磁异常和梯度的频率域三维成像方法
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摘要
三维反演在磁数据定量解释中具有重要作用。常用的空间域三维反演方法通常需要大量的正演和反演计算,因此对大规模数据的反演效率较低。三维成像是另一种定性和定量解释磁数据的重要方法。文中给出了一种磁异常与梯度三维成像的频率域迭代方法,该方法可以提高成像效率,适用于大规模数据的快速成像。笔者推导了磁总场异常和异常梯度频率域正演公式和成像公式,并将一种深度尺度因子引入成像公式中,提高了深度精度;笔者采用了迭代优化算法,减小了拟合误差,进一步提高了成像精度。通过理论模型数据试验和中国新疆某金属矿床实测数据,验证了本文方法的有效性、可行性。
3-D inversion plays an important role in the quantitative interpretation of magnetic data. However,the commonly used spacedomain 3-D inversion algorithms usually require a large number of forward modeling and inversion calculations. Hence,the inversion based on a large-scale data is usually inefficient. 3-D imaging is another significant algorithm for the qualitative and quantitative interpretation of magnetic data. This paper implements a frequency-domain iterative approach for 3-D imaging of magnetic anomalies and gradients,which can improve imaging efficiency and is suitable for rapid imaging of large-scale data. The frequency-domain forward formulae and imaging formulae of magnetic total field anomaly and magnetic gradients are derived in this paper. A depth scaling factor is added to the imaging formulae to significantly improve the depth resolution. In order to reduce the fitting error and improve the imaging accuracy,this paper adopts an iterative optimization algorithm. The effectiveness and feasibility of the presented approach were verified by the synthetic data and real data from a metallic deposit area in Xinjiang.
3-D inversion plays an important role in the quantitative interpretation of magnetic data. However,the commonly used spacedomain 3-D inversion algorithms usually require a large number of forward modeling and inversion calculations. Hence,the inversion based on a large-scale data is usually inefficient. 3-D imaging is another significant algorithm for the qualitative and quantitative interpretation of magnetic data. This paper implements a frequency-domain iterative approach for 3-D imaging of magnetic anomalies and gradients,which can improve imaging efficiency and is suitable for rapid imaging of large-scale data. The frequency-domain forward formulae and imaging formulae of magnetic total field anomaly and magnetic gradients are derived in this paper. A depth scaling factor is added to the imaging formulae to significantly improve the depth resolution. In order to reduce the fitting error and improve the imaging accuracy,this paper adopts an iterative optimization algorithm. The effectiveness and feasibility of the presented approach were verified by the synthetic data and real data from a metallic deposit area in Xinjiang.
引文
[1] Li Y,Oldenburg D W. 3-D inversion of magnetic data[J]. Geophysics,1996,61(2):394-408.
[2] Pilkington M. 3D magnetic data-space inversion with sparseness constraints[J]. Geophysics,2009,74(1):L7-L15.
[3]杨文采.地球物理反演的理论与方法[M].北京:地质出版社,1997.Yang W C. Theory and Method of Geophysical Inversion[M]. Beijing:Geological Publishing House,1997.
[4]管志宁,侯俊胜,黄临平,等.重磁异常反演的拟BP神经网络方法及其应用[J].地球物理学报,1998,41(2):242-251.Guan Z N,Hou J S,Huang L P,et al. Inversion of gravity and magnetic anomalies using pseudo-BP neural network method and its application[J]. Chinese Journal of Geophysics,1998,41(2):242-251.
[5]王万银,冯旭亮,高玲举,等.重磁方法在吐尔库班套铜镍矿区勘查中的应用[J].物探与化探,2014,38(3):423-429.Wang W Y,Feng X L,Gao L J,et al. The application of gravity and magnetic techniques to the prospecting for the Tuerkubantao copper-nickel ore district[J]. Geophysical and Geochemical Exploration,2014,38(3):423-429.
[6] Blakely R J. Potential Theory in Gravity and Magnetic Applications[M]. Cambridge:Cambridge University Press,1995.
[7]李焓,邱之云,王万银.复杂形体重、磁异常正演问题综述[J].物探与化探,2008,32(1):36-43.Li H,Qiu Z Y,Wang W Y. A review of the forward calculation of gravity and magnetic anomalies caused by irregular models[J].Geophysical and Geochemical Exploration,2008,32(1):36-43.
