时频分析方法在形变数据中的应用研究

The Application of Time Frequency Analysis Methods in Deformation Data

摘要:

时频分析是分析非线性非平稳信号的有力工具。本文在小波变换、S变换和Hilbert-Huang变换基础上，通过设计仿真数据及运用地形变数据，分析了形变数据处理中三种方法各自的优劣、适用范围及需要改进的地方；运用三种方法分别对汶川地震前后的宽频带及整时采样数据进行分析，得到了不同时频方法在分析震前异常时的结果。

Abstract:

The time-frequency method is a useful tool for analyzing nonlinear and non-stationary signals.The earthquake data we obtained from the deformation instrument are both nonlinear and non stationary；therefore，this method is suitable for earthquake data analysis.Fast Fourier Transform（FFT）has resulted in significant improvements in signal analysis and is used to determine the frequency resolution of the signals.The obvious advantage of the time-frequency method over the traditional FFT transform is that it offers a frequency trend that varies with time，which means that it has both time resolution and frequency resolution.In recent years，this method was gathered increasing attention in earthquake data processing.Its applications include seismic signal analysis，geological exploration，and mechanical vibration signal analysis.However，its application in terrain data analysis is still in its infancy.Many different methods are used in time-frequency analysis，including linear and nonlinear analysis methods.In this paper，we introduce the theories of wavelet transform，Stransform，and Hilbert-Huang transform，which are all nonlinear analysis methods，and design signals that are similar to the deformation signals.Moreover，we list terrain data to compare the respective merits，scope of application，and areas for improvement of these three methods.Through the analysis of the signals designed in this paper，we determine that the time-frequency methods can demonstrate the frequency variation over time，and all of the methods we mention in this paper can display the characteristics of the data in the time-frequency domain.By using various time-frequency analyses methods，we analyze wide broadband data and sampling data hours before and after the Wenchuan earthquake to obtain different results of impending earthquake events in these methods and to propose a proper method for analyzing the terrain deformation data.The analysis of impending earthquake events offers a method of forecasting earthquakes.In this paper，we also determine that the wavelet transform has its own advantages of frequency resolution in the high-frequency area，although the low-frequency analysis results are insufficient；the S transform has its own advantages of low-frequency resolution；and the Hilbert-Huang transform is not suitable for terrain deformation data analysis，which is needed to display the change trends of the data.Further，we obtained the scope of application of these three methods.Wavelet transform can be used to analyze a large number of data and to obtain the high-frequency characteristics of the signals；the S transform can analyze data that includes many low-frequency components；and the Hilbert-Huang transform can analyze the data that requires information of the component in detail because the analysis uses empirical mode decomposition （EMD）.Recently，a new method based on the Hilbert-Huang transform，known as ensemble empirical mode decomposition（EEMD），has been proposed for signal analysis.However，its improvement in the Hilbert-Huang transform method has not been determined and requires extensive research.