用新型正则化让神经场地震波速反演媲美经典方法
Total Generalized Variation regularization closes the gap between neural-eld and classical methods in seismic travel-time tomography
- 将速度场建模为傅里叶特征神经网络，结合二阶总广义变差正则化
- 在三种合成数据上均优于经典方法，尤其在层状和断层结构中降低33%误差
- 证明了正则化设计比网络结构更关键，且可在消费级硬件快速运行
地震走时层析成像面临网格分辨率与稳定性之间的权衡，正则化选择决定可恢复内容。本文提出MIMIR，一种可微框架，将二维速度场表示为傅里叶特征神经网络，用连续、无限可微函数替代网格化的慢度向量。以往神经场层析成像在总变差（TV）先验下呈现阶梯状平滑，在L²拉普拉斯平滑下靠近界面产生振荡。本文采用二阶总广义变差（TGV²），并将辅助向量场参数化为第二个神经网络，与速度场联合优化，消除了经典TGV计算中的内层Chambolle-Pock对偶迭代。在三个合成基准测试（高斯、水平分层、受OpenFWI启发的弯曲断层）中，使用井间采集、5%走时噪声和五组随机种子，MIMIR-TGV²在高斯模型上与自调参的经典FMM-LSMR基线持平（p=0.134，配对t检验），在分层模型上显著更优（p<0.0001，RMSE降低44%），在弯曲断层模型上也更优（p=0.0002，RMSE降低33%）。替换TGV²为TV导致高斯模型（p=0.004）和分层模型（p=0.003）性能下降；课程学习型TV仅使高斯模型RMSE降低5.4%，证实了TV的阶梯偏差是正则化固有特性而非调度伪影。结果实证验证了Bredies-Kunisch-Pock的预测：分段仿射先验比分段常数的TV先验更适合地下速度恢复。我们主张，物理信息神经场反演的核心设计选择并非网络架构，而是正则化。整个流程在消费级硬件上可在一小时内完成。
原文摘要 · Abstract (English)
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.
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