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The analysis of earthquake recordings from three-component instruments can be challenging due to overlapping events. Time–frequency (TF) polarization methods are efficient tools for this purpose, which can discriminate these events. Previous polarization methods did not consider all three components simultaneously while transferring data to TF domain, which can cause inaccuracies in the reconstruction of wave amplitudes. Therefore, the three-component sparse adaptive S transform (3C-SAST) algorithm is preferred to other TF decompositions since it is mainly developed for polarization analysis purposes, and outperforms other TF methods. In this paper, we developed the 3C-SAST by adding a parameter to adjust the sparseness of the solution and make the resolution flexible. The developed TF decomposition is then used to extend the Morozov & Smithson method to TF domain, and devise a new TF polarization filter whose invertibility and resolution flexibility make it a promising tool for wavefield separation. This filter can eliminate the out-of-plane arrival energies and extract the Rayleigh waves for multicomponent data, which has application in Rayleigh wave tomography and seismological studies. We demonstrated the efficiency of the proposed method for seismic surface waves separation using synthetic signals and three-component teleseismic earthquake recording. [ABSTRACT FROM AUTHOR]

Obtaining geological information from seismic data motivates researchers to innovate and improve seismic wave processing tools. Polarization‐based methods have received much attention regarding their ability to discriminate between different phases of the seismic wave based on polarity. Combining the intuitive definition of polarity in the frequency domain (monochromatic waves) with the non‐stationary properties provided by time‐domain methods, time‐frequency approaches are attracting widespread interest because they localize the information extracted from the seismic waves in the joint time and frequency domains. Due to the lack of high‐resolution time‐frequency maps, the time‐frequency polarization approach was not able to resolve specific temporal polarity changes in the seismic signal. The main objective of this study was to devise a robust time‐frequency‐based polarization filtering method using high‐resolution polarization attributes obtained directly from the sparse time‐frequency map without using Eigen analysis or analytic signals. The method proposed here utilizes a computationally effective sparsity‐based adaptive S‐transform to obtain a high‐resolution polarization map of an inherently non‐stationary seismogram for the entire frequency content of the signal at different times. The superiority of the proposed method over the S‐transform method was verified using synthetic and real data sets to calculate the polarization attributes in the time‐frequency domain and separate the Rayleigh waves from the seismogram. [ABSTRACT FROM AUTHOR]