SEP-199 (2026)

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Full Waveform Inversion & Machine Learning
 

Progress and Current Directions with Latent Diffusion Priors for Acoustic Full-Waveform Inversion
Joe Stitt
Resolving onlapping sediments against salt flanks is one of the harder problems in subsalt imaging and one of the more valuable: stratigraphic pinch-outs against salt form the trap geometry for a large fraction of producing Gulf-of-Mexico fields. Fullwaveform inversion (FWI) is the standard tool for recovering velocity at that scale, but at the sparse acquisition geometries common in field surveys it leaves a large null space in which many velocity models fit the data equally well, and classical regularizers like total variation pick among them on mathematical rather than geological grounds. We develop a learned, geology-aware regularizer for this setting: a two-stage latent-diffusion prior built from a 128-px AutoencoderKL and an ϵ-prediction UNet operating in the compressed latent, split into low- and high-wavenumber specialist networks through a structure-oriented-smoothing-matched training scheme. The prior is coupled to FWI through interchange and three plug-and-play ADMM variants, the most aggressive of which injects the FWI gradient into the latent through a decoder vector-Jacobian product. On a sparse-acquisition GOM-151 test (2 sources, 200 receivers), this variant reaches MAE 0.263 km/s and SSIM 0.540, against the data-fit-only baseline’s 0.309 and 0.443, with visibly cleaner onlapping sediment packages along the salt flank in both the velocity model and the post-inversion RTM image. The 3-D extension is fully trained at 643 patch scale and is being integrated into the Cardamom 259-node ocean-bottom-node inversion through the SEPDevito 3-D path.

Bayesian Full-waveform Monitoring of CO2 Storage with Fluid-flow Priors via Generative Modeling
Haipeng Li, Nanzhe Wang, Louis J. Durlofsky and Biondo L. Biondi
Quantitative monitoring of subsurface changes is essential for ensuring the safety of geological CO2 sequestration. Full-waveform monitoring (FWM) can resolve these changes at high spatial resolution, but conventional deterministic inversion lacks uncertainty quantification and incorporates only limited prior information. Deterministic approaches can also yield unreliable results with sparse and noisy seismic data. To address these limitations, we develop a Bayesian FWM framework that combines reservoir flow physics with generative prior modeling. Prior CO2 saturation realizations are constructed by performing multiphase flow simulations on prior geological realizations. Seismic velocity is related to saturation through rock physics modeling. A variational autoencoder (VAE) trained on the priors maps high-dimensional CO2 saturation fields onto a low-dimensional, approximately Gaussian latent space, enabling efficient Bayesian inference while retaining the key geometrical structure of the CO2 plume. Hamiltonian Monte Carlo (HMC) is used to infer CO2 saturation changes from timelapse seismic data and to quantify associated uncertainties. Numerical results show that this approach improves inversion stability and accuracy under extremely sparse and noisy acquisition, and baseline errors, whereas deterministic methods become unreliable. Statistical seismic monitoring provides posterior uncertainty estimates that identify where additional measurements would most reduce ambiguity and mitigate errors arising from biased rock physics parameters. The framework combines reservoir physics, generative priors, and Bayesian inference to provide uncertainty quantification for time-lapse monitoring of CO2 storage and other subsurface processes.

