SUMMARY The proliferation of large seismic arrays have opened many new avenues of geophysical research; however, most techniques still fundamentally treat regional and global scale seismic networks as a collection of individual time-series rather than as a single unified data product. Wavefield reconstruction allows us to turn a collection of individual records into a single structured form that treats the seismic wavefield as a coherent 3-D or 4-D entity. We propose a split processing scheme based on a wavelet transform in time and pre-conditioned curvelet-based compressive sensing in space to create a sparse representation of the continuous seismic wavefield with smooth second-order derivatives. Using this representation, we illustrate several applications, including surface wave gradiometry, Helmholtz–Hodge decomposition of the wavefield into irrotational and solenoidal components, and compression and denoising of seismic records.

中文翻译：

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使用预处理小波-曲线压缩传感方法的地震波场重建

总结 大型地震台阵的普及为地球物理研究开辟了许多新途径。然而，大多数技术仍然从根本上将区域和全球规模的地震网络视为单个时间序列的集合，而不是单个统一的数据产品。波场重建使我们能够将单个记录的集合转换为单个结构化形式，将地震波场视为连贯的 3-D 或 4-D 实体。我们提出了一种基于时间小波变换和空间中基于预条件曲波的压缩感知的分割处理方案，以创建具有平滑二阶导数的连续地震波场的稀疏表示。使用这种表示，我们说明了几种应用，包括表面波梯度测量，