基于泰勒级数的重力异常数据快速相关成像
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摘要
为了提高重力勘探中数据成像的效率,对地球物理勘探中的重力异常数据进行快速三维成像.在相关成像的理论基础上针对立方体元提出利用泰勒级数的算法,重新定义了异常值的计算模型,从而得到新的几何函数.该成像方法通过级数展开、积分等方式,减少了计算量和迭代次数.在理论模型试验中,证明了提出的方法具有良好的成像能力和抗噪性,并通过效率分析说明了该算法能够大幅缩短几何函数矩阵的计算时间,提高成像效率.对文顿盐丘地区的实测重力异常数据进行快速成像,地质体的位置能够被较好地显示出来,验证了算法的可行性.
In order to improve the data tomography efficiency in the gravity exploration,gravity anomaly data from the geophysical exploration were processed by fast three-dimensional tomography. The algorithm of Taylor series was used for the prism unit based on the related probability tomography theory,in which the calculation model of anomaly data were redefined to obtain new geometric functions. The tomography method reduces the calculation amount and the number of iterations by series expansion and integral. In the theoretical model test,it is proved that the proposed method has good tomography ability and anti-noise characteristic. The efficiency analysis shows that the algorithm can greatly shorten the calculation time of the geometric function matrix and improve the imaging efficiency. Fast tomography was applied for the real gravity anomaly data of Vinton Dome,the location of geological body could be show n w ell,which verifies the algorithm feasible.
In order to improve the data tomography efficiency in the gravity exploration,gravity anomaly data from the geophysical exploration were processed by fast three-dimensional tomography. The algorithm of Taylor series was used for the prism unit based on the related probability tomography theory,in which the calculation model of anomaly data were redefined to obtain new geometric functions. The tomography method reduces the calculation amount and the number of iterations by series expansion and integral. In the theoretical model test,it is proved that the proposed method has good tomography ability and anti-noise characteristic. The efficiency analysis shows that the algorithm can greatly shorten the calculation time of the geometric function matrix and improve the imaging efficiency. Fast tomography was applied for the real gravity anomaly data of Vinton Dome,the location of geological body could be show n w ell,which verifies the algorithm feasible.
引文
[1]Patella D. Introduction to ground surface self-potential tomography[J]. Geophysical Prospecting,1997,45(4):653-681.
[2]Patella D. Self-potential global tomography including topographic effects[J]. Geophysical Prospecting,1997,45(5):843-863.
[3]郭良辉,孟小红,石磊,等.重力和重力梯度数据三维相关成像[J].地球物理学报,2009,52(4):1098-1106.(Guo Liang-hui,Meng Xiao-hong,Shi Lei,et al. 3D correlation imaging for gravity and gravity gradiometry data[J]. Chinese Journal of Geophysics,2009,52(4):1098-1106.)
[4]郭良辉,孟小红,石磊.磁异常ΔT三维相关成像[J].地球物理学报,2010,53(2):435-441.(Guo Liang-hui,Meng Xiao-hong,Shi Lei. 3D correlation imaging for magnetic anomalyΔT data[J]. Chinese Journal of Geophysics,2010,53(2):435-441.)
[5]Guo L H,Meng X H,Shi L. 3D correlation imaging of the vertical gradient of gravity data[J]. Journal of Geophysics and Engineering,2011,8(1):6-12.
[6]Guo L H,Shi L,Meng X H. 3D correlation imaging of magnetic total field anomaly and its vertical gradient[J].Journal of Geophysics and Engineering,2011,8(2):287-293.
[7]Mauriello P,Patella D. Resistivity anomaly imaging by probability tomography[J]. Geophysical Prospecting,1999,47(3):411-429.
[8]Mauriello P,Patella D. Principles of probability tomography for natural-source electromagnetic induction fields[J].Geophysics,1999,64(5):1403-1417.
[9]孟小红,刘国峰,陈召曦,等.基于剩余异常相关成像的重磁物性反演方法[J].地球物理学报,2012,55(1):304-309.(Meng Xiao-hong,Liu Guo-feng,Chen Zhao-xi,et al. 3D gravity and magnetic inversion for physical properties based on residual anomaly correlation[J]. Chinese Journal of Geophysics,2012,55(1):304-309.)
[10]Liu G F,Yan H,Meng X H,et al. An extension of gravity probability tomography imaging[J]. Journal of Applied Geophysics,2014,102:62-67.
[11]Chen Z X,Meng X H,Guo L H,et al. GICUDA:a parallel program for 3D correlation imaging of large scale gravity and gravity gradiometry data on graphics processing units with CUDA[J]. Computers&Geosciences,2012,46:119-128.
[12]侯振隆.重力全张量梯度数据的并行反演算法研究及应用[D].长春:吉林大学,2016.(Hou Zhen-long. Research and application of the parallel inversion algorithms based on the full tensor gravity gradiometry data[D]. Changchun:Jilin University,2016.)
[13]Hou Z L,Huang D N,Wei X H. Fast inversion of probability tomography with gravity gradiometry data based on hybrid parallel programming[J]. Journal of Applied Geophysics,2016,124:27-38.
[14]Hou Z L,Huang D. Multi-GPU parallel algorithm design and analysis for improved inversion of probability tomography with gravity gradiometry data[J]. Journal of Applied Geophysics,2017,144:18-27.
[15]Okabe M. Analytical expressions for gravity anomalies due to homogeneous polyhedral bodies and translations into magnetic anomalies[J]. Geophysics,1979,44(4):730-741.