Evaluating the Feasibility of Low Frequency Enhancement and Extrapolation Methods with Paired Field Airgun and TPS Reference Data
Ivan Deiana, Hamad Alswaidan, Giacomo Roncoroni, Shuki Ronen
We perform a field based feasibility study of low frequency (LF) enhancement and extrapolation using paired airgun and Tuned Pulse Source (TPS) data. The airgun data provide the limited bandwidth input, while the TPS data provide an independent LF reference for assessing whether recovered energy is physically meaningful or mainly the result of denoising and spectral enhancement. We compare three complementary approaches. The first is a supervised Bidirectional Long Short Term Memory (BiLSTM) model trained on synthetic reflectivity and source signature pairs. This model operates trace by trace and provides a low tuning neural signal processing baseline. The second is a physics aware conditional diffusion framework for two dimensional gathers, where constrained sampling can promote lateral coherence through a plane wave slope constraint. The third is a signal processing baseline based on coherence weighted spectral shaping, designed to enhance weak coherent LF energy already present in the airgun data. The corrected BiLSTM estimate improves the global 0.2–3 Hz correlation with TPS relative to the airgun input and recovers substantially more relative 2–4 Hz energy than the airgun data. The coherence weighted spectral shaping baseline still gives the strongest conservative 1–3 Hz enhancement, indicating that part of the apparent LF gain can be explained by stabilizing pre-existing coherent airgun energy. The lateral BiLSTM candidate is most useful in the 2–5 Hz near and mid offset windows, where it improves correlation and phase behavior relative to the tracewise BiLSTM, but amplitude calibration remains incomplete. The diffusion framework remains an ongoing direction for laterally coherent generative recovery, but current field results are status-only: they show laterally smooth LF energy and limited 3–5 Hz near/midoffset consistency, while 0.2–3 Hz correlation, spectral balance, and precursor/side-lobe behavior remain insufficient for a physical recovery claim. This study frames LF recovery as a feasibility and interpretability problem rather than only a spectral extension task. By comparing learned methods against a paired LF reference and a signal processing baseline, we aim to distinguish physical LF recovery from enhancement and from auxiliary LF continuations that may be useful mainly for future inversion workflows.

Neural Warp FWI: A Time-Shift Model Extension for Cycle-Skipping Mitigation
Hamad Alswaidan, Ivan Deiana, Biondo Biondi
We propose a neural time-warping extension for diving-wave full-waveform inversion (FWI) to mitigate cycle skipping and improve convergence from smooth initial models. The method applies bounded local time shifts to the synthetic data through a coordinate-based neural network, allowing waveform alignment to adapt during inversion while preserving the physical forward model. To separate alignment from velocity reconstruction, the warp parameters are optimized using an envelope least-squares objective, whereas the velocity model is updated using a waveform least-squares objective applied to the warped synthetic data. A bounded logit reparameterization is further used to enforce physically plausible velocity updates. Results demonstrate that the proposed approach improves waveform alignment, mitigates cycle-skipping, and converges more reliably than conventional least-squares FWI for diving-wave inversion.

General Full Waveform Inversion 
 

High-Resolution Elastic Full-Waveform Imaging for CO2 Storage at the CO2CRC Site
Haipeng Li and Biondo L. Biondi
We develop and apply a 2-D elastic full-waveform inversion (FWI) workflow for baseline subsurface characterization using strain-rate data recorded by a permanently cemented borehole distributed acoustic sensing (DAS) fiber-optic cable. The resulting high-resolution elastic models provide quantitative constraints on the pre-injection subsurface state, which is essential for reliable time-lapse interpretation and long-term CO2 storage monitoring. We apply this workflow to dense DAS vertical seismic profile (VSP) data from the CO2CRC Otway site in Victoria, Australia, where the borehole fiber-optic array provides dense spatial sampling near the CO2 injection interval. The workflow directly models and inverts the DAS strain-rate response for multiparameter estimation of Vp, Vs, and Ip. The final model, inverted with frequencies up to 100 Hz, resolves stratigraphic detail and the main velocity and impedance contrasts observed in the CRC-3 well. These results demonstrate that borehole DAS elastic FWI can provide a high-resolution baseline model for CO2 storage-site characterization. Such a baseline defines the reference state required for future time-lapse FWI.

