33 3 2014 9 GLOBAL GEOLOGY Vol. 33 No. 3 Sept. 2014 1004 5589 2014 03 0653 06 2. 5D 130026 : 针对聚焦反演方法在实测数据应用中存在的趋肤效应和反演结果发散问题, 设计应用深度加权 和数据加权的双重加权系数灵敏度矩阵, 进行核函数处理通过反演拟合理论正演模型实验, 证明了 该方法的可靠性将双重加权系数运用到山东某矿区的实测数据, 反演结果清晰地反映出地下异常体 的边界和深度, 与剖面电阻率结果比较, 两者异常位置接近, 该方法可反应实际异常情况 : 重力 ; 双重加权 ; 2. 5 维反演 ; 聚焦反演 : P631. 12 : A doi: 10. 3969 /j. issn. 1004-5589. 2014. 03. 017 2. 5D dual-weight focusing inversion of gravity and its application SUN Rui-xue DU Xiao-juan LIANG Quan-you College of Geo-exploration Science and Technology Jilin University Changchun 130026 China Abstract Aiming at the problems such as skin effect of imaging and divergence of anomalous source for focusing inversion in the practical application the authors designed sensitivity matrix with double weighted coefficients including depth-and data weights in order to deal kernel function. By fitting inversion theoretical forward model experiments it is proved that the method is of reliability. The double weighting factors were applied to the practical data of a mine in Shandong in which the inversion results clearly reflect the boundaries and depth of underground anomalies. Compared with the results of the cross-section resistivity the both are close in abnormal positions. The method can reflect the actual anomalies. Key words gravity focusing inversion 2. 5D inversion dual-weighting 0 2. 5D 4 Boulanger Chouteau 5 1 Li Barbosa Silva 3 Zhdanov 6 Last Kubik 2 2014-03-20 2014-06-20 2009BAB43B00. 1957 -. E-mail dtdxj@ jlu. edu. cn
654 33 4 A i = l log u i +1 + D i +1 u i + D i - w i arctan u i +1l - arctan u il w i D i +1 w i D i 1 1. 1 u ( ) w = cosφ i sinφ i - sinφ i cosφi g = Aρ 1 ρ M ρ k g N d 2 i = u 2 i + w 2 i g z A N M d 2 i +1 = u 2 i +1 + w 2 i +1 10 D 2 i = u 2 i + w 2 i + l 2 D 2 i +1 = u 2 i +1 + w 2 i +1 + l 2 1 1 Fig. 1 6 Diagram of griding i = M a ij v j i = 1 N 2 g i j = 1 v j j a ij j i w j = v 2 j + β -1 9 A 1. 2 2. 5D β Rasmussen Pedersen 8 2. 5D g z = γρ N i = 1 2cosφ i A i 3 + u i +1 log l + D i +1 - u d i log l + D i 4 i +1 d i ( ) x ( ) z 5 φ i = arctan z i +1 - z i x i +1 - x i 6 7 l 2. 5D x i z i φ i u ( i w ) i l x y 2 2. 1 Last Kubik 3 δp = M j w j v 2 j δp min V = W -1 A T AW -1 A T -1 G 8 10
3 2. 5D 655 i V i = W -1 i -1 A T AW -1 i -1 A T -1 G 11 W i -1 = v 2 i -1 + β -1 12 10 2. 2 2 Fig. 2 Tendency of weight variation 2. 2. 2 数据加权 13 Zhdanov 9 2. 2. 1 深度加权 11 Oldenburg 4 Zhdanov W s = α + exp r /dz Z - Z 0 1 + exp r /dz Z - Z 0 13 z z 0 α W 2 d = diag A ik 2 = diag AA T 1 /2 15 A w = AW s 14 δd k = A w ikδm w i 12 S w i = δd = 槡 k A w ik 2 δm w i δm w i δm w i 16 = k A w 2 ik = k A ik W -1 2 i = W -1 2 i k A ik = W 槡 -1 i S i = I S w = I S I d 2 m W d W d = W i = S i = S A w 槡 k 槡 槡
656 33 2. 3 2. 3. 1 理论值反演 15 A = A w W -1 d 17 Fig. 3 a b 3 2. 5 Diagram of 2. 5D focusing inversion 3 0. 000 181 6 75 m 0. 003 879 6 570 m 65 m 2. 3. 2 实际数据的反演 10 m 2. 5D 2. 5D 1. 46 km 29 4 5 6a b Fig. 4 4 7 Profile of gravity abnormal from an area in Shandong 5 Fig. 5 2. 5D Diagram of 2. 5 D focusing inversion result of a place in Shandong
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