[8] Tikhonov A N,Arsenin V Y. Solutions ofⅢ-posed problems[M].Washington D.C:V. H. Winston&Sons,1977.
[9] Li Y,Oldenburg D W. Fast inversion of large-scale magnetic data using wavelet transforms and a logarithmic barrier method[J]. Geophysics Journal International,2003,152(2):251-265.
[10] Commer M. Three-dimensional gravity modelling and focusing inversion using rectangular meshes[J]. Geophysical Prospecting,2011,59(5):966-979.
[11]姚长利,郝天珧,管志宁.重磁反演约束条件及三维物性反演技术策略[J].物探与化探,2002,26(4):253-257.Yao C L,Hao T Y,Guan Z N. Restrictions in gravity and magnetic inversions and technical strategy of 3D properties inversion[J].Geophysical and Geochemical Exploration,2002,26(4):253-257.
[12] Portniaguine O,Zhdanov M S. Focusing geophysical inversion images[J]. Geophysics,1999,64(3):874-887.
[13] Portniaguine O,Zhdanov M S. 3-D magnetic inversion with data compression and image focusing[J]. Geophysics,2002,67(5):1532-1541.
[14]罗凡,严加永,付光明.基于已知信息约束的重磁三维反演在深部磁铁矿勘查中的应用——以安徽泥河铁矿为例[J].物探与化探,2018,42(1):50-60.Luo F,Yan J Y,Fu G M. The application of gravity and magnetic three-dimensional inversion based on known information constraint in deep magnetite exploration:A case study of the Nihe iron deposit in Anhui Province[J]. Geophysical and Geochemical Exploration,2018,42(1):50-60.
[15] Lv Q,Qi G,Yan J. 3D geologic model of Shizishan ore field constrained by gravity and magnetic interactive modeling:A case history[J]. Geophysics,2012,78(1):B25-B35.
[16] Zhang Y,Yan J,Li F,et al. A new bound constraints method for3-D potential field data inversion using Lagrangian multipliers[J].Geophysical Journal International,2015,201(1):267-275.
[17] Li Y,Oldenburg D W. Joint inversion of surface and three-component borehole magnetic data[J]. Geophysics,2000,65(2):540-552.
[18]姚长利,郝天珧,管志宁,等.重磁遗传算法三维反演中高速计算及有效存储方法技术[J].地球物理学报,2003,46(2):252-258.Yao C L,Hao T Y,Guan Z N,et al. High-speed computation and efficient storage in 3-D gravity and magnetic inversion based on genetic algorithms[J]. Chinese Journal of Geophysics,2003,46(2):252-258.
[19]姚长利,郑元满,张聿文.重磁异常三维物性反演随机子域法方法技术[J].地球物理学报,2007,50(5):1576-1583.Yao C L,Zheng Y M,Zhang Y W. 3-D gravity and magnetic inversion for physical properties using stochastic subspaces[J]. Chinese Journal of Geophysics,2007,50(5):1576-1583.
[20] Vatankhah S,Renaut R A,Ardestani V E. A fast algorithm for regularized focused 3D inversion of gravity data using randomized singular-value decomposition[J]. Geophysics,2018,83(4):G25-G34.
[21] Parker R L. The rapid calculation of potential anomalies[J]. Geophysical Journal International,1973,31(4):447-455.
[22] Oldenburg D W. The inversion and interpretation of gravity anomalies[J]. Geophysics,1974,39(4):526-536.
[23] Cribb J. Application of the generalized linear inverse to the inversion of static potential data[J]. Geophysics,1976,41(6):1365-1369.
[24] Kobrunov A I,Varfolomeev V A. On one method ofε-equivalent redistribution and its practical application in the interpretation of gravity fields[J]. Earth Physics USSR Academy of Science,1981,10:25-44.
[25] Pedersen L B. Relations between potential fields and some equivalent sources[J]. Geophysics,1991,56(7):961-971.
[26] Priezzhev I I. Integrated interpretation technique of geophysical data for geological modeling[D]. Moscow:State university of Sergo ordjonikidze,2010.
[27] Priezzhev I I,Scollard A,Lu Z,Schlumberger. Regional production prediction technology based on gravity and magnetic data from the Eagle Ford formation,Texas,USA[C]//SEG Technical Program Expanded Abstracts,2014,1354-1358.