Toward Practical Time-Lapse Full Waveform Inversion: A Unified and Scalable Framework for High-Resolution Monitoring Based on Devito
Cewen Liu, Antoine Guitton, Thomas Cullison, and Biondo Biondi
We investigate time-lapse full-waveform inversion (FWI) on the Opera dataset using a high-resolution acoustic inversion framework implemented with Devito. The Opera dataset poses severe challenges due to its non-inverse-crime setup, high-frequency data, and large-scale multi-shot acquisition, which impose immense computational and memory demands. To address these challenges, we develop a unified, high-performance computational workflow integrating optimized PML absorbing boundaries, MPI-based domain decomposition, checkpointing for memory reduction, and a variable-grid multiscale inversion strategy. Within this framework, we systematically evaluate parallel, double-difference, and joint inversion methods for time-lapse FWI. Our results show that double-difference inversion effectively suppresses background noise and delivers a cleaner, well-focused time-lapse image, while joint inversion can recover higherresolution changes but requires careful regularization. The experiments demonstrate that a combination of a robust multi-scale strategy and scalable computing is key to practical time-lapse FWI. This work provides an efficient and practical framework for large-scale, high-resolution time-lapse inversion on realistic datasets.

Scalable Uncertainty Quantification in Full Waveform Inversion: A Comparative Study of HMC, SVGD, and Variational Inference
Ivan Deiana, Hamad Alswaidan, Haipeng Li, Biondo Biondi
In this work, we benchmark three representative Bayesian strategies within a unified two stage workflow: a deterministic FullWaveform Inversion (FWI) warm start followed by posterior characterization using (i) the No-U-Turn Sampler (NUTS), an adaptive Hamiltonian Mont Carlo (HMC) variant used here as a reference, (ii) Stein Variational Gradient Descent (SVGD), and (iii) Stochastic Variational Inference (SVI) with a full covariance Gaussian guide. To make inference tractable, we use a Radial Basis Function (RBF) reparameterization that reduces the model space to 30 coefficients while preserving spatial structure. The experiment is built around a Vertical Seismic Profiling (VSP) geometry that creates strongly heterogeneous illumination, with parameters near the borehole being well constrained and parameters toward the model edges remaining weakly informed. Results on a 2D acoustic checkerboard test show that the posterior behavior is controlled not only by the inference algorithm, but also by the likelihood calibration and the deterministic warm start. After calibration, SVGD provides the most visually consistent posterior mean and ensemble behavior, SVI is the fastest method and gives the broadest credible intervals in this setting, and NUTS remains the most principled sampling strategy but it’s reliability depends on the finite computational budget used here. These results highlight that Bayesian FWI method comparisons must be interpreted through the combined effects of posterior geometry, likelihood scaling, initialization, and algorithmic hyperparameters.

Distributed Acoustic Sensing
 

Imaging and Monitoring the Transition Zone Using Ocean Breakers as Sources
Haipeng Li and Biondo L. Biondi
We present a passive seismic approach for imaging and monitoring nearshore transition zones using naturally occurring ocean breaking waves as repeatable, continuous seismic sources. Recorded with Distributed Acoustic Sensing (DAS), these wavefields provide dense illumination of the shallow subsurface in settings where active-source surveys are difficult to conduct and repeat. At Rockaway Beach, Oregon, we use a cross-shore DAS array to retrieve coherent surface waves from ocean-breaker-generated ambient noise through interferometric processing. We then apply wave-equation dispersion inversion to estimate a high-resolution 2-D shear-wave velocity model, which images the structural transition from the submerged foreshore to the subaerial backshore. Because ocean breaking waves are continuous in time, the same recordings can also be used for monitoring. Over multiple tidal cycles, we observe repeatable changes in seismic velocity and attenuation that are consistent with tidally driven variations in near-surface mechanical conditions. The method is most sensitive to the upper tens of meters, but this shallow sensitivity is directly relevant to transition-zone seismic studies: near-surface structure affects wave propagation, coupling, statics, and corrections required for deeper imaging. Thus, shallow characterization provides both a target in its own right and an important constraint for imaging deeper structures. Although demonstrated here with DAS, the approach can also be applied with nodal arrays, offering a practical route toward repeated seismic imaging and monitoring in coastal environments.

