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 u ( ) w = cosφ i sinφ i - sinφ i cosφi g =

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1 GLOBAL GEOLOGY Vol. 33 No. 3 Sept D : 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 : P : A doi: /j. issn D 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 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 D 4 Boulanger Chouteau 5 1 Li Barbosa Silva 3 Zhdanov 6 Last Kubik BAB43B dtdxj@ jlu. edu. cn

2 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 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 D 2 i = u 2 i + w 2 i + l 2 D 2 i +1 = u 2 i +1 + w 2 i +1 + l 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 D β Rasmussen Pedersen D 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 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 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 Fig. 2 Tendency of weight variation 数据加权 13 Zhdanov 深度加权 11 Oldenburg 4 Zhdanov W s = α + exp r /dz Z - Z 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.

000 181 6 75 m 0. 003 879 6 570 m 65 m 2. 3.

4 理论值反演 15 A = A w W -1 d 17 Fig. 3 a b Diagram of 2. 5D focusing inversion m m 65 m 实际数据的反演 10 m 2. 5D 2. 5D km a b Fig Profile of gravity abnormal from an area in Shandong 5 Fig D Diagram of 2. 5 D focusing inversion result of a place in Shandong

3 2. 5D 657 a 6 b 7 Fig. 6 6 Diagram of linear inversion result of a place in Shandong 2. 5D 5 7 1.

. 1979 10-20. Tikhonov A N Arvinen V YA. Ill-posed problems M. WANG Bing-chen Translated. Beijing Geological Publishing House 1979 10-20.

5 3 2. 5D 657 a 6 b 7 Fig. 6 6 Diagram of linear inversion result of a place in Shandong 2. 5D m /s a 6b 1 2D m 550 m m 100 ~ 150 m 感谢刘银萍马国庆在论文研究与写作阶段 300 m ± 800 ~ 900 m m 给予的帮助与支持 1 A N V YA. M Tikhonov A N Arvinen V YA. Ill-posed problems M. WANG Bing-chen Translated. Beijing Geological Publishing House Barbosa V C F Silva J B C. Generalized compact gravity inversion J. Geophysics Last B J Kubik K. Compact gravity inversion J. Geophysics Fig. 7 Result of resistivity for the adjacent profile

6 Li Y G Douglas W. Oldenburg. 3-D inversion of gravity data J. Geophysics Boulanger O Chouteau M. Constraints in 3D gravity inversion J. Geophysical Prospecting Zhdanov M S Ellis R Mukherjee S. Three-dimensional GUO Wu-lin. Wave number method using gravity and magnetic data to determine the base interface in foreign J Geophysical and Geochemical Exploration J regularized focusing inversion of gravity gradient tensor component data J. Geophysics Yunus L E. 2D focusing inversion of gravity data with the use of parameter variation as a stopping criterion J. Journal of the Balkan Geophysical Society ZHOU Wen-na ZENG Zhao-fa DU Xiao-juan et al. Gravity anomaly separation based on empirical mode decomposition J. Global Geology J Rasmussen R Pedersen L B. End corrections in potential WANG Mao-ji. Development and prospect of gravity field modeling J. Geophysical Prospecting Portniaguine O Zhdanov M S. Focusing geophysical inversion images J. Geophysics prospecting in China J. Chinese Journal of Geophysics Suppl C / / WANG Yan-fei. Optimization and regularizing theory J LI Xue-lei LI Wen-cheng WANG Feng-gang et al. Focusing inversion image improvement and application of gravity data J. Global Geology and methods for computational geophysics C / /Chinese Geophysical Society J CHEN Shi ZHANG Jian. The view of the spectral analysis method of gravity potential field J. Progress in 11. Geophysics J

1 3D 211 Vasco 6 V xx = Gρ μ ijk arctan y jz k Routh 7 i = 1 j = 1 k = 1 x i r ijk V xy = - Gρ μ ijk ln( z k + r ) Li 8 ijk Martinez i = 1 j = 1 k = 1

1 3D 211 Vasco 6 V xx = Gρ μ ijk arctan y jz k Routh 7 i = 1 j = 1 k = 1 x i r ijk V xy = - Gρ μ ijk ln( z k + r ) Li 8 ijk Martinez i = 1 j = 1 k = 1 34 1 2015 3 GLOBAL GEOLOGY Vol. 34 No. 1 Mar. 2015 1004 5589 2015 01 0210 09 3D 266580 Tikhonov P631. 11 A doi 10. 3969 /j. issn. 1004-5589. 2015. 01. 025 Three-dimensional focusing inversion of gravity