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OpenFWI: Large-Scale Multi-Structural Benchmark Datasets for Seismic Full Waveform Inversion

Chengyuan Deng, Shihang Feng, Hanchen Wang, Xitong Zhang, Peng Jin, Yinan Feng, Qili Zeng, Yinpeng Chen, Youzuo Lin

arXiv:2111.02926v6cs.LGeess.SP

TL;DR

Data-driven FWI needs public datasets to support fair comparisons, but existing seismic datasets have not been released publicly. OpenFWI contributes 12 varied datasets and benchmarks deep learning methods; the benchmarks show promising results on some datasets, while others need further improvement.

  • Problem

    Existing seismic datasets for data-driven FWI have not been released publicly, making fair comparisons among methods difficult.

    Source: §1 · p. 2

  • Method

    OpenFWI provides 12 open-source datasets across 2D and 3D scenarios and benchmarks four deep learning methods, including supervised and unsupervised approaches.

    Source: §1 · pp. 2–3, §4.1 · p. 5

  • Results

    Benchmarks show promising results on some datasets, while the rest may need further improvement.

    Source: §7 · p. 10

  • Takeaways & Limitations

    OpenFWI provides a baseline for future work and supports studies of complexity, generalization, and uncertainty quantification.

    Source: §1 · p. 3

    Existing methods show non-negligible generalization degradation, related to the complexity of target-dataset subsurface structures.

    Source: §1 · p. 3, §6.1 · p. 10

Abstract

from arXiv · show

Full waveform inversion (FWI) is widely used in geophysics to reconstruct high-resolution velocity maps from seismic data. The recent success of data-driven FWI methods results in a rapidly increasing demand for open datasets to serve the geophysics community. We present OpenFWI, a collection of large-scale multi-structural benchmark datasets, to facilitate diversified, rigorous, and reproducible research on FWI. In particular, OpenFWI consists of 12 datasets (2.1TB in total) synthesized from multiple sources. It encompasses diverse domains in geophysics (interface, fault, CO2 reservoir, etc.), covers different geological subsurface structures (flat, curve, etc.), and contains various amounts of data samples (2K - 67K). It also includes a dataset for 3D FWI. Moreover, we use OpenFWI to perform benchmarking over four deep learning methods, covering both supervised and unsupervised learning regimes. Along with the benchmarks, we implement additional experiments, including physics-driven methods, complexity analysis, generalization study, uncertainty quantification, and so on, to sharpen our understanding of datasets and methods. The studies either provide valuable insights into the datasets and the performance, or uncover their current limitations. We hope OpenFWI supports prospective research on FWI and inspires future open-source efforts on AI for science. All datasets and related information can be accessed through our website at https://openfwi-lanl.github.io/

1 Introduction

FWI reconstructs subsurface velocity structures from seismic data, but data-driven methods lack large public datasets for fair comparison. OpenFWI introduces an open, multi-structural collection and benchmarks representative methods, while its studies identify generalization degradation related to target-structure complexity.

1 Introduction

  • OpenFWI is an open-access collection of 12 seismic FWI datasets spanning 2D and 3D scenarios and multiple geological structures.The paper presents it as the first large-scale collection of its kind, based on the authors’ knowledge.Source: §1 · p. 2
  • The collection spans dataset scales: its smallest 2D dataset has 15K samples, its largest has 60K, and its 3D dataset occupies 1.4TB.Four 2D datasets each occupy 43GB and support training without massive computational power.Source: §1 · p. 2
  • OpenFWI supports both 2D and 3D FWI across domains including time-lapse imaging, carbon sequestration, and geologic fault detection.Its subsurface structures range from interfaces and faults to CO2 storage and natural-image-derived structures.Source: §1 · p. 3
  • The benchmarks evaluate InversionNet, VelocityGAN, and UPFWI on 2D datasets and InversionNet3D on the 3D Kimberlina-V1 dataset.The authors position these results as a baseline for future work.Source: §1 · p. 3
  • Existing data-driven FWI methods show non-negligible generalization degradation, related to the complexity of target-dataset subsurface structures.The paper also identifies high computation, cycle-skipping, and ill-posedness as complications of physics-driven approaches.Source: §1 · pp. 1, 3

2 Seismic FWI and Forward Modeling

The paper frames acoustic forward modeling as calculating pressure from a velocity map under a governing wave equation. Data-driven FWI uses neural networks to learn the inverse mapping from seismic data to velocity.

