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

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1 GLOBAL GEOLOGY Vol. 34 No. 1 Mar D Tikhonov P A doi /j. issn Three-dimensional focusing inversion of gravity gradient tensor data based on depth weighting YANG Jiao-jiao LIU Zhan CHEN Xiao-hong XU Kai-jun School of Geosciences in China University of Petroleum Qingdao Shandong China Abstract The focusing inversion method of gravity gradient tensor data based on depth weighting was proposed to avoid resting on phenomenon of inversion results. In the classic Tikhonov regularization theory framework a minimum support functional was introduced to constrain inversion model which can avoid instability of inverse problem solution. And the index depth weighting function was also added in the model objective function to o- vercome the accumulation of density occurring at shallow depths. Some single components of gravity gradient tensor and their joint-components of theoretical models were inverted based on regularized focusing inversion which proves the validity of the regularized focusing inversion method with depth weighting function. The proposed method was applied to the practical data of Sebei 1 gas field and the inversion results could well reflect the position of the gas field. Key words gravity gradient tensor focusing inversion minimum support functional depth weighting function AA09A liuzhan5791@ sina. com

2 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 = V xz = - Gρ μ ijk ln y j + r 11 V yz = - Gρ 12 5 Li V zz = Gρ 13 3 BP x i = x - a i y j = y - b j z k = z - c k r ijk Zhdanov = 槡 x 2 i + y 2 j + z 2 k μ ijk = ( - 1) i +j+k G = cm 3 /g s 2 Wilsond d = Am 7 A A ij i i = m j j = n m 1 d 7 1 A d A = A 1 A 2 A q d = [ d 1 d 2 d q ] A q V d q 3 3 q D V xx V xy V xz G = V yx V yy V yz 1 7 V zx V zy V Tikhonov zz P m = Φ m + αs m min 8 ( a 1 b 1 c ) 1 ( a 2 b 2 c ) 21 Φ m Ф 2 m = W d d obs - Am 2 d obs i = 1 i = 1 i = 1 j = 1 k = 1 j = 1 k = 1 μ ijk ln x i ( ) ijk + r ( ) ijk μ ijk arctan x iy j j = 1 k = 1 z k r ijk

3 W d W d = diag 1 /ε 1 1 /ε 2 1 /ε i ε i i W α s m m = diag F T F 1 /4 13 F 9 10 F = A m - m ref 2 s m = V m - m ref 2 + 2dv 9 β d = A β m β 15 A β = AW - 1 mβ 18 P m = d obs - A β m β T W 2 d d obs - A β m β + [ ω H h j = e λ h j -H ] 0 10 h j j λ H 0 17 λ λ = 1 /H 0 ω β m ω β m = m - m ref ω H m - m ref 2 + β [ 2 ] W m 9 P m = d obs - Am T W 2 d d obs - Am + α m - m ref T ω 2 β W2 m m - m ref β m = 0 m ref m β = ω β W m m = W mβ m 14 α m β - m β ref T m β - m β ref 16 m k + 1 = W - 1 mβ mβ k + 1 = W - 1 m ω - 1 βk m β k + 1 W m α α k = α 0 p k p > 0 18 k α 0 α 2. 3

1 3D 213 16 16 9 m max m min 19 256 2304 A 256 2304 m( j ) m( j ) = m max if( m( j) > m ) = m min if( m( j) < m ) j = 1 2 3... n 3 min max 19 50 m 3.

4 1 3D m max m min A m( j ) m( j ) = m max if( m( j) > m ) = m min if( m( j) < m ) j = n 3 min max m a 150 m 150 m 150 m 100 m 250 m 1. 0 g /cm 3 V zz a b V zz c V zz d V zz. Fig. 1 1 V zz First theoretical model and inversion results of different methods of V zz component

214 34 0. 1 g /cm 3 1. 0 g / cm 3 0 g /cm 3 2 V xy V xx 30 V zz 1 V zz 1a 1d V zz 2 V xy V xx V xx a V xy b V xx c Fig.

5 g /cm g / cm 3 0 g /cm 3 2 V xy V xx 30 V zz 1 V zz 1a 1d V zz 2 V xy V xx V xx a V xy b V xx c Fig. 2 2 V xy V xx Inversion results of V xy component and V xx component and joint-inversion results of three independent components

1 3D 215 V xy V zz 3. 2 Y 3 1 0. 8 g /cm 3 2 1.

4 a 110 m b x = 400 m Joint-inversion results of three independent components Black

6 1 3D 215 V xy V zz 3. 2 Y g /cm g /cm 3 4 4a 4b 110 m x = 400 m 3 Fig. 3 Second theoretical model 4 Fig. 4 a 110 m b x = 400 m Joint-inversion results of three independent components Black box marked range represents true position of anomalous body g /cm V zz ± μgal 5a 5b V zz < m m

216 34 V zz 600 ~ 1 900 m 7 a b V zz 5 V zz Fig.

