TIME-FREQUENCY ANALYSIS OF SEISMIC SIGNALS

Abstract

Prognosis of seismic signal has always been a great interest for the engineers and seismologists worldwide. Seismic signal represents inelastic response of the ground and structures, which are mainly characterized by the ground motion of finite duration and short duration. These signals originate from the two major sources: natural and artificial source. The seismic waves which originate deep inside of the earth, such as earthquakes, are considered as the results of natural source. These waves occur naturally when energy is released in the earth's lithosphere. On the other hand, artificial seismic signal generates from the explosions, mining activities etc. Recorded seismic signals contain important characteristics and information that are used indirectly or directly in seismic analysis and design of structures. Earthquake ground motions are inherently non-stationary in nature. The non-stationary seismic signal is generated by earthquake and some other sources like explosion and landslide. Classical detection and estimation techniques, like Fourier-based technique has been employed to analyse these seismic signals. The Fourier spectrum of a ground motion may be narrow or broad. A narrow spectrum can produce a smooth, almost sinusoidal timehistory. A broad spectrum contains a variety of frequency components that produce an irregular time-history. This method is applied to overcome the problem encountered upon the analysis of seismic signal, but it fails to provide temporal information of the seismic signal, and thus it is not suitable for analysis of earthquake records. However, time-frequency method has a potential which greatly facilitates the extraction of the time-frequency information from the signals. It transforms a time-domain signal into a two-dimensional representation of frequency contents with respect to time. The most commonly used method in earthquake engineering is short time Fourier transform (STFT) and Gabor transform (GT). The STFT are not generally used due to leakage problem whereas GT eliminates the discrepancy by considering a Gaussian window which reduces the leakage of energy in signal. In this work, GT is employed for noise removal of seismic signals and its application extended to the generation of synthetic time-histories for earthquake signals. The comparison of GT with wavelet transform for the de-noising of seismic signals reflects that the performance of the GT is superior in comparison to wavelet transform. For this reason, application of GT has been extended for the generation of synthetic time-histories of earthquake signals. Further, Stransform was introduced to overcome the limitations of wavelet transform. S-transform retains the absolutely phase information in contrast to the wavelet approach. However, S transform is also not suitable for the analysis of seismic signals as it holds the poor energy iv distribution over the time-frequency plane. Improvement of the signal resolution is the main objective for the time-frequency signal processing and has extensively been utilized in extraction of attribute parameters and in geophysical data processing. In time-frequency signal processing, Wigner-Ville distribution is another well known method to improve the signal resolution for better analysis. The Wigner-Ville distribution is distinguished and much more effective from the running Fourier transform, wavelet transform and S-transform in terms of increased resolution in the time-frequency plane. However, this method introduces the complexity due to cross-terms interference and makes the interpretation tedious for the human analyst. The research has been done with different kernel functions (or low pass filter) which reduce the effect of cross-terms. However, it limits the time-frequency resolution on the removal of cross-terms. An alternate time-frequency method known as Gabor-Wigner transform (GWT) is introduced and applied for the analysis of seismic signals. GWT is developed by combining the Gabor transform (GT) and Wigner-Ville distribution (WVD). In comparison with WVD, GT is free from the cross-term interference. Hence to obtain the better clarity and to remove the cross-term interferences, GT and WVD are carefully combined and the resultant GWT is employed for the analysis of signals. Later it is applied into the assessment of building damage analysing the shifting of fundamental frequency. Records obtained at four different buildings during earthquake. Further, application of GWT has been extended for detection of predominant frequency/period of the first 3 sec data of the initial portion of P-wave to estimate the magnitude for earthquake early warning systems. Analysing a signal visually doesn’t lead to an accurate and precise result. Therefore, in order to quantify the results, Renyi entropy is considered in this thesis. The Renyi entropy is used to investigate the synthetic as well as digital data for different window length of the GWT. Present study confirms the efficiency of GWT in comparison with the performance of GT, WVD and other time-frequency methods. The simulation results are quantified by entropy measures and proved to be an efficient technique in providing localized response for structural damage detection, where frequency shifting occurred in the earthquake damaged buildings are observed. In addition to GWT method, synchrosqueezing transform (SST) is also applied in the analysis of seismic signals, which is found to be an efficient method for signal analysis.