2 Seismic FWI and Forward Modeling

  • Forward modeling calculates the pressure field from the velocity map using the acoustic wave equation, with the source term given for controlled-source methods.The paper denotes the forward problem as p = f(c).Source: §2 · p. 4
  • The velocity map depends on spatial location, while pressure and source also depend on time.The passage defines c as velocity, p as pressure, and s as source.Source: §2 · p. 4
  • Data-driven FWI uses neural networks to learn the inverse mapping from seismic data to a velocity map.The passage expresses this inverse as c = f^-1(p).Source: §2 · p. 4

3 OPENFWI Datasets and Domain Interests

OpenFWI’s 12 datasets cover diverse subsurface structures and geophysical domains, organized into four dataset families. Their designs address applications including interfaces, faults, field-data diversity, CO2 storage, and 3D seismic techniques.

3 OPENFWI Datasets and Domain Interests

  • OpenFWI contains 11 2D datasets and one 3D dataset, grouped into Vel, Fault, Style, and Kimberlina families.The first three families each have easy (A) and hard (B) versions based on subsurface-structure complexity.Source: §3 · p. 4
  • Vel Family provides flat and curved layers for interface detection, while Fault Family represents rock-layer discontinuities for fault identification.Fault Family’s version B has more discontinuities and more severe velocity changes than version A.Source: §3 · p. 4
  • Style Family derives velocity maps from diverse natural images to represent field-data diversity; version B has higher-resolution maps than version A.Version A maps are Gaussian-smoothed, and their seismic data contain fewer events.Source: §3 · p. 4
  • Kimberlina-CO2 represents supercritical CO2 plume migration over 200 years and can support leakage detection and measurement.The datasets are simulated with high fidelity through a geologic carbon sequestration reservoir.Source: §3 · p. 4
  • 3D Kimberlina-V1 is presented as the first large-scale public 3D FWI dataset, with high-resolution velocity maps and seismic data.It is generated by multiple institutions and designed for 3D seismic technique development, not only FWI.Source: §3 · p. 4
  • OpenFWI’s velocity maps come from mathematical functions, natural images, and geological reservoirs.The paper says these sources enhance the maps’ diversity and generality.Source: §3 · p. 4

4 OPENFWI Benchmarks

OpenFWI benchmarks three deep-learning methods for 2D FWI and InversionNet3D for 3D FWI, reporting baseline inversion performance. Across 2D datasets, VelocityGAN slightly outperforms InversionNet on most datasets, while harder datasets leave room for improvement.

4.1 Deep Learning Methods for FWI

  • The benchmark covers InversionNet, VelocityGAN, and unsupervised UPFWI for 2D FWI, plus InversionNet3D for 3D FWI.InversionNet3D uses group convolution and partially reversible layers to address memory footprint and computational efficiency challenges in 3D inversion.Source: §4.1 · p. 5

4.2 Inversion Benchmarks

  • The 2D benchmark reports MAE, RMSE, and SSIM, and provides training-time estimates across OPENFWI datasets.UPFWI and InversionNet3D training occupied 32 GPUs; the other methods used a single GPU.Source: §4.2 · p. 5, Table 5 · p. 6

4.2.1 2D FWI Benchmarks

  • VelocityGAN slightly outperforms InversionNet on most 2D datasets, while UPFWI trails the supervised methods slightly and difficult datasets leave room for improvement.UPFWI is not evaluated on Kimberlina-CO2 because of its high computational cost; VelocityGAN takes much more training time to achieve better results than InversionNet.Source: §4.2.1 · p. 6, Table 4 · p. 6
  • All three 2D methods perform well on simple datasets such as FlatVel-A and FlatFault-A.Figure 3 illustrates both successful and less promising InversionNet velocity-map predictions alongside ground truth.Source: §4.2.1 · p. 6, Figure 3 · p. 7

4.2.2 3D FWI Benchmarks

  • Compared with ℓ1 loss, ℓ2 loss degrades SSIM by 3% on the 3D Kimberlina-V1 benchmark.The study reports InversionNet3D performance for this dataset, which previously had only that model's performance reported.Source: §4.2.2 · p. 7, Table 6 · p. 7

5 Ablation Study

The ablation studies examine velocity-map complexity, generalization, and uncertainty, and report that generalizability limitations are closely related to subsurface complexity. Additional experiments probe robustness, method comparisons, and dataset selection.

