SubsurfaceGen: Procedural Generation of Field-Scale Earth Models and Seismic Data

Technical Summary: SubsurfaceGen

Problem Statement
Full Waveform Inversion (FWI) is the standard method for subsurface imaging, critical for carbon sequestration verification, resource exploration, and hazard assessment. However, FWI involves solving high-dimensional, non-convex, PDE-constrained optimization problems that suffer from cycle skipping, sensitivity to initial models, and prohibitive computational costs. While machine learning (ML) offers promising alternatives—such as neural operators for accelerating PDE solves and encoder-decoders for direct inversion—progress is bottlenecked by a lack of suitable training data. Existing datasets (e.g., Marmousi, SEAM, OpenFWI) fail to simultaneously satisfy four critical criteria: field-scale spatial and temporal extent, geological diversity, physical realism, and extendability (the ability to generate new data on demand). Small-scale datasets do not capture the worsening of cycle skipping and illumination gaps at large scales, while static datasets cannot support studies on generalization across unseen geological settings.

Methodology
The authors introduce SubsurfaceGen, a GPU-accelerated procedural generator for 3D velocity models and corresponding seismic data. The system is built on PyTorch for model generation and Devito for seismic data generation.

1. Procedural Velocity Model Generation: SubsurfaceGen constructs velocity models by sequentially applying a catalog of eight geological modules to a homogeneous basement volume. These modules emulate real-world features:

   • Deposit: Adds stratified layers with interbeds (alternating velocity layers).
   • Squish: Warps layers to simulate basin-scale folding.
   • Fault: Applies listric and V-shaped fault deformations.
   • SaltSDT & SaltWedge: Generates irregular salt bodies and deforms surrounding sediments to create halokinetic sequences (onlap and drape geometries).
   • CarbonatePlatform: Builds asymmetric reef structures with distinct facies.
   • DeltaClinoformDeposit: Stacks clinoform-like bed surfaces to simulate deltaic geometries.
   • StructuralSmoother: Applies structure-oriented smoothing to suppress numerical artifacts while preserving geological discontinuities.
     The generation process is deterministic based on parameter vectors but allows for stochastic sampling to create diverse realizations within a specific geological setting.

2. Seismic Data Generation: For each 3D velocity model, SubsurfaceGen extracts 2D slices and solves the 2D acoustic wave equation using Devito. It generates paired data consisting of:

   • Wavefields: Full wavefield propagation over 5 seconds.
   • Shot Gathers: 8-second recordings from 64 sources and 1000 receivers, simulating marine streamer acquisition.
     The system supports five different source bandwidths to facilitate multiscale training strategies.

3. Dataset Construction: The authors released a field-scale dataset on Hugging Face containing 4,276 2D velocity slices (10 m resolution, 10 km × 10 km lateral, 6.19 km depth) paired with wavefields and shot gathers. These are derived from 42 distinct 3D models spanning six geological settings: four generated by SubsurfaceGen (Penobscot, F3, Gulf of Mexico, Fault) and two from prior sources (SEAM, Salt Canopy). The Penobscot setting is held out as an out-of-distribution (OOD) test set.

Key Contributions

• SubsurfaceGen Software: A novel, open-source, GPU-accelerated tool that enables the procedural generation of geologically diverse, physically realistic, field-scale velocity models. It is the first open-source software to support the procedural generation of features like salt bodies, carbonate platforms, and clinoforms in a unified pipeline.
• Field-Scale Dataset: The release of a large-scale, paired dataset (velocity models + seismic data) that addresses the limitations of existing benchmarks. It provides the necessary spatial extent (10 km) and temporal depth (5–8 s) to study field-scale phenomena like cycle skipping and deep imaging.
• Benchmarking ML-based FWI: The paper demonstrates the utility of this dataset by evaluating two distinct ML tasks:
  • Wavefield Prediction: Training neural operators (TFNO, DPOT) to predict wavefields. The authors introduce a "chunked autoregressive rollout" strategy necessitated by the field-scale grid size and propose TFNO-interp, a variant using optimal checkpointing principles to reduce error drift over long horizons.
  • End-to-End Inversion: Training encoder-decoder networks (InversionNet, Transformer, CNN) to map shot gathers directly to velocity models. The dataset enables the first cross-geology generalization studies at field scale, revealing how different architectures handle distribution shifts.

Results

• Performance: SubsurfaceGen achieves a 7.2× to 26.8× speedup in velocity model generation on an NVIDIA A100 GPU compared to a 16-core CPU.
• Wavefield Prediction: Neural operators successfully track dominant wavefronts but exhibit error compounding over long time horizons (5 s). The TFNO-interp variant, which anchors predictions at intermediate time steps, reduced the L2 relative error in prediction gaps by approximately 6× compared to standard forward operators, demonstrating the value of the field-scale dataset in surfacing long-horizon failure modes.
• Inversion: Among the tested architectures, the 3D CNN outperformed the 2D InversionNet and Transformer in terms of RMSE and SSIM, particularly in capturing large-scale features like salt bodies and faults. However, all models struggled with fine-scale features. Crucially, the CNN showed a significant drop in performance on the OOD (Penobscot) set, whereas the Transformer maintained stable SSIM scores, highlighting architecture-dependent generalization capabilities.

Significance
The paper claims that SubsurfaceGen and its associated dataset democratize ML for seismic imaging by lowering the barrier to entry for researchers lacking proprietary data. It argues that the field-scale nature of the data is essential for uncovering failure modes (such as drift in autoregressive rollouts and generalization limits in inversion) that are invisible in small-scale datasets. The authors position this work as a foundation for future benchmarks and method development, cautioning that models trained on this synthetic data require further validation before real-world deployment. The work bridges the gap between theoretical ML advances and the practical, large-scale requirements of geophysical imaging.