Full-waveform inversion (FWI) is a method that utilizes seismic data to invert the physical parameters of subsurface media by minimizing the difference between simulated and observed waveforms. Due to its ill-posed nature, FWI is susceptible to getting trapped in local minima. Consequently, various research efforts have attempted to combine neural networks with FWI to stabilize the inversion process. This study presents a simple yet effective training framework that is independent of dataset reliance and requires only moderate pre-training on a simple initial model to stabilize network outputs. During the transfer learning phase, the conventional FWI gradients will simultaneously update both the neural network and the proposed adaptive residual learning module, which learns the residual mapping of large-scale distribution features in the network's output, rather than directly fitting the target mapping. Through this synergistic training paradigm, the proposed algorithm effectively infers the physically-informed prior knowledge into a global representation of stratigraphic distribution, as well as capturing subtle variations in inter-layer velocities within local details, thereby escaping local optima. Evaluating the method on two benchmark models under various conditions, including absent low-frequency data, noise interference, and differing initial models, along with corresponding ablation experiments, consistently demonstrates the superiority of the proposed approach.

翻译：全波形反演（FWI）是一种利用地震数据，通过最小化模拟波形与观测波形之间的差异来反演地下介质物理参数的方法。由于其不适定性，FWI 容易陷入局部极小值。因此，诸多研究尝试将神经网络与 FWI 结合以稳定反演过程。本研究提出了一种简单而有效的训练框架，该框架不依赖于数据集，仅需在简单初始模型上进行适度预训练即可稳定网络输出。在迁移学习阶段，传统的 FWI 梯度将同时更新神经网络和所提出的自适应残差学习模块；该模块学习网络输出中大规模分布特征的残差映射，而非直接拟合目标映射。通过这种协同训练范式，所提算法有效地将物理先验知识推断为地层分布的全局表征，并在局部细节中捕捉层间速度的细微变化，从而逃离局部最优。通过在缺失低频数据、噪声干扰及不同初始模型等多种条件下对两个基准模型进行评估，并结合相应的消融实验，结果一致证明了所提方法的优越性。