SEP-196 (2025)

Rustam Akhmadiev, Hamad Alswaidan, Biondo Biondi, Edward Caunt, Robert Clapp, Thomas Cullison, Ivan Deiana, Julio Oliva Frigerio, Antoine Guitton, Seunghoo Kim, Haipeng Li, Cewen Liu, Jingxiao Liu, Shujuan Mao, Giacomo Roncoroni, Shuki Ronen, Joe Stitt, Siyuan Yuan

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SEP-196 (Password Protected) (May 2025)

Full-waveform inversion 
 

Daily Elastic Full-waveform Inversion for Groundwater Monitoring
Haipeng Li, Jingxiao Liu, Shujuan Mao, Siyuan Yuan, Robert Clapp
Monitoring groundwater is essential for effective water resource management, especially in the face of increasing climate variability. Yet, existing methods often lack the resolution required for precise aquifer monitoring. In this study, we present a novel method for tracking groundwater changes by applying daily time-lapse elastic full-waveform inversion (EFWI), utilizing fiber-optic cables as seismic receivers and vehicular traffic as repeatable surface wave sources. Implemented along Sandhill Road, California, over a two-year span, this technique successfully maps fine-scale spatiotemporal variations in shear-wave velocity of the near surface. Following atmospheric river events during Water Year 2023, we detect a 2.9% velocity decrease associated with a 9.0-meter rise in the groundwater table. Thanks to their high resolution, our results reveal highly variable subsurface velocity responses, with smaller reductions under paved surfaces compared to grassy areas, highlighting how urban infrastructure can influence groundwater recharge. These findings demonstrate the promise of daily EFWI for detailed, real-time monitoring and analysis of near-surface groundwater systems. Our developed workflow can be further extended to continuously monitor hydrocarbon reservoir and geologic carbon sequestration.

Review of Surface-Wave-Driven FWI: The Potential to Incorporate Distributed Acoustic Sensing Data for 3D Nearsurface Characterization
Thomas Cullison  
Accurate near-surface characterization is valuable for applications ranging from carbon storage monitoring to urban infrastructure planning. However, conventional seismic inversion techniques often struggle in complex environments due to low-velocity zones and scattering effects. Distributed Acoustic Sensing (DAS), which leverages fiber-optic cables for high-density seismic acquisition, has emerged as a promising tool for nearsurface imaging. This review explores the potential of integrating DAS with 3D surfacewave-driven Full Waveform Inversion (SWD-FWI), emphasizing its potential to resolve near-surface heterogeneities. We highlight recent advances, ongoing challenges– such as data volume and accounting for DAS’s directional sensitivity– and opportunities for future development, particularly for carbon storage and urban applications.

Time-Lapse Seismic Full Waveform Inversion of 2D VSP Data: A Comparison of Methods and Applications
Cewen Liu, Antoine Guitton, Thomas Cullison, Robert Clapp, and Biondo Biondi
We developed an extensible acoustic 4D FWI framework based on the scalar wave equation within the symbolic high-performance Devito platform. Devito enables rapid prototyping of wave-equation-based solvers while maintaining computational efficiency through automatic generation of highly optimized stencil code. Leveraging this capability, we implement and compare multiple 4D inversion strategies, including parallel, sequential, central double-difference, and joint 4D FWI schemes. We validate the framework through comprehensive numerical experiments on both the synthetic Marmousi model and a modified SEAM 4D benchmark. In particular, we demonstrate the applicability of our methods to vertical seismic profiling (VSP) datasets from the SEAM model, with implications for DAS (Distributed Acoustic Sensing)-based timelapse monitoring. Furthermore, we evaluate the robustness of the inversion schemes under various noise scenarios by introducing Gaussian and uniform-distributed noise at different energy levels. The results show that double-difference and joint inversion methods consistently deliver improved stability and imaging accuracy, especially under strong noise conditions. Our work provides a flexible and extensible platform for future developments in 4D FWI and contributes to advancing practical time-lapse seismic monitoring applications.

