多维分形奇异功率谱分析与应用

地球物理信号中普遍含有噪声，消除噪声是地球物理信号处理中的关键技术之一.奇异功率谱分析（SSA）是在状态空间（又称相空间）中研究（系统）动力学、非线性科学与混沌现象的方法.本文在状态空间中通过SSA分解，研究、应用地球物理序列的尺度不变性进行多维分形滤波：通过在状态空间的SSA分解，构造了经验正交函数系（EOF）；在EOF子空间中定义了两种尺度与测度后，发现了两种测度与尺度皆在多个尺度范围内存在尺度不变性；利用这种尺度~测度的尺度不变性，设计、实现了多维分形奇异功率谱(MSSA)滤波模型；处理解释了大洋钻探（ODP）1143A孔岩芯自然反射性（NGR）资料；Fourier功率谱分析结果证明，MSSA能有效地压制噪声，提取有用信号.研究得出，嵌入维数对MSSA基本无影响（小于1/1000），多维分形滤波器（MSSA）能有效压制噪声或提取有用信号.

Multifractal singular spectrum analysis model and application

As noise widely exists in geophysical signals, it is one of key techniques for successful data processing to erase noise in geophysical records. In this approach, the scale invariance of geophysical series in their state space are examined, verified, and applied. The singular spectrum analysis (SSA) is a method of studying state space, and is commonly used in studying system dynamics, nonlinear dynamics, and chaos in state space, or phase space. The experiment orthogonal function (EOF) is constructed by SSA decomposition; scale invariance in different ranges is found by definition of two kinds of scale and measurement in EOF subspace; the scale invariance is used in implementing multifractal singular spectrum analysis (MSSA) filtering model; the core natural radiation (NGR) from Hole 1143A, ODP LEG 184 is processed as a case study; the effectiveness of MSSA for noise erasing and useful signal extraction is verified through power spectrum estimation in Fourier domain. The factor of embedding dimension, which is used in the state space generating is quantitatively assessed and proved that there is less effects on the MSSA results (less than 1/1000).