Total Generalized Variation regularization closes the gap between neural-eld and classical methods in seismic travel-time tomography
2026-05-11 • Machine Learning
Machine Learning
AI summaryⓘ
The authors introduce MIMIR, a new method to create smoother and more accurate 2D velocity maps from travel-time tomography data using neural networks. They replace traditional grid-based methods with a continuous neural network approach and use an advanced regularizer called second-order total generalized variation (TGV²) to improve stability and detail. Their tests show MIMIR matches or beats classical methods, especially in complex layered and fault-like scenarios, and outperforms total variation (TV) regularizers which tend to create blocky images. They conclude that choosing the right regularizer is more important than the network design itself. Also, their method runs quickly on normal computers.
travel-time tomographyFourier-feature neural networksecond-order total generalized variation (TGV²)total variation (TV)regularizervelocity fieldChambolle-Pock algorithmFMM-LSMRphysics-informed neural networksinversion
Authors
Isao Kurosawa
Abstract
Travel-time tomography forces a trade-off between mesh resolution and stability in which the regularizer choice dominates what can be recovered. We introduce MIMIR, a differentiable framework that represents the 2D velocity field as a Fourier-feature neural network, replacing the grid-based slowness vector with a continuous, infinitely differentiable function. Prior neural-field tomography has staircased smooth fields under total-variation (TV) priors or oscillated near interfaces under $L^2$ Laplacian smoothing. We adopt second-order total generalized variation (TGV$^2$) and parametrize its auxiliary vector field as a second neural network jointly optimized with the velocity field, eliminating the inner Chambolle-Pock primal-dual loop that classically dominates TGV computation. On three synthetic benchmarks (Gaussian, horizontally layered, curved-fault inspired by OpenFWI) using cross-well acquisition, 5% travel-time noise, and five seeds, MIMIR-TGV$^2$ ties a classical FMM-LSMR baseline with auto-tuned hyperparameters on the Gaussian ($p=0.134$, paired $t$-test) and significantly outperforms it on layered ($p<0.0001$, 44% RMSE reduction) and curved-fault ($p=0.0002$, 33% reduction). Replacing TGV$^2$ with TV degrades performance on Gaussian ($p=0.004$) and layered ($p=0.003$); curriculum-annealed TV improves Gaussian RMSE by only 5.4%, confirming that TV's staircase bias is intrinsic to the regularizer rather than a scheduling artifact. The results empirically validate the Bredies-Kunisch-Pock prediction that piecewise-affine priors are better suited to subsurface velocity recovery than piecewise-constant TV priors. We argue that the central design choice in physics-informed neural-field inversion is not the network architecture but the regularizer. The full pipeline reproduces in under one hour on consumer hardware.