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

The singularity of a geophysical or geochemical data reflects their spatial self-similar or self-affine property.It is useful in data estimation(interpolation),mineral exploration,and environment assessment.The current singularity estimation algorithm assumes the data is isotropic in the vicinity of every location.However,geophysical or geochemical data is often anisotropic,and it is often happened that the most hopeful target in mineral exploration locates at the sub-tectonic structures,where anisotropy occurs,inside the major tectonics.The new anisotropy singularity estimation method is implemented in a GIS environment in this study to use the strong spatial analysis power of GIS.The Bouguer anomaly of the southern Nova Scotia,Canada,is used to demonstrate the anisotropy parameters estimation for mineral potential mapping.The results demonstrated that the given anisotropy singularity method is a power tool in mineral potential assessment.