改进S变换的地震信号时频分析方法：去尺度化与高斯窗优化

Improved S-Transform Time-Frequency Analysis Method for Seismic Signals: Descaling and Gaussian Window Optimization

摘要: 时频分析作为一种用于研究信号在时间和频率联合域中特性的数学工具，它通过将信号在时间和频率两个维度上同时展开，揭示信号的局部时频特征。S变换是一种常用且有效的时频分析方法，但它存在窗口单一、时频分辨率不足和主频偏移等问题，针对这些问题，本文提出了四参数调控的去尺度广义S变换，在该方法中，首先引入了具有四个可变参数的高斯窗口，使窗口形状变化更灵活；其次修改了广义S变换中的尺度因子，以此来优化传统时频分析中常有的主频向高频方向偏移问题，有利于更好地确定地震信号的主频位置。此外，将提出的方法应用在地震信号中，结果表明，该方法既提高了信号的时频分辨率，又能有效地解决主频偏移问题。

Abstract: Time-frequency analysis, a mathematical tool for studying the characteristics of signals in the joint time and frequency domain, reveals the local time-frequency characteristics of a signal by simultaneously expanding it in both time and frequency dimensions. The S transform is a commonly used and effective time-frequency analysis method, but it suffers from problems such as a single window, insufficient time-frequency resolution, and dominant frequency offset. To address these issues, this paper proposes a descaling generalized S transform with four-parameter control. First, a Gaussian window with four variable parameters is introduced to make the window shape more flexible. Second, the scale factor in the generalized S transform is modified to optimize the dominant frequency offset toward high frequencies, a common problem in traditional time-frequency analysis. This helps better determine the dominant frequency position of seismic signals. Furthermore, the proposed method is applied to seismic signals. Results show that it not only improves the time-frequency resolution of the signal but also effectively addresses the dominant frequency offset problem.