Time–frequency (TF) analysis algorithms are widely used to process seismic data. Unfortunately, most TF analysis algorithms cannot process 2-D seismic data, which contain more information than 1-D data. In fact, 2-D $x$ – $t$ domain seismic data should be analyzed in the multi-dimensional phase space (MDPS). In this letter, we develop and explain an MDPS analysis method for 2-D seismic data. In order to map the 2-D seismic data into MDPS, the synchrosqueezed curvelet transform (SSCT) is extended from the $x$ – $y$ domain to the $x$ – $t$ domain. By comparing the 2-D synchrosqueezing transform (SST) with the 1-D SST, we explain how the 2-D SST makes the connection between the 4-D curvelet domain and the 4-D space-time-wavenumber-frequency domain (xt–kf domain). This new analytical method can help us to obtain the angle, scale, frequency, and wavenumber information, which are useful to separate the overlapped seismic data. The numerical example and real data example illustrate the effectiveness of this method.

中文翻译：

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使用同步压缩曲线波变换分离混合地震数据

时频 (TF) 分析算法被广泛用于处理地震数据。不幸的是，大多数 TF 分析算法无法处理二维地震数据，其中包含比一维数据更多的信息。事实上，二维 $x$ —— $t$ 域地震数据应在多维相空间 (MDPS) 中进行分析。在这封信中，我们开发并解释了二维地震数据的 MDPS 分析方法。为了将二维地震数据映射到 MDPS，同步压缩曲线波变换 (SSCT) 从 $x$ —— $y$ 域到 $x$ —— $t$ 领域。通过比较二维同步压缩变换 (SST) 和一维 SST，我们解释了二维 SST 如何在 4-D 曲波域和 4-D 时空波数-频域之间建立联系（xt——kf领域）。这种新的分析方法可以帮助我们获得角度、尺度、频率和波数信息，这些信息有助于分离重叠地震数据。数值算例和实际数据算例说明了该方法的有效性。