Modeling Strain and Strain Rate for First-Order Acoustic and Elastic Wavefields Using Devito
Thomas Cullison and Cewen Liu
This report explores the feasibility of deriving volumetric and axial strain to simulate Distributed Acoustic Sensing (DAS) data in an acoustic medium, including projecting the strain onto a curve representing a fiber cable, and validates the results by comparison with an elastic formulation. Both formulations are implemented as first-order coupled PDEs in Devito, and the acoustic results match the elastic results to near machine-epsilon precision. A related secondary thread explores whether agent-driven development workflows, guided by structured skills, can yield accurate, reproducible outcomes when building a notebook and supporting code to compute DAS-related strain on a curve (a ring). The agent-driven results appear reasonable but are not yet sufficient, indicating that their correct use may require more advanced experience or that further development and improvement of the agent ecosystem are needed.

A Consistent Acoustic Framework for Distributed Acoustic Sensing Modeling and Inversion
Cewen Liu, Thomas Cullison, Antoine Guitton, and Biondo Biondi
We develop a consistent modeling and inversion framework for Distributed Acoustic Sensing (DAS) data within the second-order acoustic wave equation using Devito. Starting from the acoustic formulation, we derive a pressure-based DAS forward operator that enables the computation of strain-rate measurements without explicitly solving for particle velocity. We further establish the connection between the proposed formulation and the conventional first-order (velocity-based) approach, and demonstrate their consistency. We incorporate gauge-length effects into the modeling operator to account for the finite spatial averaging inherent in DAS measurements. Based on the derived forward operator, we construct the corresponding adjoint formulation and compute gradients for FWI within the same acoustic framework. The proposed approach is validated through many numerical experiments on two-dimensional synthetic models, including forward comparisons and gradient verification tests. The results confirm the correctness and consistency of the formulation, providing a practical and scalable foundation for incorporating DAS data into acoustic FWI workflows.

Minimum-Effort DAS Cross-Correlation
Benz Poobua, Haipeng Li, and Biondo L. Biondi
We present an optimized, memory-efficient processing pipeline for passive seismic interferometry that directly addresses the computational waste of conventional full-lag Fast Fourier Transform (FFT) cross-correlation. While standard frequency-domain methods inherently compute the entire correlation space, our workflow leverages a block-by-block spectral accumulation algorithm to strictly target geophysically meaningful short-lag regimes (target lag ≪ correlation window). We benchmark this approach on a CPU-only execution platform across three distinct Distributed Acoustic Sensing (DAS) environments: an urban array, an offshore marine cable, and a civil infrastructure bridge deployment. Across all datasets, the algorithm maintains absolute numerical fidelity near single-precision machine epsilon (10−7 to 10−8), preserving exact phase and amplitude characteristics without spectral distortion. Computational profiling demonstrates decisive performance gains, accelerating pure cross-correlation throughput by a factor of 2 within operational short-lag windows. By mapping precise algorithmic limits—demonstrating that the block-wise method outperforms conventional global FFTs up to a 3.0 s lag for urban DAS and a 16.0 s lag for offshore DAS, while transitioning to a highly stable, persistently advantageous runtime plateau for high-frequency bridge assessments-we demonstrate that this formulation substantially mitigates the dominant mathematical cost. On the CPU-only platform used here, the cross-correlation kernel remains the single largest contribution to per-file runtime; halving its cost at every operationally relevant short-lag setting therefore yields a directly observable end-to-end acceleration of the ambient-noise interferometry pipeline, with pre-FFT preprocessing emerging as the compute-bound secondary cost.

