论文详情
时频分析将一维时域信号转换到二维的时频域中,并在时频域对信号进行分析和处理。目前常用的时频分析方法往往需要在时间和频率分辨率之间进行权衡,因而在很多情况下应用效果不尽人意。提出了一种新的时频分析方法,即采用最小二乘方法直接求解信号的频谱。首先,将三角函数作为基函数,建立描述频谱、不同频率的三角函数和地震信号之间关系的正演方程,并在正演过程中加入一个对角矩阵,得到改进的正演方程,从而提高了正演过程的稳定性;其次,将频谱分析转换成一个求解反问题的过程,基于正则化约束最小二乘原理,通过迭代求解矩阵方程组得到信号的频谱;最后,逐点对地震道数据进行以上频谱分析,得到地震道的最小二乘时频分析结果。理论模型数据和实际应用结果表明,改进的最小二乘时频分析方法的分析结果不仅可以描述地震信号频谱随时间的变化,同时也描述了地震信号瞬时振幅的大小,有效提高了储层预测的准确度和可靠性,具有广阔的应用前景。
Time-frequency analysis transforms a 1D signal in the time domain into a 2D time-frequency domain that represents localized frequency data as a function of time.Commonly-used time-frequency analysis methods,including the short-time Fourier transform and wavelet transforms,generally require a trade-off between time and frequency resolution that may render them ineffective for certain interpretive applications.Consequently,a novel time-frequency analysis method was proposed.Instead of using a Fourier transform,least-squares analysis was used to solve for the Fourier series coefficients directly.First,a forward equation,which describes the relationships among frequency spectrum,trigonometric function and seismic signal,was established,and an improved forward equation was obtained by adding a diagonal matrix to the forward process.Second,the spectrum analysis was transformed into an inverse problem,based on the principle of least squares.The spectrum of the signal can be obtained by solving matrix equations iteratively.Finally,the least-squares time-frequency analysis results of seismic trace were obtained by analyzing the seismic spectrum signal point-by-point.Application of the proposed method to theoretical model data and actual seismic data demonstrated that it can describe the change of seismic signal spectrum with time,and also describes the magnitude of the instantaneous amplitude of seismic signals.This method can improve the accuracy and reliability,of reservoir characterization and has a broad potential for application.
中国石化科技攻关项目“济阳坳陷C-P不同组构砂岩岩石物理特征及有利储层预测”(P18051-6)资助。