5 Ablation Study

  • The ablation studies include complexity analysis, generalization tests, and uncertainty quantification, and identify generalizability as closely related to subsurface complexity.Other experiments include robustness testing, comparisons between physics-driven and data-driven methods, and real-scenario dataset selection.Source: §5 · p. 7, §5.4 · p. 9

5.1 Velocity Map Complexity Analysis

  • In the Vel and Fault families, inversion performance is negatively related to velocity-map complexity across three metrics and three 2D methods.The study uses spatial information, gradient sparsity index, and Shannon entropy; the reported relationship covers eight datasets.Source: §5.1 · p. 8, Figure 5 · p. 8

5.2 Generalization Study

  • Within dataset families, generalization from harder datasets to easier ones is more promising; across domains, performance drops as target complexity increases.Datasets labeled A have higher graph degree than those labeled B, while Style-B has no edges to datasets in other families.Source: §5.2 · pp. 8–9, Figure 6 · p. 8

5.3 Uncertainty Quantification

  • InversionNet uncertainty on CurveVel-A is higher at boundaries, rises with noise, and is much higher under cross-dataset testing than same-dataset testing.The authors interpret the boundary pattern as indicating more sensitive predictions around boundaries, and the cross-dataset pattern as indicating increased uncertainty under domain shifts.Source: §5.3 · p. 9, Figure 7 · p. 9

5.4 Additional Experiments

  • Models trained on clean 2D data degrade on noisy seismic data, and InversionNet is the most noise-sensitive model.Data-driven methods have better inversion results by a large margin and are faster when the training-to-test sample ratio is below 62; 2D-slice results are comparable to InversionNet3D, which slightly performs better (0.9652 compared to 0.9838).Source: §5.4 · p. 9

6 Discussion

The discussion identifies four challenges for data-driven FWI: complex velocity maps, generalization, computational efficiency, and passive imaging. It also describes OPENFWI’s intended role in evaluation, research, and future development.

6.1 Future Challenges

  • Complex velocity maps degrade performance, motivating more advanced methods, especially methods that do not rely on more data.The discussion presents this as a future challenge for data-driven FWI.Source: §6.1 · p. 10
  • Existing methods show non-negligible generalization degradation, while field data usually differ from training data.The paper identifies robustness across domains as important for field applications.Source: §6.1 · p. 10
  • UPFWI and InversionNet3D have high computational costs; InversionNet3D’s down-sampled training data may lose information and affect performance.The paper calls for more efficient algorithms.Source: §6.1 · p. 10
  • The benchmarks mainly address controlled, active-source imaging, leaving passive seismic imaging for further study.The paper reports a preliminary passive-data event-picking test as a starting point for future work.Source: §6.1 · p. 10

6.2 Broader Impact

  • OPENFWI is intended to support unified evaluation, further improvement, and reproducibility, while helping domain experts and machine-learning researchers engage with data-driven FWI.The paper also anticipates maintaining the platform through new datasets and benchmarks, workshops, and data competitions.Source: §6.2 · p. 10
  • The authors hope OPENFWI will shed light on data challenges in scientific machine learning, including sparse direct measurements, unbalanced distributions, and noise.They place this effort in the context of geoscience and other science-rich, data-starved fields.Source: §6.2 · p. 10

7 Conclusion

The paper presents OPENFWI as an open-source platform with twelve datasets and benchmarks for four deep-learning methods. It also documents the platform’s data generation, dataset formats, network architectures, training configurations, and supplementary analyses.

7 Conclusion

  • OPENFWI provides twelve datasets and benchmarks on four deep-learning methods, spanning varied scales, geophysical domains, and simulated subsurface structures.The conclusion also reports complexity analysis, generalization study, and uncertainty quantification; benchmark results are promising on some datasets, while others need further improvement.Source: §7 · p. 10

Appendix arrangement:

  • The supplementary appendices cover uncertainty quantification, robustness, physics-driven comparisons, 2D-slice evaluation, real-world testing, passive inference, and current dataset limitations.They also provide complexity metrics and further generalization analyses.Source: Appendix arrangement · p. 15

A OPENFWI Public Resources and Licenses

  • Appendices A–A describe public resources, licenses, data and code availability, and the resources supporting benchmark reproducibility.The data use a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 license; code is released under OSS and BSD-3 licenses.Source: A OPENFWI Public Resources and Licenses · p. 15

B Velocity Map Generation; C Seismic Forward Modeling Details

  • Appendices B–C describe velocity-map generation from mathematical, natural-image, and reservoir priors, followed by seismic-data generation through forward modeling.Forward modeling uses finite differences, an absorbing boundary condition, and a Ricker-wavelet source.Source: B Velocity Map Generation · pp. 15–16

