Abstract:Seismic waves have characteristics of non-stationary signals,and their energy distribution is in a finite frequency band.In addition,they contain a significant amount of information about sources and media.Analysis of seismic signals is used to determine the sources and propagation medium and for further study of earthquake mechanisms.Fourier transform is a classic method used for signal processing.Because it is a pure frequency domain analysis method,its shortcoming is lost time information.The Fourier transform method stringently requires that the system is linear and that the signal is stationary.Therefore,high limitations are placed on non-stationary signals.For short-time Fourier transform,constraints of the window function result in difficulties in simultaneously obtaining good resolution in time and frequency domain.Because the wavelet transform has the characteristic of multi-resolution,the time and frequency windows can be dynamically adjusted as the signals changes;thus,the characteristics of local information expression capability is improved in the time and frequency domain.Therefore,the dynamic characteristics of the seismic waves in the frequency and time domain should be determined by the multi-resolution decomposition of seismic signals.In this paper,the multiresolution decomposition of discrete wavelet transform is used to show decomposition of a synthetic waveform that is rebuilt by different level signals of decomposition.The standard square error is 1.554 2e-019,and the root mean square error is 7.351 2e-012 between original and rebuilt signals.The signal is not distorted due to decomposition and reconstruction processing.These results satisfy the requirements of computational analysis.Moreover,nine earthquakes records obtained from the Gansu Seismic Network with a magnitude range of ML3.3-4.2 were processed by using the same methods. Results indicate a relative energy distribution range of 1-15 Hz and an energy peak of 3-6 Hz for the local seismic wave（Δ300 km）.For one earthquake,the relative energy distribution of the earthquake differs among stations,which is caused by the focal radiation pattern and medium differences.The statistical test results show that the error level and results of synthetic waveform testing are consistent.This method can accurately determine near seismic energy distribution in the frequency domain characteristics,which is conducive to the study of seismic wave variation in various frequency bands.Moreover,statistical results show that this method is effective and reliable for obtaining details of seismic wave variation.However,it is difficult to explain the phenomenon such that the frequency of the peak energy changes from low to high with an increase in epicenter distance.Therefore,this topic requires further study.In addition,it should be noted that if such a method is used to process data for wavelet window length,some energy may be lost in the calculation process.The results of this study provide reference value in the research of earthquake sources,radiation patterns and seismic wave propagation in an anisotropic medium,and aseismic design for engineering applications.