Uncertainty Quantification in Time-lapse Full-waveform Inversion Using Hamiltonian Monte Carlo
Haipeng Li, Robert Clapp and Biondo Biondi
Time-lapse Full-Waveform Inversion (FWI) enables high-resolution monitoring of subtle subsurface changes. However, conventional time-lapse FWI lacks uncertainty quantification, which limits its value in applications such as geological carbon sequestration. In this study, we propose a Bayesian time-lapse FWI framework using Hamiltonian Monte Carlo (HMC) combined with a prior-guided Radial Basis Function (RBF) model-order reduction strategy. We validate the method on synthetic CO2 injection scenarios derived from multi-physics simulations. Results show that the proposed approach achieves well-characterized uncertainty estimates with significantly fewer parameters. The resulting CO2 credibility maps derived from HMC FWI offer actionable insights for seismic monitoring, informing practical operations to reduce uncertainty for better risk mitigation. This study shows the potential of using Bayesian inversion and spatially adaptive model reduction for effective time-lapse seismic monitoring with uncertainty quantification.

Geometry-Aware Strategies for 4D Full Waveform Inversion: Comparative Study of 4D Time-Lapse Inversion Schemes on the SEAM Model
Cewen Liu, Antoine Guitton, Thomas Cullison, Robert Clapp, and Biondo Biondi
We investigate the performance of multiple time-lapse full-wave form inversion (4D FWI) strategies—including parallel, sequential, central difference, double-difference, and joint inversion schemes for different acquisition geometry configurations designed to closely mimic realistic field conditions.Our implementation is based on a 2D acoustic wave equation solver using the Devito platform, providing a flexible and efficient framework. Leveraging a 4D benchmark model , which features a geologically complex overburden and a representative evolving CO2 plume , we conduct a series of tests in which source locations remain fixed while receiver configurations vary. Specifically, we evaluate four acquisition scenarios: (1) surface-only, (2)VSP-only, (3) combined surface and VSP, and(4) sparse surface + VSP arrays. To assess the robustness of each inversion strategy under varying data quality conditions, we introduce two types of perturbations: (1) uniformly distributed random noise to simulate measurement uncertainty, and(2)non-repeated velocity anomaly arising from shallow subsurface velocity changes not related to the target CO2 plume. Through this geometry- and noise-aware analysis, we evaluate the sensitivity of each 4D FWI approach to data coverage, inversion stability, and resolution. Experimental results suggest that, under the tested conditions, the double-difference strategy demonstrates consistently strong performance across all geometries and noise types, while joint inversion remains competitive with appropriate parameter tuning. Parallel, sequential, and central difference strategies show more variable performance, particularly under noise and non-repeatable acquisition. In our synthetic setting, the sparse surface + VSP configuration leads to improvements over VSP - only in several strategies, while the addition of dense surface receivers does not always yield better results and may increase inversion complexity. These findings provide geometry - and noise-aware insights into the practical deployment of 4D FWI methods and may help guide acquisition and inversion design in future field applications.

Constrained optimization in geophysics: method of proximal gradient and ADMM
Rustam Akhmadiev
I investigate the application of proximal gradient methods and the Alternating Direction Method of Multipliers (ADMM) for solving constrained optimization problems within the category of the geophysical inverse problems. After understanding the fundamental principles and mathematical formulations of both proximal gradient methods and ADMM,Iexplore their specific application in geophysical inverse problems. Specifically, I demonstrate examples of L1 and TV regularization, and their application for the full waveform inversion (FWI) problem. In the case of constraints represented by an L2 norm, the proximal operator turns out to be equivalent to the shaping operator, which allows its efficient computation using fast explicit diffusion.

Distributed acoustic sensing (DAS) 
 

First Look: Aquistore DAS Data from a 2023 ActiveShot Field Survey
Thomas Cullison
This report presents an initial assessment of DAS data acquired during an active-source f ield survey in 2023 at the Aquistore CO2 storage site. The survey is a novel hybrid deployment that incorporates both surface-trenched and vertical loops of fiber in shallow boreholes, allowing for a comparison of wavefield characteristics across different channel subsets (e.g., surface and borehole channels). The objective is to evaluate the effectiveness of separating these subsets to isolate coherent surface-wave energy for potential use in surface-wave-driven full waveform inversion (SWD-FWI). The results indicate that removing borehole and adjacent channels improves the continuity of surface-wave events, though some incoherency remains, possibly due to residual spooled channels, static shifts, and amplitude variability. These effects may be related to channel geometry, coupling, and near-surface velocity structure, but additional curation and metadata validation may be required.

