生成式波传播器
Generative wave propagator
AI总结：
研究针对地震波场模拟，传统有限差分法受限，提出基于条件扩散的波场传播器，利用波场历史等条件训练网络直接预测下一快照，引入因果时间加权损失提升稳定性，实验表明该方法能准确再现波场并加速。
摘要：
地震波场模拟是地震学的基础，但传统有限差分（FD）方法受数值色散和稳定性约束限制，常需密集空间网格和小时间步长，严重限制迭代反演工作流程的有效性。我们引入一种基于条件扩散的波场传播器，它从一个时间步递归推进到下一个时间步的地震波场。该模型不是学习波场演化的无条件数据分布，而是由最近波场时间步（快照）的短历史、速度模型和波场时间步索引进行条件设定，使其能够表示相邻物理状态之间的条件转换。通过训练网络直接预测干净的下一波场快照，这种强大的物理条件设定使得可以用对每个预测快照的单个网络评估来代替迭代反向扩散过程。为了在长递归展开中提高稳定性，我们进一步引入因果时间加权损失，其中自适应权重作为每个快照训练误差的指数移动平均值累积，强调与正向传播序列一致的训练方向，并减少一步预测误差的放大。由于学习到的传播器与训练快照的时间间隔相关联，而不是与FD稳定性极限相关联，它可以使用比底层求解器所需的物理时间步长十倍大的时间步长来推进波场。在逆冲、SEG/EAGE和Marmousi模型上的实验表明，所提出的方法能够准确地再现波场快照和炮集，并在匹配硬件条件下比GPU加速的十阶交错网格FD实现实现了2.17倍的端到端加速。
英文摘要：
Seismic wavefield simulation is fundamental to seismology, but conventional finite-difference (FD) methods remain limited by numerical dispersion and stability constraints, which often require dense spatial grids and small time steps and thereby severely limit the effectiveness of iterative inversion workflows. We introduce a conditional diffusion-based wavefield propagator that advances seismic wavefields recursively from one time step to the next. Instead of learning an unconditional data distribution of wavefield evolution, the model is conditioned by a short history of recent wavefield time steps (snapshots), the velocity model, and the wavefield time step index, allowing it to represent the conditional transition between adjacent physical states. By training the network to directly predict the clean next wavefield snapshot, this strong physical conditioning makes it possible to replace the iterative reverse diffusion process with a single network evaluation for each predicted snapshot. To improve stability over long recursive rollouts, we further introduce a causal time-weighted loss, in which adaptive weights, accumulated as exponential moving averages of per-snapshot training errors, emphasize training directions that are consistent with the forward propagation sequence and reduce the amplification of one-step prediction errors. Because the learned propagator is tied to the temporal spacing of the training snapshots rather than to the FD stability limit, it can advance the wavefield using a physical time step ten times larger than that required by the underlying solver. Experiments on the Overthrust, SEG/EAGE, and Marmousi models show that the proposed method accurately reproduces wavefield snapshots and shot gathers and achieves an end-to-end speedup of 2.17 x over a GPU-accelerated tenth-order staggered-grid FD implementation under matched hardware conditions.
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