D OPENFWI Datasets: Illustration, Format, Naming, Loading

E OPENFWI Benchmarks: Network Architecture

  • Appendices E–E.3 describe the 2D benchmark architectures: InversionNet’s encoder-decoder CNN, VelocityGAN’s InversionNet-based generator and CNN discriminator, and UPFWI’s unsupervised encoder-decoder.UPFWI minimizes pixel-wise and perceptual differences between input and reconstructed seismic data.Source: E OPENFWI Benchmarks: Network… · p. 19, §E.1 · p. 19, §E.2 · p. 21

E.4 InversionNet3D

  • Appendix E.4 presents InversionNet3D, a 13-layer-per-part 3D encoder-decoder using group convolution and invertible layers to reduce memory use and computational complexity.The baseline has 14.42 million parameters and uses 9.93GB of memory at batch size one.Source: §E.4 · p. 21

F OPENFWI Benchmarks: Training Configurations

  • Appendix F records benchmark training configurations, including optimizers, learning rates, batch sizes, epochs, and data normalization.The experiments ran on NVIDIA Tesla P100 GPUs; configurations differ across methods and datasets.Source: F OPENFWI Benchmarks: Training… · pp. 21–22

G Illustration of Inversion Results

Across the illustrated benchmarks, VelocityGAN usually gives the best inversion results but takes longer to train. UPFWI is sensitive to layer boundaries, and its deep-region inversions are difficult under limited seismic illumination.

G Illustration of Inversion Results

  • VelocityGAN usually provides the best results, but requires more training time.Figure 14 compares ground truth with InversionNet, VelocityGAN, and UPFWI results across FlatVel-A, FlatVel-B, CurveVel-A, and CurveVel-B.Source: G Illustration of Inversion Results · p. 22, Figure 14 · p. 22
  • UPFWI is sensitive to layer boundaries because its loss compares predicted and observed seismic data, whose reflections arise from those boundaries.The paper also notes that limited seismic illumination makes deep velocity-map regions hard to invert with UPFWI.Source: G Illustration of Inversion Results · p. 22

H Velocity Map Complexity

The paper measures velocity-map complexity with three metrics, finding that hard versions and curved structures are more complex, while no metric provides a coherent evaluation across all datasets. Generalization degrades across domains, and InversionNet uncertainty is higher near boundaries and under domain shifts.

H Velocity Map Complexity

  • Spatial information, gradient sparsity index, and Shannon entropy are used to measure velocity-map complexity.The paper describes spatial information as an estimate of border magnitude obtained with the Sobel edge-detection operator.Source: H Velocity Map Complexity · pp. 22–24
  • Version B datasets have higher complexity than version A, and curved structures are more complex than their flat counterparts.The three complexity metrics are mostly consistent within each dataset, but none provides a coherent evaluation across all datasets.Source: H Velocity Map Complexity · pp. 24–25
  • None of the three complexity metrics provides a coherent evaluation across all datasets.Style-family detail aligns with Shannon entropy, but the same ordering cannot be inferred from spatial information.Source: H Velocity Map Complexity · p. 25

I Generalization Test

  • VelocityGAN and UPFWI generalize better than InversionNet, while cross-family tests generally have larger values than within-family tests.InversionNet’s larger batch size may degrade its generalization ability.Source: I Generalization Test · p. 25

J Uncertainty Quantification

K Robustness Test

The robustness tests show that noise sensitivity differs across models and dimensions: 2D InversionNets are most sensitive, while 3D InversionNet3D is robust to Gaussian noise under the reported metrics. Training with noise improves robustness at high test-noise levels, though results are mixed at lower levels.

K Robustness Test

  • InversionNets trained with either ℓ1 or ℓ2 loss are the most sensitive to noise across the 2D models tested.Table 14 averages performance across 2D datasets, excluding Kimberlina-CO2.Source: K Robustness Test · p. 27, Table 14 · p. 28
  • Both ℓ1- and ℓ2-trained InversionNet3D models are robust to Gaussian noise; MAE/RMSE increase by 175% on average, while SSIM decreases by at most 1.76%.The authors attribute the small SSIM decrease partly to unchanged background velocity receiving more weight than the reservoir region.Source: K Robustness Test · p. 27, Table 14 · p. 28
  • Noisy training improves all three models’ robustness at high test-noise levels, but results are mixed when test noise is lower than training noise.At lower test-noise levels, InversionNet improves over clean-data training, while VelocityGAN and UPFWI show a slight performance drop.Source: K Robustness Test · p. 28, Figure 21 · p. 28

L Comparison with Physics-driven Methods

Physics-driven inversion depends strongly on initial-map quality and can produce artifacts, whereas data-driven methods are faster at the train/test ratios typical of OPENFWI. For 3D Kimberlina-V1, physics-driven inversion also faces convergence and acquisition-footprint problems under the tested initializations.