Leveraging Counter-Propagating Signals in Distributed Acoustic Sensing for Combined Static and Dynamic Strain Monitoring
Seunghoo Kim
Distributed Acoustic Sensing (DAS) has emerged as a transformative technology for geophysical monitoring, yet conventional implementations face limitations in reliably recovering low-frequency and static strain components, particularly in complex urban environments utilizing existing telecommunication fibers. This study addresses these limitations by adapting bidirectional calibration principles, originally developed for Distributed Temperature Sensing (DTS), to a dual-ended DAS configuration. I present a comprehensive processing workflow that includes spatial alignment of counter propagating signals, amplitude calibration to correct for differential attenuation, time integration of strain rate to derive strain, baseline referencing to mitigate long-period drift, and directional averaging to improve signal-to-noise ratio. Application of this methodology to DAS data acquired on an urban dark fiber network demonstrates a substantial reduction in instrumental drift, approaching machine precision, and significant suppression of incoherent noise. Crucially, these improvements are achieved while preserving coherent low-frequency strain signals down to 0.1Hz. The method’s robustness is confirmed through an alysis of datasets with varying noise characteristics. The enhanced stability and fidelity afforded by this dual-ended approach enable more accurate characterization of quasi-static phenomena, such as vehicle-induced ground deformation, and potentially the resolution of persistent localized static strain anomalies. This work illustrates that a DTS-inspired bidirectional calibration framework can significantly improve the capability of DAS to function as a true broadband sensor, unlocking new opportunities for long-term deformation monitoring and a more complete understanding of subsurface processes in challenging settings.

Microseismic Monitoring with deep learning applied in the image-domain: preliminary results to 3D DAS records in geothermal field
Julio Oliva Frigerio
Detecting and locating microseismic events with low magnitudes relative to background noise remains a significant challenge. I present an algorithm that integrates seismic imaging with machine learning techniques to enhance the detection and localization of such events under low signal-to-noise conditions. The approach has shown promising results in synthetic experiments, and preliminary applications to field data—acquired using Distributed Acoustic Sensing (DAS) during the stimulation of an enhanced geothermal system—demonstrate strong potential for successful deployment in real-world scenarios.

Machine learning 
 

Latent Diffusion Regularization on FWI
Joe Stitt, Robert Clapp, Biondo Biondi
This paper introduces a novel latent diffusion-based regularization technique integrated within acoustic full waveform inversion (FWI), enhancing inversion quality by leveraging velocity-based geological priors learned in a compressed latent space. Our method employs a single-channel autoencoder coupled with a U-Net featuring multi-scale attention mechanisms, enabling efficient and targeted conditioning of velocity models toward geologically realistic structures. Synthetic experiments on models representing Gulf of Mexico geology—including complex salt bodies and finely interbedded sediments—demonstrate significant improvements, particularly at salt boundaries and within sedimentary sequences. We find that smaller patch sizes (256×256) outperform larger ones (512×512) because the network more effectively learns localized geological details, capturing subtle sedimentary layering and sharper local contrasts essential for realistic velocity representations. When integrated with FWI under sparse acquisition conditions, our latent diffusion regularization method substantially improves salt body delineation and internal velocity consistency, with high-pass filtering (0.001 cycles/m cutoff) successfully controlling unwanted velocity drift through depth. Statistical analyses confirm that our approach yields higher structural similarity than traditional FWI, selectively enhancing challenging-to-recover wavenumber bands. Future refinements include the inclusion of a low-frequency network, band-pass wavenumber control, formalized balancing of data and priors via ADMM optimization, adaptive update scaling, and targeted 3D implementation for industrial-scale velocity inversion problems.

