., et al. (2025). A large transient multi-scenario multi-model ensemble of future streamflow and groundwater projections in France. *EGUsphere*, 2025, 1–41. https://doi.org/10.5194/egusphere-2025-1788

Savitzky, A., & Golay, M. J. E. (1964). Smoothing and differentiation of data by simplified least squares procedures. *Analytical Chemistry*, 36(8), 1627–1639. https://doi.org/10.1021/ac60214a047

Shapiro, N. M., Campillo, M., Stehly, L., & Ritzwoller, M. H. (2005). High-resolution surface-wave tomography from ambient seismic noise. *Science*, 307(5715), 1615–1618. https://doi.org/10.1126/science.1108339

Shen, Z., Yang, Y., Fu, X., Adams, K. H., Biondi, E., & Zhan, Z. (2024). Fiber-optic seismic sensing of vadose zone soil moisture dynamics. *Nature Communications*, 15(1), 6432. https://doi.org/10.1038/s41467-024-50690-6

Snieder, R., Grét, A., Douma, H., & Scales, J. (2002). Coda wave interferometry for estimating nonlinear behavior in seismic velocity. *Science*, 295(5563), 2253–2255. https://doi.org/10.1126/science.1070015

Solazzi, S. G., Bodet, L., Holliger, K., & Jougnot, D. (2021). Surface-wave dispersion in partially saturated soils: The role of capillary forces. *Journal of Geophysical Research: Solid Earth*, 126(12), e2021JB022074. https://doi.org/10.1029/2021JB022074

Talarico, E., Leão Neto, W., & Grana, D. (2021). Comparison of recursive neural network and Markov chain models in facies inversion. *Mathematical Geosciences*, 53(3), 395–413. https://doi.org/10.1007/s11004-020-09914-w

Tarantola, A., & Valette, B. (1982). Generalized nonlinear inverse problems solved using the least squares criterion. *Reviews of Geophysics*, 20(2), 219–232. https://doi.org/10.1029/RG020i002p00219

Tarnus, R., Bardainne, T., Michel, L., Deladjerriere, N., Cai, C., Hallier, A., & Boisson-Gaboriau, J. (2022). A case study for underground imaging using trains as seismic signal to investigate subsidence phenomena. In *NSG2022 28th European meeting of environmental and engineering geophysics, European Association of Geoscientists and Engineers* (Vol. 2022, pp. 1–5). https://doi.org/10.3997/2214-4609.202220033

van Genuchten, M. T. (1980). A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. *Soil Science Society of America Journal*, 44(5), 892–898. https://doi.org/10.2136/ssaj1980.036159950044000500002x

Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., et al. (2017). Attention is all you need. https://doi.org/10.48550/arXiv.1706.03762

Vergnes, J.-P., Caballero, Y., & and, S. L. (2023). Assessing climate change impact on French groundwater resources using a spatially distributed hydrogeological model. *Hydrological Sciences Journal*, 68(2), 209–227. https://doi.org/10.1080/02626667.2022.2150553

Voisin, C., Garambois, S., Massey, C., & Brossier, R. (2016). Seismic noise monitoring of the water table in a deep-seated, slow-moving landslide. *Interpretation*, 4(3), SJ67-SJ76. https://doi.org/10.1190/INT-2016-0010.1

Wang, H., Lin, J., Dong, X., Lu, S., Li, Y., & Yang, B. (2023). Seismic velocity inversion transformer. *Geophysics*, 88(4), R513–R533. https://doi.org/10.1190/geo2022-0283.1

Weinzierl, W., & Wiese, B. (2021). Deep learning a poroelastic rock-physics model for pressure and saturation discrimination. *Geophysics*, 86(1), MR53-MR66. https://doi.org/10.1190/geo2020-0049.1

Zhang, G., Wang, Z., & Chen, Y. (2018). Deep learning for seismic lithology prediction. *Geophysical Journal International*, 215(2), 1368–1387. https://doi.org/10.1093/gji/ggy344

Zhang, Z., & Lin, Y. (2020). Data-driven seismic waveform inversion: A study on the robustness and generalization. *IEEE Transactions on Geoscience and Remote Sensing*, 58(10), 1–14. https://doi.org/10.1109/TGRS.2020.2977635