摘要
将布格异常作为二维实矩阵对其进行了奇异值分解 .用其左特征向量矩阵与右特征向量矩阵的直积构造了一个二维完备 (特征空间 )正交基 .布格异常投影到该正交基上的系数是布格异常矩阵的特征值 (奇异值的平方 ) .奇异值代表了布格异常在其特征空间的一种功率密度 .对比了密度分布函数、密度分布函数的变化率、密度分布函数的积分能量后 ,定义了奇异值谱半径量度下的能量测度 .能量测度与能量谱半径符合 (简单分形 )指数或 (多维分形 )分段指数变化 .利用最优分段方法得到这些分段点 ,利用这些分段点在特征空间中对地球物理场进行了重建、滤波 .编制了与GIS结合的程序 .用该方法分析和处理加拿大NovaScotia的地球物理资料 ,并将结果与已知的地质、金矿点进行了对比 .结果表明 ,可以很好地提取地球物理场中的背景、异常场 ,该结果与岩性、构造、已知矿点关联 ,可进行矿产资源评价和靶区预测 .该方法还可用于各种地球物理信号的分离、图像处理、图像压缩等 .作者开发的结合GIS的应用程序 ,使得这些分析能快速完成 .
In this paper, Bouguer anomaly was reconstructed as 2 D arrays by singular decomposition method. The cross multiplying of left and right eigenvector matrix created an orthogonal base. The projection coefficients for Bouguer anomaly are its eigenvalues (square of singular values). These singular values are one kind of power spectra or energy density. After comparison of energy density, changing rate of energy density and accumulated energy density, the energy measurement was defines as the function of energy density radii. The energy measurement defined by this way is related with the radii by multi fractal power law. Use optimal least square (LS) segmentation, the breaks points on radii coordinate were got. Use these breaks, geophysical fields could be reconstructed, filtered or decomposed in this orthogonal space. A program was made and integrated into GIS environment fro this purpose. Then using this tool, the geophysical data from Nova Scotia, Canada, were processed and the results were compared with known gold deposit ores positions and geology. It approved that the reconstructed fields represent background and anomalies very nicely. This method could also be used in image processing and compressing. By this software, the singular analysis and reconstruction can be done on a fly and with most facilities and could overlay with other known datasets.
出处
《地球物理学进展》
CSCD
2003年第1期97-102,共6页
Progress in Geophysics
基金
国家自然科学基金项目 ( 4 97742 3 7)资助 .
关键词
GIS
奇异值分解
异常分离
图像处理
金矿勘探
正交空间
GIS(geographical information system), singular decomposition, anomaly separation, image processing, gold exploration, orthogonal space
