AI 中文总结
提出C2F-IFWI方法，通过逐步激活多分辨率哈希级别实现粗到细反演，避免周期跳跃，提升收敛速度、精度及鲁棒性，无需额外参数。
AI 中文摘要
隐式全波形反演（IFWI）通过神经网络对速度模型进行重参数化，但该方法存在频谱偏差问题，且需要大量迭代才能收敛。多分辨率哈希编码利用可学习的特征网格在多尺度上恢复高波数细节，并提供强大的局部表示能力。然而，从反演一开始就激活所有分辨率级别会引入高波数分量，这可能加剧周期跳跃问题。本文提出了一种粗到细的隐式全波形反演方法（C2F-IFWI），该方法逐步激活多分辨率哈希级别，而非一次性全部激活。具体而言，初始化时仅保留少数粗基级别处于激活状态，其余级别则逐步引入。冻结的哈希级别在被激活前不贡献梯度，因此无论数据频率范围如何，粗级别都能先解析长波长背景，然后再引入更细的级别。连续激活索引随迭代次数增加而增大，并决定训练过程中任意时刻激活的级别数量。每个新加入的级别通过平滑加权逐渐淡入，而非突然开启，从而在过渡期间保持优化稳定性。该方案使模型容量随波数同步增长，且不增加任何额外可训练参数，计算开销可忽略不计。在合成Overthrust和BP 2004模型以及Viking海洋野外数据集上的实验表明，与全分辨率哈希基线相比，粗到细方案收敛更快，精度更高，并且对初始模型选择和强数据噪声的鲁棒性显著增强。
英文摘要
Implicit full waveform inversion (IFWI) reparameterizes the velocity model with a neural network, but it suffers from spectral bias and requires many iterations to converge. Multi-resolution hash encoding uses a learnable feature grid to recover high wavenumber details at multiscales and provides strong local representations. However, activating all resolution levels from the start of the inversion introduces high wavenumber components, which can exacerbate cycle skipping. In this paper, we propose a coarse-to-fine IFWI (C2F-IFWI) that activates the multi-resolution hash levels progressively rather than all at once. Specifically, only a few coarse base levels are kept active at initialization, while the remaining levels are introduced progressively. A frozen hash level contributes no gradient until it is activated, so the coarse levels resolve the long-wavelength background before the finer levels are introduced regardless of the frequency range of the data. A continuous activation index increases with iterations and determines how many levels are active at any point in training. Each newly admitted level is then faded in gradually through a smooth weighting rather than switched on abruptly, which keeps the optimization stable during transition. This scheme allows model capacity to grow synchronously with wavenumber without adding any additional trainable parameters and with negligible computational overhead. Experiments on the synthetic Overthrust and BP 2004 models and on the Viking marine field dataset show that, compared with the all-resolution hash baseline, the coarse-to-fine scheme converges faster, attains higher accuracy, and is markedly more robust to the choice of initial model and to strong data noise.
