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Auto-Linear Phenomenon in Subsurface Imaging
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Proposes Auto-Linear, which self-supervises separate MAE encoders and decoders for seismic data and velocity maps and links their frozen latents with a small trained linear converter, for FWI and EM inversion.
Problem
Full waveform inversion (FWI) is usually treated as image-to-image translation with jointly trained encoder-decoder networks that need abundant paired seismic/velocity data; prior decoupled method InvLINT still needs paired data for its decoder and performs poorly on complex datasets and under noise
Approach
Independently self-supervised MAEs for seismic data and velocity maps yield latent spaces that are automatically linearly correlated, so only a low-rank linear converter between frozen encoder and decoder needs paired supervision, enabling both forward and inverse modeling.
Key results
- Auto-Linear achieves MAE of 0.0081 on FlatVel-A vs 0.0131 for InversionNet and 0.0532 for InvLINT, and comparable results to InversionNet overall with 12.3M vs 24.4M parameters.
- On Kimberlina-Reservoir EM inversion, Auto-Linear reaches MAE 0.00438 vs 0.00703 for InvLINT and 0.01330 for InversionNet.
- Under Gaussian noise (sigma^2=5e-4) on CurveFault-A, Auto-Linear MAE is 0.1093 vs 0.4496 for InversionNet, and it outperforms InversionNet for sigma^2 >= 5e-5.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Auto-Linear instead of InversionNet for forward modeling | Fault Family forward modeling · FlatFault-A, FlatFault-B, CurveFault-A, and CurveFault-B | MAE: 0.0332 -> 0.0099; 0.0397 -> 0.0193; 0.0373 -> 0.0132; 0.0594 -> 0.0253 | Helped |
| Use Auto-Linear instead of InversionNet for EM inversion | Kimberlina-Reservoir · Kimberlina-Reservoir | MAE: 0.01330 -> 0.00438 | Helped |
| Use Auto-Linear instead of InvLINT | OpenFWI inverse modeling · CurveFault-A | MAE: 0.0853 -> 0.0277 | Helped |
| Use Auto-Linear instead of InversionNet | OpenFWI inverse modeling · CurveFault-A | MAE: 0.0260 -> 0.0277 | Hurt |
| Replace the linear converter with a two-layer MLP (ablation) | Auto-Linear · CurveFault-A | MAE: 0.0277 -> 0.0280 | Hurt |
| Replace the linear converter with a two-piece Maxout converter (ablation) | Auto-Linear · CurveFault-A | MAE: 0.0277 -> 0.0260 | Helped |
| Replace masked autoencoder pretraining with vanilla autoencoder pretraining (ablation) | Auto-Linear · CurveFault-A | MAE: 0.0277 -> 0.0614 | Hurt |
| Replace masked autoencoder pretraining with Masked FINOLA-B pretraining (ablation) | Auto-Linear · CurveFault-A | MAE: 0.0277 -> 0.0287 | No clear effect |
| Decrease linear converter bottleneck dimension from 128 to 32 (ablation) | Auto-Linear · CurveFault-A | MAE: 0.0277 -> 0.0304 | Hurt |
| Increase linear converter bottleneck dimension from 128 to 512 (ablation) | Auto-Linear · CurveFault-A | MAE: 0.0277 -> 0.0271 | Helped |
| Set encoder mask ratio to 0.5 instead of 0.75 (ablation) | Auto-Linear · CurveVel-A | MAE: 0.0738 -> 0.0785 | Hurt |
| Use 25Hz instead of 15Hz source wavelet (ablation) | Auto-Linear · CurveFault-A | MAE: 0.0277 -> 0.0181 | Helped |
Surprising findings
- Encoder and decoder pretrained on the Fault Family transfer to other datasets and sometimes beat models trained directly on those datasets, e.g., on simpler Vel Family datasets.
- A simple vanilla autoencoder (mask ratio 0) performs much worse on inversion (MAE 0.0614) than masked autoencoding (MAE 0.0277), even though its reconstruction errors are lower.
Limitations
- Requires paired seismic-velocity data to train the linear converter, and evaluation is only on simulated data with no real field data.
- Performs worse than InversionNet on several OpenFWI datasets (e.g., CurveVel-B, FlatFault-B, Style-A in MAE/MSE) and on the Marmousi downsample test, so it is not uniformly better.
- Forward-inverse cascade amplifies errors, and the elastic FWI extension is only preliminary.
Experimental setup
Datasets: OpenFWI (FlatVel-A/B, CurveVel-A/B, FlatFault-A/B, CurveFault-A/B, Style-A/B, Kimberlina-CO2) Kimberlina-Reservoir (EM) Marmousi (constructed slices) elastic FWI dataset
Benchmarks: OpenFWI Kimberlina-Reservoir Marmousi slice and downsample
Metrics: MAE MSE SSIM PSNR R^2
Baselines: InversionNet InvLINT Masked FINOLA-B vanilla autoencoder
Builds on: masked autoencoder InvLINT InversionNet OpenFWI
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