Software, Algorithms, and Machine Learning
 

SubsurfaceGen: A Dataset for Field-Scale Earth Models and Seismic Data with applications to neural operator wavefield prediction and interpolation
Joseph Stitt, Pratik Rathore, Madeleine Udell, Ching-Yao Lai
Full-waveform inversion (FWI) is the gold standard for subsurface imaging, with applications from carbon sequestration to energy and mineral exploration to earthquake hazard assessment. Machine-learning approaches to FWI need field-scale, geologically diverse, and physically realistic training data, but existing resources such as Marmousi, SEAM, and OpenFWI fall short on spatial extent, temporal extent, geological diversity, and physical realism. We address these limitations with SubsurfaceGen, a GPUaccelerated procedural generator for 3D velocity models and seismic data. Alongside SubsurfaceGen we release a paired dataset of 4,276 2D velocity slices, 5 s acoustic wavefields, and 8 s shot-gather cubes drawn from 42 realistic, field-scale 3D velocity models, each spanning 10km°ø10km laterally and 6.19km deep at 10m resolution. The dataset covers six geological settings (four built with SubsurfaceGen and two drawn from prior sources) relevant for carbon sequestration and hydrocarbon exploration. We use the dataset to evaluate two neural-operator architectures (TFNO, DPOT) on wavefield prediction and three encoder–decoders (CNN, Transformer, InversionNet) on end-to-end velocity inversion, holding out one geological setting for out-of-distribution testing. A second wavefield-prediction experiment frames neural-operator interpolation as a candidate replacement for Revolve-style optimal checkpointing in the FWI adjoint pass; we discuss what the current 20-frame anchor configuration shows and what the natural production form (a two-frame momentum anchor on each side) would unlock for 3D.

Devito at SEP: Toward an End-to-End Seismic Processing Framework
Thomas Cullison, Joe Stitt, and Cewen Liu
We report progress toward developing a user-friendly, general-purpose package for Devito-based seismic modeling and inversion at SEP. Two frameworks were explored in parallel. One framework was developed to support acoustic full-waveform inversion (FWI), time-lapse FWI, and distributed acoustic sensing (DAS) modeling and inversion in two dimensions. The other framework, SEPDevito, was developed in collaboration with LLM agents to encapsulate the DevitoPro acoustic operators, to integrate the PySolver optimization library for FWI in two and three dimensions, and to incorporate a diffusion neural network regularizer. SEPDevito is the more general of the two frameworks and is the focus of our continued development.

A Readable and Compiler-Accelerated PyTorch Framework for Elastic Full-Waveform Inversion Prototyping
Ivan Deiana and Giacomo Roncoroni
We present a PyTorch-based framework for 2D isotropic elastic wave propagation and full-waveform inversion (FWI) prototyping. The implementation follows a staggeredgrid velocity-stress finite-difference formulation, with configurable stencil order, explicit parameter staggering, directional source injection, receiver sampling of particle velocities and pressure-like stress combinations, and hand-derived adjoint operators for gradient computation. The code is written to make the numerical steps visible: finite-difference derivatives, stress and velocity updates, damping terms, source terms, wavefield storage, and adjoint correlations remain close to the mathematics. The main goal is not to replace mature finite-difference domain-specific languages or production frameworks. Instead, the goal is to provide a research code that is easy to read, modify, validate, and still fast enough for meaningful experiments. PyTorch is used as the numerical backend because it gives a single programming model for CPU, CUDA, ROCm, and Apple MPS execution, while also exposing automatic differentiation, optimizer tools, distributed execution, and the torch.compile compiler stack. On a Tesla V100 benchmark, the compiled custom propagator is faster than the tested Deepwave CUDA elastic configuration for grids of 20002–60002, reaching about 3.0°ø– 3.5°ø speedup in this setting. On a MacBook Pro, the same PyTorch code runs on MPS and gives a practical laptop-scale accelerator path, with a 60002 forward run taking about 25 s and using about 2.5 GB of MPS allocated memory. The current implementation should be read as a proof of concept and a methodological platform. It already supports adjoint and finite-difference validation, Deepwave comparison, MPS/CUDA/CPU benchmarking, and an initial custom-gradient inversion loop. Natural next steps include a stress-free surface, broader boundary-condition options, 3D propagation, cleaner optimization abstractions, more systematic multi-GPU runs, and optional Triton or custom kernels where PyTorch’s generated kernels are not yet enough.