TN1180 : Multi-Synchrosqueezed Optimized S-transform and Its Application in Spectral decomposition of Seismic Data
Thesis > Central Library of Shahrood University > Mining, Petroleum & Geophysics Engineering > PhD > 2024
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Seismic signals are non-stationary, and their frequency content changes over time. Therefore, Fourier transform is incapable of obtaining their local frequency content, necessitating the use of time-frequency representations. There are several time-frequency methods, each with its own advantages and limitations. Resolution is a crucial criterion in determining the efficiency and popularity of a time-frequency transform. Linear time-frequency methods baxsed on Fourier transform that use signal windowing in their algorithm have time-frequency resolution dependent on the window length. The S-transform is one such transform where the window length is a function of frequency, allowing it to provide a time-frequency representation with flexible resolution power. However, the Heisenberg uncertainty principle resulting from windowing limits the achievement of ideal resolution. Windowing causes the energy of the ideal time-frequency representation to spread around the instantaneous frequency and group delay in both time and frequency directions, reducing resolution. Generally, the resolution of a time-frequency representation in the time direction is inversely related to the window length, while in the frequency direction, it is directly related. Therefore, achieving the optimal window length at each moment in time and for each frequency component in the time-frequency transform, particularly the S-transform, is very important. The goal of developing new time-frequency methods is to minimize the energy spreading caused by windowing around the instantaneous frequency and group delay. The SST is one of the newest and most commonly used time-frequency transforms introduced to address this challenge. In this method, to maintain the reversibility of the transform, the spread energy in the time-frequency plane around the instantaneous frequency and group delay in the time-frequency representation is concentrated in only one direction of frequency or time on the instantaneous frequency or group delay. This process is carried out during post-processing on the time-frequency representation resulting from a conventional transform, and the more optimal the initial time-frequency representation resolution, the more optimal the compression result will be.
In this dissertation, using an optimized S-transform whose window is optimized baxsed on energy concentration in time or frequency and combining it with the MSST method, a new time-frequency transform with high simultaneous temporal and frequency resolution is introduced. This transform can produce a time-frequency representation with the highest sparsity and energy concentration and is also highly reversible. To evaluate the performance of the proposed transform, it was tested on various synthetic non-stationary signals and compared with conventional and new time-frequency methods. Additionally, by applying the transform to several two-dimensional and three-dimensional seismic data, the performance of the proposed transform in interpreting seismic data, such as low-frequency shadow indicators and amplitude versus offset analysis in the time-frequency domain, was utilized. The results of applying the proposed transform in this dissertation on synthetic and real data and comparing it with conventional and new time-frequency methods showed that the proposed method can produce a time-frequency representation with high simultaneous temporal and frequency resolution with the highest energy concentration and can be used as a new transform in the spectral analysis of seismic signals.
Keywords:
#spectral analysis #S-transform #optimization #simultaneous multiple compression #seismic data Keeping place: Central Library of Shahrood University
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