Learning-Based Seismic Velocity Inversion with Synthetic and Field Data

The paper addresses the challenge of building accurate subsurface velocity models from seismic data, a critical step impacting seismic imaging and reservoir interpretation. Conventional velocity model-building methods (e.g., NMO, tomography, FWI) rely on linearized inversion and simplifying assumptions that struggle in areas with complex overburden (e.g., salt, basalts, karst), leading to suboptimal images. Deep learning offers a data-driven alternative capable of learning nonlinear mappings from seismograms to velocity models, but prior demonstrations have largely focused on synthetic data or field data in simpler regimes. This study investigates whether learning-based inversion can recover accurate velocity profiles from field-recorded seismograms in a complex Gulf of Mexico setting, quantifying the impact of training data source (field vs. synthetic) and data augmentation on performance, and examining how to bridge domain gaps when training on synthetic data.

The study situates itself within velocity model building and DL-based inverse problems. Classic methods (NMO analysis, tomographic inversion, FWI) are effective but limited by linearizations and assumptions, particularly in complex geology. DL has successfully addressed inverse problems across imaging domains and has seen adoption in geophysics. Prior DL work in seismic inversion primarily reported results with synthetic datasets or simple field cases. Bridging synthetic-to-real domain gaps has been recognized as necessary, with recommendations to incorporate more realistic physics (e.g., elastic effects, anisotropy, attenuation) and geological priors. This work extends prior efforts by rigorously applying DL to complex field data and systematically comparing field- vs. synthetic-trained models.

Data: The study uses an open-source 3D seismic dataset from the Tiber field (Gulf of Mexico) with a legacy velocity model that partially overlaps the seismic data. Field data were industry-preprocessed (denoising, deghosting, direct arrival removal, 5D interpolation). A representative shot gather has energy from 3–60 Hz. Problem formulation: Seismic experiment f maps a subsurface velocity model x to measured seismograms y via y = f(x) + ε. The inversion seeks x* ≈ f^-1(y) using a DL model g_θ, trained to minimize a loss L(x, g_θ(y)) over N labeled pairs. Network architecture: A purely convolutional encoder–decoder without skip connections or fully connected layers, totaling just over 6M parameters. The encoder uses 3D convolutions and pooling; the decoder uses 2D convolutions and upsampling. The model maps 3D seismic features to 2D velocity slices. Features and labels: Each input feature yi ∈ R^{64×128×256} is built from 64 adjacent shot gathers (shots spaced 125 m), 128 receivers (60 m spacing) and 256 time samples (24 ms sampling; window starting 1.5 s after recording; field data high-cut at 20 Hz). Output labels are 2D velocity models x ∈ R^{128×128}, representing a 17 km (x) by 12 km (z) area corresponding to the probed region. Data split: Spatial split by inline to mimic acquisition and avoid leakage due to overlap. Train inlines: 800–1000 (2679 shots; 1122 feature-label pairs). Validation: 1010–1020 (234 shots; 108 pairs). Test: 1030–1130 (1285 shots; 592 pairs), overlapping incomplete portions of the legacy model for partially labeled evaluation. Training datasets (features differ; labels are legacy model slices): - Dataset 1 (Field): Field Tiber shot gathers. - Dataset 2 (Acoustic): Synthetic gathers via acoustic wave equation with field acquisition parameters. - Dataset 3 (Elastic): Synthetic gathers via elastic wave equation. - Dataset 4 (Acoustic + sediment priors): Acoustic modeling with added sediment reflection events from geologic priors. - Dataset 5 (Elastic + sediment priors): Elastic modeling with added sediment reflection events. Synthetic data generation: Forward modeling uses field acquisition geometry. Acoustic modeling uses constant-density acoustic wave equation. Elastic modeling uses isotropic elastic equations; density derived via Gardner’s relation; constant Vs/Vp ratio assumed; hydrophone pressure approximated by sampling diagonal stress components. To address missing high-wavenumber reflectivity in the legacy model, a geologic model builder simulates stochastic sedimentary layering (velocities, densities, thickness, folding sampled from distributions) to add realistic reflectors above/within/below salt; multiple realizations mitigate overfitting and aim to span plausible field variability. Data augmentation: Applied to synthetic training features in various combinations—horizontal flip (counteracts sailing-direction bias), random bandpass (lowcut 3–9 Hz, highcut 14–20 Hz) to vary source wavelets, and 2D wave-propagation correction to address 2D modeling artifacts. A test-time augmentation (structure-oriented smoothing) is applied to field test data to reduce noise and partially bridge the synthetic–field gap. Training setup: All models share optimization settings—Adam optimizer, MSE loss, 80 epochs, learning rate 5e-5, batch size 24, trained on 4× NVIDIA V100 GPUs. Approximate training time ~75 s/epoch (~100 min per model), with GPU memory near 32 GB due to 3D features and deep convolutions. Evaluation: Threefold—(1) Quantitative: MSE, SSIM, and R^2 against available legacy-model regions in the test fold; (2) Qualitative: visual/geologic plausibility where the legacy model is absent; (3) Geophysical: Reverse Time Migration (2D RTM) using ensembled inline predictions as migration velocities to assess image coherence above/within/below salt. Ensemble regression aggregates per-feature predictions along inlines.