7 V zz 600 ~ m 7 a b V zz 5 V zz Fig. 5 Gravity anomaly and V zz component contour Fig. 6 6 Distribution of drillings and oil and gas on one line in Sanhu gas field

8 1 3D 217 Fig. 7 a m b MM' 7 V zz Apparent density inversion results of V zz component imaging using gravity and tensor gravity data C / /2001 SEG Annual Meeting SEG Technical Program Expanded 4 Abstracts. San Antonio Society of Exploration Geophysicists Li Y. 3-D inversion of gravity gradiometer data C / / 2001 SEG Annual Meeting SEG Technical Program Expanded Abstracts. San Antonio Society of Exploration 1 Zhdanov M S Liu X Wan L et al. 3D potential field Geophysicists migration for rapid imaging of gravity gradiometry data a 9 Martinez C Li Y Krahenbuhl R et al. 3D Inversion of case study from Broken Hill Australia with comparison airborne gravity gradiomentry for iron ore exploration in to 3D regularized inversion C / /2011 SEG Annual Brazil C / /2010 SEG Annual Meeting SEG Technical Meeting SEG Technical Program Expanded Abstracts. Program Expanded Abstracts. Denver Society of Exploration San Antonio Society of Exploration Geophysicists 2011 Geophysicists airborne gravity gradiometry data in mineral exploration J. a case study in the Quadrilátero Ferrífero Brazil J Geophysics B1-B11. MA Guo-qing DU Xiao-juan LI Li-li. Comparison of the tensor local wavenumber method with the conventional local wavenumber method for interpretation of total tensor data of potential fields J. Chinese Journal of Geophysics J SUN Zhong-ke ZHU Zi-qiang LU Guang-yin et al. Research on gravity tensor inversion based on particle swarm optimization J. Computing Techniques for Geophysical and Geochemical Exploration J YUAN Yuan HUANG Da-nian YU Qing-lu et al. Noise filtering of full gravity gradient tensors data J. Applied Geophysics J WANG Hao-ran CHEN Chao DU Jin-song. 3-D inversion method and application of gravity gradient tensor data J. Oil Geophysical Prospecting Vasco D W Taylor C. Inversion of airborne gravity gradient data southwestern Oklahoma J. Geophysics Routh P S Jorgensen G J Kisabeth J L. Base of the salt 10 Martinez C Li Y Krahenbuhl R et al. 3D inversion of 11. J GUO Liang-hui MENG Xiao-hong SHI Lei et al. 3-D

9 correlation imaging for gravity and gravity gradiometry data J. Chinese Journal of Geophysics Focusing inversion image improvement and application of J. gravity data J. Global Geology CHEN Shao-hua ZHU Zi-qiang LU Guang-yin et al. Inversion of gravity gradient tensor based on preconditioned conjugate gradient J. Journal of Central South University Science and Technology GUO Wen-bin ZHU Zi-qiang LU Guang-yin. Quasi- BP neural network inversion of gravity gradient tensor J. Journal of Central South University Science and Technology Zhdanov M S Ellis R G Mukherjee S et al. Regularized focusing inversion of 3-D gravity tensor data C / / 2002 SEG Annual Meeting SEG Technical Program Expanded Abstracts. Salt Lake City Society of Exploration Geophysicists Zhdanov M S Ellis R Mukherjee S. Three-dimensional regularized focusing inversion of gravity gradient tensor component data J. Geophysics Le W Zhdanov M S. Focusing inversion of marine fulltensor gradiometry data in offshore geophysical exploration C / /2008 SEG Annual Meeting SEG Technical Program Expanded Abstracts. Las Vegas Society of Exploration Geophysicists Wilson G Čuma M Zhdanov M S. Massively parallel 3D inversion of gravity and gravity gradiometry data J. Preview J LI Xue-lei LI Wen-cheng WANG Feng-gang et al D J SUN Rui-xue DU Xiao-juan LIANG Quan-you. 2. 5D dual-weight focusing inversion of gravity and its applica- 13. BP tion J. Global Geology J. 20. J JIANG Fu-yu GAO Li-kun HUANG Lin-yun. Study on gravity gradient tensor of oil-gas model J. Journal of Jilin University Earth Science Edition Pilkington M. Evaluating the utility of gravity gradient tensor components J. Geophysics G1-G C / / LIU Li-jun. Focusing inversion regularization application in gravity gradient independent component C / / Proceedings of the Chinese geophysical society 27th annual meeting. Beijing Chinese Geophysics Society D LIU Xiao-jun. Focusing inversion images of magnetotelluric data Ph'D dissertation D. Shanghai Tongji U- niversity 2007.

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