ADMM-Guided Physics-Informed Deep Learning for Two-Dimensional Acoustic Impedance Inversion with Reweighted ℓ1 Sparse Regularization

DEEPAK KUMAR , Jayant Nath Tripathi

Acoustic impedance inversion is ill-posed because post-stack seismic data are band-limited and noisy. Reweighted ℓ1 sparse inversion sharpens impedance boundaries but, applied trace by trace, ignores lateral geological continuity. We present a two-dimensional ADMM-guided physics-informed neural framework in which a reweighted ℓ1 ADMM estimate (after He et al., 2022) serves as a physics prior for a convolutional refinement network trained with a differentiable wavelet-convolution data term, reweighted ℓ1 sparsity, model proximity, and lateral smoothness. Three architectures (a 2D U-Net, a residual CNN, and an Attention ResUNet) are compared against two classical baselines: trace-wise reweighted ℓ1 and a stronger spatially-coupled 2D inversion with lateral total variation. On a controlled synthetic section and two geologically distinct Marmousi-2 crops, the networks markedly improve noisy-data reconstruction: the U-Net reduces RMSE by about 45% over trace-wise ADMM and, after transfer, by 44% on Marmousi-2 (a 5 dB SNR gain). The advantage is stable across five training seeds, persists against the spatially coupled baseline, and holds at every input-noise level under matched training. A wavelet-mismatch study identifies a deployment caveat: without retraining, the networks are only as reliable as the estimated wavelet, whereas the spatially coupled classical inversion degrades most gracefully.