DualTCN: A Physics-Constrained Temporal Convolutional Network for 2 Time-Domain Marine CSEM Inversion

Abstract: DualTCN is the first deep-learning framework for inverting time-domain marine controlled-source electromagnetic (MCSEM) transient data. Moving away from traditional subsurface discretization, the framework regresses four earth-model parameters -- $σ_1$, $σ_2$, $d_1$, $d_2$ -- and reconstructs conductivity-depth profiles using a differentiable soft-step decoder. The optimized architecture (379K parameters) features a Temporal Convolutional Network (TCN) encoder paired with a late-time branch and an auxiliary seafloor-depth head. This design achieves a 25.3\% loss reduction over baseline models, with high predictive accuracy ($R² = 0.898$ for $σ_2$) and an inversion speed of 3.5~ms per sample on an A100 GPU. The framework demonstrates high robustness to noise through curriculum-based amplitude augmentation, maintaining a mean $\bar{R}<sup>2$ of 0.858 at $\pm2\%$ random amplitude error, compared to $0.363$ without augmentation. DualTCN generalizes effectively to three-layer extensions (seawater/resistive layer/basement), accurately resolving basement conductivity ($R² \approx 0.88$), though thin-layer resolution remains a physical limitation ($R² \approx 0.23$). In comparative benchmarks, DualTCN significantly outperforms traditional local optimization methods like Levenberg-Marquardt and L-BFGS-B, yielding a mean $\bar{R}² = 0.877$ versus 0.129-0.439 for multi-start baselines, while operating at up to 21,000$\times$ lower computational cost. Finally, the framework incorporates uncertainty quantification via Monte Carlo (MC) Dropout. While well-calibrated for $σ_1$ (PICP90 = 0.944), inherent signal limitations at short offsets (200m) lead to under-coverage for $d_2$ (PICP90 = 0.572), which can be mitigated through post-hoc temperature scaling or split conformal prediction.