- Models trained on field data (Dataset 1) achieved the best overall performance across metrics, with the highest reported R^2 = 0.909 and superior MSE/SSIM compared to synthetic-trained models. Predictions were geologically plausible and yielded sharper, more coherent RTM images. - Synthetic-trained models are viable but underperform field-trained models unless the domain gap is reduced. Incorporating elastic physics improved performance versus acoustic modeling. Adding realistic sediment reflectors via geologic priors further improved accuracy for both acoustic and elastic datasets. - Representative R^2 scores for the standout models from each dataset (as reported): Field 0.909; Acoustic 0.558; Elastic 0.662; Acoustic+Sediment 0.761; Elastic+Sediment 0.860. - Example per-inline test metrics (illustrative from Figure 6) show low MSE and high SSIM for field- and elastic-trained models near the training region (e.g., inline 1040: Field MSE 0.089, SSIM 0.858; Elastic MSE 0.089, SSIM 0.870), while acoustic-trained models had higher MSE and lower SSIM (e.g., inline 1040: MSE 0.463, SSIM 0.716). Performance degrades with spatial distance from the training area (e.g., inline 1120 shows increased MSE and reduced SSIM across models). - Data augmentation effects are nuanced and sometimes inconsistent; however, augmentations were necessary to achieve the best synthetic-trained model performance (notably combining flipping, random bandpass, and wave-propagation corrections, with structure-oriented smoothing at test time). - Both field- and synthetic-trained models produced usable migration images with coherent reflections above, within, and below salt near the training region. Coherency decreased farther from training inlines, evidencing spatial generalization limits.

The study demonstrates that learning-based inversion can recover subsurface velocity models from field-recorded seismograms in a geologically complex Gulf of Mexico setting. Field-trained models excel by leveraging labeled real data, leading to strong quantitative agreement with legacy models and geologically plausible predictions that support coherent RTM imaging. When field labels are scarce, synthetic training is a viable alternative, provided the domain gap is minimized. Incorporating more realistic physics (elastic over acoustic) and geologic priors (sedimentary reflectors) materially improves synthetic-trained model performance. The results emphasize the importance of domain expertise in curating synthetic training data and suggest that organizations with archives of labeled field data can repurpose them to accelerate and reduce the cost of velocity model building. Spatial generalization diminishes with increasing distance from the training region, highlighting the need for diversified training coverage and augmentation strategies aligned with acquisition variability.

The work establishes the feasibility and advantages of deep learning for seismic velocity inversion in complex geologic settings. Models trained on field data deliver the best accuracy and imaging quality, while synthetic-trained models become competitive when enhanced with realistic physics and geologic priors. The approach demonstrates a practical path to leveraging existing labeled field datasets to accelerate industrial-scale workflows. Future directions include improved feature engineering to further close the synthetic–field gap, extending the approach to fully 3D data, and using more advanced wave equations (e.g., including anisotropy and attenuation) for synthetic data generation.

- Ground truth incompleteness: The legacy velocity model is incomplete in the test fold, restricting quantitative evaluation to overlapping regions and necessitating qualitative/geophysical assessments. - 2D output constraint: DL model outputs 2D slices, limiting geophysical validation to 2D RTM rather than full 3D imaging. - Synthetic parameter assumptions: Elastic modeling required assumptions (Gardner’s relation for density; constant Vs/Vp), which may introduce model mismatch. Anisotropy and attenuation were not explicitly modeled. - Domain gap: Despite improvements, residual discrepancies remain between synthetic and field data; test-time structural smoothing may bias comparisons toward synthetic-like characteristics. - Generalization: Performance decays with spatial distance from training inlines, indicating sensitivity to acquisition geometry and subsurface variability. - Computational constraints: Large 3D input tensors and deep networks push GPU memory limits, constraining batch sizes and training speed.