[28] Kobrunov A I. The method of functional representations in the solution of inverse problems of gravimetry[J]. Izvestiya Physics of the Solid Earth,2015,51(4):459-468.
[29]王万银,刘金兰,邱之云,等.频率域偶层位曲面位场处理和转换方法研究[J].地球物理学报,2009,52(10):2652-2665.Wang W Y,Liu J L,Qiu Z Y,et al. The research of the frequency domain dipole layer method for the processing and transformation of potential field on curved surface[J]. Chinese Journal of Geophysics,2009,52(10):2652-2665.
[30]程振炎.重磁场的有限元法曲化平[J].物探与化探,1981,5(3):153-158.Cheng Z Y.Curved leveling of gravity and magnetic field by finite element method[J]. Geophysical and Geochemical Exploration,1981,5(3):153-158.
[31]刘天佑,刘大为,詹应林,等.磁测资料处理新方法及在危机矿山挖潜中的应用[J].物探与化探,2006,30(5):377-381,396.Liu T Y,Liu D W,Shan Y L,et al. A new method of magnetic survey data processing and its application in tapping potential of crisis mines[J]. Geophysical and Geochemical Exploration,2006,30(5):377-381,396.
[32] Guo L,Yan J. 3-D wavelet-based fusion approach for comprehensively analyzing multiple physical-property voxel models inverted from magnetic data[J]. Journal of Applied Geophysics,2017,139:47-53.
[2] Pilkington M. 3D magnetic data-space inversion with sparseness constraints[J]. Geophysics,2009,74(1):L7-L15.
[3]杨文采.地球物理反演的理论与方法[M].北京:地质出版社,1997.Yang W C. Theory and Method of Geophysical Inversion[M]. Beijing:Geological Publishing House,1997.
[4]管志宁,侯俊胜,黄临平,等.重磁异常反演的拟BP神经网络方法及其应用[J].地球物理学报,1998,41(2):242-251.Guan Z N,Hou J S,Huang L P,et al. Inversion of gravity and magnetic anomalies using pseudo-BP neural network method and its application[J]. Chinese Journal of Geophysics,1998,41(2):242-251.
[5]王万银,冯旭亮,高玲举,等.重磁方法在吐尔库班套铜镍矿区勘查中的应用[J].物探与化探,2014,38(3):423-429.Wang W Y,Feng X L,Gao L J,et al. The application of gravity and magnetic techniques to the prospecting for the Tuerkubantao copper-nickel ore district[J]. Geophysical and Geochemical Exploration,2014,38(3):423-429.
[6] Blakely R J. Potential Theory in Gravity and Magnetic Applications[M]. Cambridge:Cambridge University Press,1995.
[7]李焓,邱之云,王万银.复杂形体重、磁异常正演问题综述[J].物探与化探,2008,32(1):36-43.Li H,Qiu Z Y,Wang W Y. A review of the forward calculation of gravity and magnetic anomalies caused by irregular models[J].Geophysical and Geochemical Exploration,2008,32(1):36-43.
[8] Tikhonov A N,Arsenin V Y. Solutions ofⅢ-posed problems[M].Washington D.C:V. H. Winston&Sons,1977.
[9] Li Y,Oldenburg D W. Fast inversion of large-scale magnetic data using wavelet transforms and a logarithmic barrier method[J]. Geophysics Journal International,2003,152(2):251-265.
[10] Commer M. Three-dimensional gravity modelling and focusing inversion using rectangular meshes[J]. Geophysical Prospecting,2011,59(5):966-979.
[11]姚长利,郝天珧,管志宁.重磁反演约束条件及三维物性反演技术策略[J].物探与化探,2002,26(4):253-257.Yao C L,Hao T Y,Guan Z N. Restrictions in gravity and magnetic inversions and technical strategy of 3D properties inversion[J].Geophysical and Geochemical Exploration,2002,26(4):253-257.
[12] Portniaguine O,Zhdanov M S. Focusing geophysical inversion images[J]. Geophysics,1999,64(3):874-887.
[13] Portniaguine O,Zhdanov M S. 3-D magnetic inversion with data compression and image focusing[J]. Geophysics,2002,67(5):1532-1541.
