混合多重二次插值在三维地层可视化中的应用
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摘要
地质曲面插值重构是三维地质建模的一个研究热点。针对稀疏的地质钻孔数据,提出了一种基于多重二次曲面和反距离加权的组合插值方法——混合多重二次曲面插值方法(MMQS)。为了检验MMQS的精度,以peaks曲面作为先验曲面模拟起伏的地质界面、采用均方根误差(RMSE)和平均绝对百分比误差(MAPE)作为曲面拟合效果的检验标准,验证了MMQS方法比常规的多重二次曲面插值方法有较好的插值精度。MMQS算法易于编程。把MMQS方法运用到地质界面重构中,在VB.net与IDL平台上开发了三维地层可视化系统3D Geo Vis。采用3D Geo Vis对某工程场区进行了三维地层插值和可视化,显示了3D Geo Vis的有效性和便易性。
The reconstruction of geological interfaces is a hot problem in 3D geology modeling field. A new interpolation method based on the combination of multiple quadratic surface interpolation( MQS) and inverse distance weighting interpolation( IDW),named Mixing Multiple Quadratic Surface( MMQS),is proposed to reconstruct stratum interfaces with sparse borehole data. To demonstrate the accuracy of MMQS,the classic curved surface"Peak"was chosen as a maternal sample of geological interface for interpolation,root mean square error(RMSE)and mean absolute percentage error( MAPE) were taken as standards for accuracy examination. By this way,MMQS was proved to have higher interpolation accuracy than conventional MQS. A 3D stratum visualization software system3 D Geo Vis was developed with MMQS by using VB. net & IDL. As an example,the 3D Geo Vis was applied to an actual project geological map visualization. The good performance of 3D Geo Vis in this example shows that it is an effective and convenient tool for 3 dimensional geological mapping and visualization.
The reconstruction of geological interfaces is a hot problem in 3D geology modeling field. A new interpolation method based on the combination of multiple quadratic surface interpolation( MQS) and inverse distance weighting interpolation( IDW),named Mixing Multiple Quadratic Surface( MMQS),is proposed to reconstruct stratum interfaces with sparse borehole data. To demonstrate the accuracy of MMQS,the classic curved surface"Peak"was chosen as a maternal sample of geological interface for interpolation,root mean square error(RMSE)and mean absolute percentage error( MAPE) were taken as standards for accuracy examination. By this way,MMQS was proved to have higher interpolation accuracy than conventional MQS. A 3D stratum visualization software system3 D Geo Vis was developed with MMQS by using VB. net & IDL. As an example,the 3D Geo Vis was applied to an actual project geological map visualization. The good performance of 3D Geo Vis in this example shows that it is an effective and convenient tool for 3 dimensional geological mapping and visualization.
引文
[1]Ming J,Pan M,Qu H G,et al.GSIS:A 3D geological multi-body modeling system from netty cross-sections with topology[J].Computers&Geosciences,2010,36(6):756-767.
[2]Wellmann J F,Horowitz F G,Schill E,et al.Towards incorporating uncertainty of structural data in 3D geological inversion[J].Tectonophysics,2010,490(3-4):141-151.
[3]Houlding S W.3D Geoscience Modeling:Computer techniques for geological characterization[M].Berlin:Springer-Verlag,1994.
[4]Mallet J L.Discrete modeling for nature objects[J].Mathematical Geology,1997,29(2):199-218.
[5]Kemp E A D,Sqrague K B.Interpretive tools for 3D structure geological modeling Part I:Bezier-based curves,ribbons and grip frames[J].Geolnformatica,2003,7(1):55-71.
[6]芮小平,余志伟,许友志,等.多重二次曲面插值法在地质曲面拟合中的应用[J].中国矿业大学学报,2000,29(4):377-380.(Rui Xiaoping,Yu Zhiwei,Xu Youzhi,et al.Application of multiple quadric interpolation in fitting geological surfaces[J].Journal of China University of Mining&Technology,2000,29(4):377-380.(in Chinese))
[7]方海东,刘义怀,施斌,等.三维地质建模及其工程应用[J].水文地质工程地质,2002,29(3):52-54.(Fang Haidong,Liu Yihuai,Shi Bin,et al.3D geoscience modeling and its engineering application[J].Hydrogeology&Engineering Geology,2002,29(3):52-54.(in Chinese))
[8]李晓军,王长虹,朱合华.Kriging插值方法在地层模型生成中的应用[J].岩土力学,2009,30(1):157-162.(Li Xiaojun,Wang Changhong,Zhu Hehua.Kring interpolation and its application to generation stratum model[J].Rock and Soil Mechanics,2009,30(1):157-162.(in Chinese))
[9]郭艳军,潘懋,燕飞,等.自然邻点插值方法在三维地质建模中的应用[J].解放军理工大学学报(自然科学版),2009,10(6):650-655.(Guo Yanjun,Pan Mao,Yan Fei,et al.Application of natural neighbor interpolation method in three-dimensional geological modeling[J].Journal of PLA University of Science and Technology(Natural Science Edition),2009,10(6):650-655.(in Chinese))
[10]李明超,缪正建,刘菲,等.复杂地质曲面三维插值—逼近拟合构造方法[J].中国工程科学,2011,13(12):103-107.(Li Mingchao,Miao Zhengjian,Liu Fei,et al.3D interpolation-approximation fitting construction method for complex geological surfaces[J].Engineering Sciences,2011,13(12):103-107.(in Chinese))
[11]Kumar J K,Konno M,Yasuda N.Subsurface soilgeology interpolation using fuzzy neural network[J].Journal of Geotechnical and Geoenvironmental Engineering,2000,126(7):632-639.
