Separation of Blended Seismic Data Using the Synchrosqueezed Curvelet Transform

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 <inline-formula> <tex-math notation="LaTeX">$x$ </tex-math></inline-formula>–<inline-formula> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">$x$ </tex-math></inline-formula>–<inline-formula> <tex-math notation="LaTeX">$y$ </tex-math></inline-formula> domain to the <inline-formula> <tex-math notation="LaTeX">$x$ </tex-math></inline-formula>–<inline-formula> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula> 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 (<italic>xt</italic>–<italic>kf</italic> 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.