Towards Robust Low Frequency Enhancement and Extrapolation with Bi-directional LSTM Neural Network
Ivan Deiana, Giacomo Roncoroni, Robert Clapp, Shuki Ronen and Biondo Biondi
This work investigates strategies to enhance low-frequency (LF) extrapolation in seismic data, with a focus on broadening the bandwidth at the low end. Our primary goal is to extend the usable LF range to improve full waveform inversion (FWI) performance and subsurface imaging. Building upon Bi-directional Long Short-Term Memory (LSTM) networks and using synthetic data for training, the study explores machine learning-based frequency extension by predicting, denoising, and refining LF components. Additionally, we discuss the role of data generation and representation. Wetest our methods using field data acquired with both conventional and low-frequency sources. In particular, we compare low-frequency signals estimated from conventional source data against those acquired directly with low-frequency sources. Byintegrating these components, the proposed framework aims to enable more accurate LFreconstruction, yielding better-constrained FWI models and more reliable geological interpretations. We are encouraged by our initial results; however, we recognize that there remains significant room for improvement as methods are refined.

Seismic Low-Frequency Extrapolation via Physics-Aware Conditional Diffusion Models 
Hamad Alswaidan, Ivan Deiana, Biondo Biondi
Low-frequency seismic data are essential for stable and accurate full-waveform inversion (FWI), especially in complex subsurface settings. However, acquiring reliable low frequencies remains a major challenge due to limitations in source bandwidth and low signal-to-noise ratios. This work proposes a physics-aware diffusion sampling for lowfrequency extrapolation, leveraging recent advances in score-based generative modeling. We formulate the task as conditional generation of the low-frequency wavefields given the high-frequency observations. We then train a neural network to approximate the gradient of the conditional data distribution via denoising score matching. To promote physical constraints, we introduce a physics-guidance term in the sampling process based on the plane-wave differential equation, assuming that high- and low-frequency wavefields share similar kinematics. Initial experiments on synthetic data demonstrate that the proposed method produces promising results.

Computational workflows 
 

A numerical recipe for 3D wavefield modeling based on one-way operators in the frequency-extended model (FWIX): algorithm and CUDA implementation
Rustam Akhmadiev 
I describe the implementation and benchmarking of an efficient nonlinear forward modeling operator for FWI and extended FWI (FWIX) based on frequency-domain oneway wave extrapolation, targeting GPU architectures. Benchmarks performed on an NVIDIA A100 GPU highlight the computational performance and the critical role of host-device memory transfer. Results demonstrate noticeable speedups achievable using the cuFFT library, especially when exploiting batched computations over multiple sources and frequencies (achieving up to 10-15 times speedup compared to multithreaded CPU FFTW for tested batch sizes). The final operator exhibits the expected linear scaling with the number of depth steps. Using CUDA streams allows reducing the overhead associated with increasing sources/frequencies due to memory transfers.

Exploring Devito for Acoustic and Elastic Simulations
Thomas Cullison, Edward Caunt, Cewen Liu, and Joe Stitt
Modern computational workflows for seismic modeling and inversion research can benef it from software tools and frameworks that support rapid development, reproducibility, computational acceleration, cross-platform portability, and seamless integration with the broader Python ecosystem. Previous SEP projects, including the SBP-SAT method and the PySeis package, expanded the range of computationally accelerated modeling and inversion capabilities available to researchers, but face challenges in long-term extensibility, portability across architectures, and compatibility with emerging machine learning (ML) workflows. To explore new opportunities for addressing these needs, this study investigates the use of Devito, a symbolic domain-specific language for finitedifference modeling, as a platform for 2D and 3D acoustic and elastic simulations. Initial development focused on validating Devito’s ability to support free-surface elastic simulations, generate surface waves, and capture both particle velocity and stress fields. Applications to acoustic full-waveform inversion and time-lapse inversion further demonstrated Devito’s potential for rapid prototyping, cross-platform deployment, and flexible inversion strategy development, while leveraging integration with scientific Python libraries. Future work will extend these capabilities to incorporate surface topography, strain-based measurements, advanced boundary conditions, and synthetic model generation workflows, thereby building a general-purpose Python-based package for scalable seismic modeling, inversion, and ML-integrated research workflows.