Study On Seismic Wave Propagation Model Based On Wavelet Transform

Actual earthquake ground motions reflect the characteristics of the source mechanism, wave propagation path and amplification effect of the soil layers. However, those effects cannot be recognized directly from the records due to complexity of actual ground motions. So it is of significance to find some methods either to simplify the ground motion source or to make simplified models of wave propagation. At present, there are some wave propagation models widely being used, such as impulse response, correlation functions and power spectrum, while normalized input-output minimization method for multiple linear systems(NIOM) is used mostly. Relatively speaking, NIOM is always used to speculate the direction of wave propagation, site amplification effect and analyse wave component which is because NIOM is much fast and of high precision. However, sometimes the NIOM models do not show a good relationship between input and output and it can not determine the direction of the wave precisely under the influences of high-frequency component and noise. Although the NIOM model after Fourier filtering is much better,but distortion happens a lot.In this article, we put wavelet transform into filtering to build NIOM model modified by wavelet for typical seismic waves and pulsation,also comparing the modified NIOM model and the original NIOM model by the ability to determine the wave components and the direction of wave propagation. The main experimental and theoretical work includes the following aspects:(1) In terms of filtering of seismic signals,the first thing is to compare the Fourier filtering and the wavelet filtering include threshold method, modulus maxima method and correlation coefficient by the ability to filter high-frequency component and noise from simple signal containing gaussian white noise with different intensities. As for selecting wavelets and decomposition scale, the error by decomposition and reconstruction and denoising under different scales are took account.(2) For typical seismic waves, the models are built while vertical components are as inputs, and horizontal components deviating from true north 0-180 degrees are as outputs. The wavelet modified NIOM models clearly shows 90 degrees out of phase between input and output, which indicates the wave is consist of Rayleigh wave. Certainly, the same phase can be found in the most original NIOM models, but the other models are fluctuant because of the high-frequency component. However, the Fourier filtering NIOM models have no such fluctuation, but there are some turning points between the crests and the troughs of some of the output models, so it is hard to determine the wave components in those models. These models can be used to determine the direction of wave propagation. The difference between the peaks and valleys of output models is as characterization to the relationship between inputs and outpus. And the difference between the peaks and valleys changing by degrees is gentle, which is coincide the linear systems used to build the model. Then we come to a conclusion that the wavelet modified NIOM model is much better to determine the direction of wave propagation than the original NIOM model and the Fourier filtering NIOM model.(3) As for pulsation, models also have been built while surface components are considered as inputs and underground components in the same direction are considered as outputs except the way building models for typical seismic waves. Furthermore, one can easily find Rayleigh wave from these models, however, some output models of the original NIOM models and the Fourier filtering NIOM models are nearly straight lines, from which we can not find the real relationship between inputs and outputs. But the wavelet modified NIOM model can still provide clear phase. The ability to determine direction of wave propagation is same as the models built for typical seismic waves.