[16]Steiner F,Zilahi-Sebess L. Interpretation of filtered gravity maps[M]. Budapest:Akademiai Kiado,1988:344-350.
[17]Coker M O,Bhattacharya J P,Marfurt K J. Fracture patterns within mudstones on the flanks of a salt dome:syneresis or slumping?[J]. Gulf Coast Association of Geological Societies,2007,57:125-137.
[18]Ennen C,Hall S. Structural mapping of the Vinton salt dome,Louisiana,using gravity gradiometry data[C]//SEG Annual Meeting. San Antonio,2011:830-835.
[19]Oliveira V C Jr,Barbosa V C F. 3D radial gravity gradient inversion[J]. Geophysical Journal International,2013,195(2):883-902.
[20]秦朋波,黄大年.重力和重力梯度数据联合聚焦反演方法[J].地球物理学报,2016,59(6):2203-2224.(Qin Peng-bo,Huang Da-nian. Integrated gravity and gravity gradient data focusing inversion[J]. Chinese Journal of Geophysics,2016,59(6):2203-2224.)
[2]Patella D. Self-potential global tomography including topographic effects[J]. Geophysical Prospecting,1997,45(5):843-863.
[3]郭良辉,孟小红,石磊,等.重力和重力梯度数据三维相关成像[J].地球物理学报,2009,52(4):1098-1106.(Guo Liang-hui,Meng Xiao-hong,Shi Lei,et al. 3D correlation imaging for gravity and gravity gradiometry data[J]. Chinese Journal of Geophysics,2009,52(4):1098-1106.)
[4]郭良辉,孟小红,石磊.磁异常ΔT三维相关成像[J].地球物理学报,2010,53(2):435-441.(Guo Liang-hui,Meng Xiao-hong,Shi Lei. 3D correlation imaging for magnetic anomalyΔT data[J]. Chinese Journal of Geophysics,2010,53(2):435-441.)
[5]Guo L H,Meng X H,Shi L. 3D correlation imaging of the vertical gradient of gravity data[J]. Journal of Geophysics and Engineering,2011,8(1):6-12.
[6]Guo L H,Shi L,Meng X H. 3D correlation imaging of magnetic total field anomaly and its vertical gradient[J].Journal of Geophysics and Engineering,2011,8(2):287-293.
[7]Mauriello P,Patella D. Resistivity anomaly imaging by probability tomography[J]. Geophysical Prospecting,1999,47(3):411-429.
[8]Mauriello P,Patella D. Principles of probability tomography for natural-source electromagnetic induction fields[J].Geophysics,1999,64(5):1403-1417.
[9]孟小红,刘国峰,陈召曦,等.基于剩余异常相关成像的重磁物性反演方法[J].地球物理学报,2012,55(1):304-309.(Meng Xiao-hong,Liu Guo-feng,Chen Zhao-xi,et al. 3D gravity and magnetic inversion for physical properties based on residual anomaly correlation[J]. Chinese Journal of Geophysics,2012,55(1):304-309.)
[10]Liu G F,Yan H,Meng X H,et al. An extension of gravity probability tomography imaging[J]. Journal of Applied Geophysics,2014,102:62-67.
[11]Chen Z X,Meng X H,Guo L H,et al. GICUDA:a parallel program for 3D correlation imaging of large scale gravity and gravity gradiometry data on graphics processing units with CUDA[J]. Computers&Geosciences,2012,46:119-128.
[12]侯振隆.重力全张量梯度数据的并行反演算法研究及应用[D].长春:吉林大学,2016.(Hou Zhen-long. Research and application of the parallel inversion algorithms based on the full tensor gravity gradiometry data[D]. Changchun:Jilin University,2016.)
[13]Hou Z L,Huang D N,Wei X H. Fast inversion of probability tomography with gravity gradiometry data based on hybrid parallel programming[J]. Journal of Applied Geophysics,2016,124:27-38.
[14]Hou Z L,Huang D. Multi-GPU parallel algorithm design and analysis for improved inversion of probability tomography with gravity gradiometry data[J]. Journal of Applied Geophysics,2017,144:18-27.
[15]Okabe M. Analytical expressions for gravity anomalies due to homogeneous polyhedral bodies and translations into magnetic anomalies[J]. Geophysics,1979,44(4):730-741.
[16]Steiner F,Zilahi-Sebess L. Interpretation of filtered gravity maps[M]. Budapest:Akademiai Kiado,1988:344-350.
[17]Coker M O,Bhattacharya J P,Marfurt K J. Fracture patterns within mudstones on the flanks of a salt dome:syneresis or slumping?[J]. Gulf Coast Association of Geological Societies,2007,57:125-137.
[18]Ennen C,Hall S. Structural mapping of the Vinton salt dome,Louisiana,using gravity gradiometry data[C]//SEG Annual Meeting. San Antonio,2011:830-835.
[19]Oliveira V C Jr,Barbosa V C F. 3D radial gravity gradient inversion[J]. Geophysical Journal International,2013,195(2):883-902.
[20]秦朋波,黄大年.重力和重力梯度数据联合聚焦反演方法[J].地球物理学报,2016,59(6):2203-2224.(Qin Peng-bo,Huang Da-nian. Integrated gravity and gravity gradient data focusing inversion[J]. Chinese Journal of Geophysics,2016,59(6):2203-2224.)
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