Seismic data are often irregularly or insufficiently sampled along the spatial direction due to malfunctioning of receivers and limited survey budgets. Recently, machine learning techniques have begun to be used to effectively reconstruct missing traces and obtain densely sampled seismic gathers. One of the most widely used machine learning techniques for seismic trace interpolation is UNet with the mean-squared error (MSE). However, seismic trace interpolation with the UNet architecture suffers from aliasing, and the MSE used as a loss function causes an oversmoothing problem. To mitigate those problems in seismic trace interpolation, we propose a new strategy of using coarse-refine UNet (CFunet) and the Fourier loss. CFunet consists of two UNets and an upsampling process between them. The upsampling process is done by padding zeroes in the Fourier domain. We design the new loss function by combining the MSE and the Fourier loss. Unlike the MSE, the Fourier loss is not a pixelwise loss but plays a role in capturing relations between pixels. Synthetic and field data experiments show that the proposed method reduces aliased features and precisely reconstructs missing traces while accelerating the convergence of the network. By applying our strategy to realistic cases, we show that our strategy can be applied to obtain more densely sampled data from acquired data.

中文翻译：

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具有上采样技术和傅里叶损失的粗细网络用于重建丢失的地震数据


由于接收器故障和有限的调查预算，地震数据通常沿空间方向采样不规则或不充分。最近，机器学习技术已开始用于有效重建丢失的道并获得密集采样的地震道集。地震道插值最广泛使用的机器学习技术之一是均方误差 (MSE) 的 UNet。然而，使用 UNet 架构进行地震道插值会遇到混叠问题，并且用作损失函数的 MSE 会导致过度平滑问题。为了缓解地震道插值中的这些问题，我们提出了一种使用粗细化 UNet (CFunet) 和傅里叶损失的新策略。 CFunet 由两个 UNet 和它们之间的上采样过程组成。上采样过程是通过在傅立叶域中填充零来完成的。我们结合 MSE 和 Fourier 损失设计了新的损失函数。与 MSE 不同，傅立叶损失不是像素级损失，而是在捕获像素之间的关系方面发挥作用。合成和现场数据实验表明，所提出的方法减少了混叠特征并精确地重建了丢失的痕迹，同时加速了网络的收敛。通过将我们的策略应用于实际案例，我们表明我们的策略可以应用于从获取的数据中获取更密集的采样数据。