Singular-Value Decomposition (SVD) for Extraction of Gravity Anomaly Associated with Gold Mineralization in the Tongshi Gold Orefield, Western Shandong Province, East China
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摘要: 基于MATLAB平台编制的奇异值分解(SVD)程序有效地应用于铜石金矿田1∶50 000重力数据分解.首先，利用奇异值分解将重力数据分解为一系列的特征值空间；然后运用多重分形技术确立反映不同层次控矿因素的特征空间值的临界值，最后将这些具有不同控矿因素特征的特征空间值按一定的规则进行数据重构.结果获取三幅刻画不同尺度控矿因素的重力异常图像.(1)区域控矿地质因素是位于平邑火山沉积盆地(重力异常值-56~-974 μm/s2)南西侧NW向基底隆起(重力异常值-55~567 μm/s2)的鞍谷部位(重力异常值-55~51 μm/s2)，这里为构造上的局部拉张区，控制铜石杂岩体以及所有金矿床的整体分布，是金成矿的有利地段.(2)局部控矿因素是具有重力负异常特征(重力异常值-339~-11 μm/s2)的铜石杂岩体和围绕杂岩体形成的具有环形重力正异常(重力异常值37~345 μm/s2)接触交代带，斑岩型金矿化位于岩体内部，矽卡岩型金矿化形成于接触带中，而隐爆角砾岩型和卡林型金矿化形成于接触交代带外围；因此，岩体及其环形接触交代带是金矿成矿的潜在地段.(3)具体控矿因素是NE和NW向重力异常反应的两个方向断裂交汇域，几乎所有金矿化都位于这些交汇域，因此，这里是金成矿的远景地段.(4)铜石金矿田具有典型的多重因素控矿的复杂性特征.Abstract: A singular-value decomposition (SVD) program on a MATLAB platform was effectively used to handle gravity signals for the Tongshi gold field. Firstly. The gravity signals are firstly decomposed into different eigenimages with singular-value decomposition method. Secondly, the thresholds between the eigenvalues reflecting different layers of ore-controlling factors are established by multi-fractal method. Finally the eigenvalues with different layers of ore-controlling factors were rebuilt on certain mathematical rules. This yielded three layers of two-dimensional singular-value images that meticulously depict ore-controlling factors in different scales respectively. (1) The regional ore-controlling factor is a saddle valley with the gravity anomaly values varying from -55 to 51 μm/s2 of the NW trending swell with the gravity anomaly values varying from -55 to 567 μm/s2 on the SW side of the Mesozoic volcanic sedimentary basin with the gravity anomaly values varying from -56 to -974 μm/s2. The saddle valley might be tectonically an extensional area where the Tongshi complex pluton and all gold deposits are located and thus this area is a favorable area for gold deposits. (2) The local ore-controlling factor is the Tongshi complex pluton with a negative circular gravity anomaly varying from -339 to -11 μm/s2 and the ring contact metasomatic mineralization zone around the Tongshi complex with the positive gravity anomaly varying from 37 to 345 μm/s2. The porphyry gold occurrences are located within the Tongshi intrusive complex and Skarn iron-copper-gold occurrences are located in the inner contact metasomatic zone between the intrusive complex and its host rocks. Crypto-breccia and Carlin-type gold deposits are located at the outer contact metasomatic zone between the intrusive complex and its host rocks. Thus the two areas are potential areas for gold deposits. (3) The concrete ore-controlling factor is crossing areas between the NE trending faults and NW trending faults reflected by the two trending gravity anomaly zones. Almost all gold deposits are located within crossing areas and thus these areas are prospective areas for gold deposits. (4) The Tongshi gold field has a typical complexity with multi-layers of ore-controlling factors.
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图 1 铜石金矿田地质矿产分布(据Chen and Liu, 2000修编)
1.第四纪沉积物；2.白垩纪火山沉积岩；3.侏罗纪火山沉积岩；4.奥陶纪碳酸盐岩；5.寒武纪碳酸盐岩；6.太古代泰山群；7.燕山期闪长玢岩；8.燕山期正长斑岩；9.隐爆角砾岩；10.斑岩型金矿点；11.矽卡岩型金矿点；12.隐爆角砾岩型金矿床；13.卡林型金矿床；14.断裂；15.地质界线；16.不整合地质界线
Fig. 1. Geological map of the Tongshi gold field
图 2 铜石金矿田1∶50 000原始重力数据图像(金矿点图例见图 1)
Fig. 2. The original gravity data image surveyed at scale 1∶50 000
图 3 lnλ-lnE(λ|λ＞λi)对数图
使用最小二乘法拟合3条具有不同斜率的线段，分割点p=3，q=9，lnλ3=17.13，lnλ9=14.17
Fig. 3. ln-ln plot of λ-E with two break points
图 4 第1、2特征空间对应的重力图像(金矿床类型见图 1)
Fig. 4. Image corresponding to the 1st and 2nd eigenimages
图 5 第3至第8特征空间所对应的重力图像(金矿床类型图例同图 1)
Fig. 5. Reconstructed image from the 3rd to 8th eigenimages
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