L Comparison with Physics-driven Methods

  • The physics-driven tests use six low-pass cutoff frequencies and three initial maps, with ℓ2 loss and conjugate-gradient updates.The selected initial maps are homogeneous, linearly increasing with depth, and smoothed ground-truth maps.Source: L Comparison with Physics-driven Methods · pp. 28–29
  • Physics-driven results contain more artifacts than data-driven results and depend strongly on initial-map quality; higher-SSIM initial maps yield higher-SSIM inversions.For 3D Kimberlina-V1, homogeneous and linear initializations make the loss hard to converge, while smoothed initialization is affected by acquisition footprint and yields surface artifacts.Source: L Comparison with Physics-driven Methods · p. 29, Figure 22 · p. 30, Figure 23 · p. 30
  • At train/test ratios below 62, all three data-driven methods are faster, and at the typical OPENFWI ratio of about 10 they are six times faster than physics-driven methods.The comparison includes training time for data-driven methods and test-set computation time for physics-driven methods.Source: L Comparison with Physics-driven Methods · p. 29
  • For 3D Kimberlina-V1, physics-driven total computation time is 475 times that of Vel Family, compared with 40 times for InversionNet.The authors conclude that data-driven methods have computational advantages on large velocity maps.Source: L Comparison with Physics-driven Methods · p. 29

M Comparison between InversionNet and InversionNet3D

InversionNet trained on 2D slices can achieve performance comparable to InversionNet3D, but returns only slices rather than a full volume. The paper also demonstrates dataset selection for pseudo-real data, adapts Style-B for noisy P-wave arrival picking, and notes that unified datasets differ slightly from earlier versions.

M Comparison between InversionNet and InversionNet3D

  • InversionNet trained on 2D slices performs comparably to InversionNet3D, with relative MAE/RMSE and SSIM results varying by training loss and slice-generation strategy.The 3D-simulation slice experiment uses 18K pairs and the 2D-simulation experiment uses 73K pairs; 2D training returns only slices, so interpolation may be needed to obtain a full volume.Source: M Comparison between InversionNet and… · pp. 31, 32, 34, Table 18 · p. 34

N Test Strategy in Real-world Situation

  • For pseudo-real Gulf of Mexico data, the lowest seismic-loss models came from FlatVel-B with ℓ1 training and Style-A with ℓ2 training, and both produced reasonably good velocity maps.The test simulates seismic data from a real velocity map and selects among 20 models trained across ten datasets.Source: N Test Strategy in Real-world Situation · p. 34, Figure 28 · p. 35

O Passive Picking

  • An InversionNet trained on noisy Style-B traces with manually added P-wave arrival labels accurately recognizes arrivals in the reported test.The converted data use strong Gaussian noise with σ = 5 × 10^-3.Source: O Passive Picking · p. 35, Figure 29 · p. 35

P.1 Past Version

  • OPENFWI unified earlier Vel, Fault, and Style datasets in data size and forward-modeling parameters, so results differ slightly from prior reports.The authors state future comparisons should use the OPENFWI benchmarks.Source: §P.1 · p. 36

P.2 Limitations

OpenFWI’s synthesized velocity maps are constrained by the limited prior knowledge used to generate them, which limits their representativeness and variability. The authors also identify boundaries in benchmark coverage and validation.

P.2 Limitations

  • Synthesizing all datasets from a few sources of prior knowledge inherently limits the representativeness and variability of generated velocity maps.The sources include mathematical representations, natural images, and geological reservoirs.Source: §P.2 · p. 36
  • Some specific subsurface structures may not be covered, and field-data validation would provide further evaluation.The authors describe Style Family datasets as excellent candidates for field-data inversion in general cases.Source: §P.2 · p. 36
  • The 3D benchmark is nearly solitary because literature on 3D FWI is limited, and randomly selected channel evaluation is not ubiquitous.Source: §P.2 · p. 36
  • Comparisons may omit recent data-driven FWI methods when their associated code is unavailable.Source: §P.2 · p. 36
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