[12]Smirnoff A,Boisvert E,Paradis S J.Support vector machine for 3D modelling from sparse geological information of various origins[J].Computers and Geosciences,2008,34(2):127-143.
[13]Hardy R L.Research results in the application of mutiquadric equations to surveying and mapping problems[J].Surveying and Mapping,1975,35(2):321-332.
[14]Shepard D.A two-dimensional interpolation function for irregularly-spaced data[A]//Proceedings of the 196823rd ACM national conference[C].ACM:1968:517-524.
[15]Barber C B,Dobkin D P,Huhdanpaa H.The quickhull algorithm for convex hulls[J].ACM Transactions on Mathematical Software,1996,22(4):469-483.
[16]Yao X L,Fu B J,LüY H,et al.Comparison of four spatial interpolation methods for estimating soil moisture in a complex terrain catchment[J].Plos One,2013,1(8):1-13.
[2]Wellmann J F,Horowitz F G,Schill E,et al.Towards incorporating uncertainty of structural data in 3D geological inversion[J].Tectonophysics,2010,490(3-4):141-151.
[3]Houlding S W.3D Geoscience Modeling:Computer techniques for geological characterization[M].Berlin:Springer-Verlag,1994.
[4]Mallet J L.Discrete modeling for nature objects[J].Mathematical Geology,1997,29(2):199-218.
[5]Kemp E A D,Sqrague K B.Interpretive tools for 3D structure geological modeling Part I:Bezier-based curves,ribbons and grip frames[J].Geolnformatica,2003,7(1):55-71.
[6]芮小平,余志伟,许友志,等.多重二次曲面插值法在地质曲面拟合中的应用[J].中国矿业大学学报,2000,29(4):377-380.(Rui Xiaoping,Yu Zhiwei,Xu Youzhi,et al.Application of multiple quadric interpolation in fitting geological surfaces[J].Journal of China University of Mining&Technology,2000,29(4):377-380.(in Chinese))
[7]方海东,刘义怀,施斌,等.三维地质建模及其工程应用[J].水文地质工程地质,2002,29(3):52-54.(Fang Haidong,Liu Yihuai,Shi Bin,et al.3D geoscience modeling and its engineering application[J].Hydrogeology&Engineering Geology,2002,29(3):52-54.(in Chinese))
[8]李晓军,王长虹,朱合华.Kriging插值方法在地层模型生成中的应用[J].岩土力学,2009,30(1):157-162.(Li Xiaojun,Wang Changhong,Zhu Hehua.Kring interpolation and its application to generation stratum model[J].Rock and Soil Mechanics,2009,30(1):157-162.(in Chinese))
[9]郭艳军,潘懋,燕飞,等.自然邻点插值方法在三维地质建模中的应用[J].解放军理工大学学报(自然科学版),2009,10(6):650-655.(Guo Yanjun,Pan Mao,Yan Fei,et al.Application of natural neighbor interpolation method in three-dimensional geological modeling[J].Journal of PLA University of Science and Technology(Natural Science Edition),2009,10(6):650-655.(in Chinese))
[10]李明超,缪正建,刘菲,等.复杂地质曲面三维插值—逼近拟合构造方法[J].中国工程科学,2011,13(12):103-107.(Li Mingchao,Miao Zhengjian,Liu Fei,et al.3D interpolation-approximation fitting construction method for complex geological surfaces[J].Engineering Sciences,2011,13(12):103-107.(in Chinese))
[11]Kumar J K,Konno M,Yasuda N.Subsurface soilgeology interpolation using fuzzy neural network[J].Journal of Geotechnical and Geoenvironmental Engineering,2000,126(7):632-639.
[12]Smirnoff A,Boisvert E,Paradis S J.Support vector machine for 3D modelling from sparse geological information of various origins[J].Computers and Geosciences,2008,34(2):127-143.
[13]Hardy R L.Research results in the application of mutiquadric equations to surveying and mapping problems[J].Surveying and Mapping,1975,35(2):321-332.
[14]Shepard D.A two-dimensional interpolation function for irregularly-spaced data[A]//Proceedings of the 196823rd ACM national conference[C].ACM:1968:517-524.
[15]Barber C B,Dobkin D P,Huhdanpaa H.The quickhull algorithm for convex hulls[J].ACM Transactions on Mathematical Software,1996,22(4):469-483.
[16]Yao X L,Fu B J,LüY H,et al.Comparison of four spatial interpolation methods for estimating soil moisture in a complex terrain catchment[J].Plos One,2013,1(8):1-13.