[14]罗凡,严加永,付光明.基于已知信息约束的重磁三维反演在深部磁铁矿勘查中的应用——以安徽泥河铁矿为例[J].物探与化探,2018,42(1):50-60.Luo F,Yan J Y,Fu G M. The application of gravity and magnetic three-dimensional inversion based on known information constraint in deep magnetite exploration:A case study of the Nihe iron deposit in Anhui Province[J]. Geophysical and Geochemical Exploration,2018,42(1):50-60.
[15] Lv Q,Qi G,Yan J. 3D geologic model of Shizishan ore field constrained by gravity and magnetic interactive modeling:A case history[J]. Geophysics,2012,78(1):B25-B35.
[16] Zhang Y,Yan J,Li F,et al. A new bound constraints method for3-D potential field data inversion using Lagrangian multipliers[J].Geophysical Journal International,2015,201(1):267-275.
[17] Li Y,Oldenburg D W. Joint inversion of surface and three-component borehole magnetic data[J]. Geophysics,2000,65(2):540-552.
[18]姚长利,郝天珧,管志宁,等.重磁遗传算法三维反演中高速计算及有效存储方法技术[J].地球物理学报,2003,46(2):252-258.Yao C L,Hao T Y,Guan Z N,et al. High-speed computation and efficient storage in 3-D gravity and magnetic inversion based on genetic algorithms[J]. Chinese Journal of Geophysics,2003,46(2):252-258.
[19]姚长利,郑元满,张聿文.重磁异常三维物性反演随机子域法方法技术[J].地球物理学报,2007,50(5):1576-1583.Yao C L,Zheng Y M,Zhang Y W. 3-D gravity and magnetic inversion for physical properties using stochastic subspaces[J]. Chinese Journal of Geophysics,2007,50(5):1576-1583.
[20] Vatankhah S,Renaut R A,Ardestani V E. A fast algorithm for regularized focused 3D inversion of gravity data using randomized singular-value decomposition[J]. Geophysics,2018,83(4):G25-G34.
[21] Parker R L. The rapid calculation of potential anomalies[J]. Geophysical Journal International,1973,31(4):447-455.
[22] Oldenburg D W. The inversion and interpretation of gravity anomalies[J]. Geophysics,1974,39(4):526-536.
[23] Cribb J. Application of the generalized linear inverse to the inversion of static potential data[J]. Geophysics,1976,41(6):1365-1369.
[24] Kobrunov A I,Varfolomeev V A. On one method ofε-equivalent redistribution and its practical application in the interpretation of gravity fields[J]. Earth Physics USSR Academy of Science,1981,10:25-44.
[25] Pedersen L B. Relations between potential fields and some equivalent sources[J]. Geophysics,1991,56(7):961-971.
[26] Priezzhev I I. Integrated interpretation technique of geophysical data for geological modeling[D]. Moscow:State university of Sergo ordjonikidze,2010.
[27] Priezzhev I I,Scollard A,Lu Z,Schlumberger. Regional production prediction technology based on gravity and magnetic data from the Eagle Ford formation,Texas,USA[C]//SEG Technical Program Expanded Abstracts,2014,1354-1358.
[28] Kobrunov A I. The method of functional representations in the solution of inverse problems of gravimetry[J]. Izvestiya Physics of the Solid Earth,2015,51(4):459-468.
[29]王万银,刘金兰,邱之云,等.频率域偶层位曲面位场处理和转换方法研究[J].地球物理学报,2009,52(10):2652-2665.Wang W Y,Liu J L,Qiu Z Y,et al. The research of the frequency domain dipole layer method for the processing and transformation of potential field on curved surface[J]. Chinese Journal of Geophysics,2009,52(10):2652-2665.
[30]程振炎.重磁场的有限元法曲化平[J].物探与化探,1981,5(3):153-158.Cheng Z Y.Curved leveling of gravity and magnetic field by finite element method[J]. Geophysical and Geochemical Exploration,1981,5(3):153-158.
[31]刘天佑,刘大为,詹应林,等.磁测资料处理新方法及在危机矿山挖潜中的应用[J].物探与化探,2006,30(5):377-381,396.Liu T Y,Liu D W,Shan Y L,et al. A new method of magnetic survey data processing and its application in tapping potential of crisis mines[J]. Geophysical and Geochemical Exploration,2006,30(5):377-381,396.
[32] Guo L,Yan J. 3-D wavelet-based fusion approach for comprehensively analyzing multiple physical-property voxel models inverted from magnetic data[J]. Journal of Applied Geophysics,2017,139:47-53.
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