利用EMD和子波振幅谱与相位谱关系的时变子波提取方法

本文首先分析了地震波在黏弹介质的传播规律，基于黏弹介质地震波动方程总结了时变子波振幅谱和相位谱的关系，从而得出结论，准确估计子波相位谱初值和不同时刻的子波振幅谱是实现时变子波准确提取的必要条件.在此基础上，针对传统方法限制子波振幅谱形态且受限于分段平稳假设的问题，提出了一种利用EMD（Empirical Mode Decomposition）和子波振幅谱与相位谱关系的时变子波提取方法，根据子波对数振幅谱光滑连续而反射系数对数振幅谱振荡剧烈的特点，采用EMD方法将不同时刻地震记录的对数振幅谱分解为一组具有不同振荡尺度的模态分量，通过滤除振荡剧烈分量、重构光滑连续分量提取时变子波振幅谱；再应用子波振幅谱和相位谱的关系提取时变子波相位谱，将分别提取的振幅谱和相位谱逐点进行合成，最终实现时变子波的准确提取.本文方法不需要求取Q值，适用于变Q值的情况，具有良好的抗噪性能.数值仿真和叠后实际资料处理结果表明，相比传统的分段提取方法，利用本文方法提取的时变子波准确度更高，研究成果对提高地震资料分辨率具有重要意义.

A time-varying wavelet extraction method using EMD and the relationship between wavelet amplitude and phase spectra

The propagation and attenuation law of seismic wavelets is analysed, and the relationship between the amplitude and phase spectra of time-varying wavelets is obtained by deriving the wave equation for a viscoelastic medium. We find that accurately estimating the amplitude spectrum at different time points and the initial phase spectrum is necessary to extract accurate time-varying wavelets. Based on this conclusion, to overcome the defects of the classical methods, we propose a time-varying wavelet extraction method that utilizes EMD (Empirical Mode Decomposition) and the relationship between the wavelet amplitude and phase spectra. According to the differences that the logarithm amplitude spectra of wavelets and reflection coefficient are smooth and oscillating respectively, the logarithm amplitude spectra of the seismogram at different time points are decomposed into multi-layer components with different oscillation scales by EMD, and the amplitude spectra of time-varying wavelets can be estimated by filtering the oscillating components and reconstructing the smooth components. Then the phase spectra of time-varying wavelets are estimated by applying the obtained relationship, so that time-varying wavelet extraction is achieved by combining the estimated amplitude and phase spectra of wavelets correspondingly. This method does not need to calculate the Q value and can be applied to the case of variable Q, exhibiting good anti-noise performance. The numerical simulation and real seismic data processing results demonstrate that the proposed method can improve the accuracy of time-varying wavelet extraction compared to the classical method.