Full-Text Search：
《Chinese Journal of Geophysics》 2012-10

## Iterative solution of integral equation for potential field continuation from an irregular surface to a horizontal plane

LIU Dong-Jia1,HONG Tian-Qiu1,LIAO Xu-Tao1,ZHANG Guo-Hong2,JIA Zhi-Hai1,LU Zhi-Tang1 1 School of Resources and Environmental Engineering,Hefei University of Technology,Hefei 230009,China 2 Anhui Institute of Geophysical and Geochemical Prospecting Techniques,Hefei 230022,China
A new method is proposed for continuation of the potential field from a measurement surface S to a horizontal plane P which lies below S.Given the potential field on S and relative elevation between S and P,we want to determine the potential field on P.According to the integral formula of upward continuation from P to S,an integral equation is established which is determined by the potential field on S,the potential field on P and the relative elevation,and it is a Fredholm integral equation of the first kind.The integral formula is changed from space domain to wave number domain by the inverse Fourier transform formula,and is further changed into a series by the Taylor expansion of the exponential function.Solution of the integral equation is gained by successive approximation iteration.That is,observation values of potential field on S are used as an initial guess of potential field on P,and theoretical values of potential field on S are calculated by the series,and the values of potential field on P is corrected by the difference between the observation values and the theoretical values,and multiple iterations are made until the termination criterion is satisfied.Wave number domain iteration method is also given for solving the integral equation.Theoretical examples show that the rms error between the reduction anomaly and the theoretical anomaly is 0.0008 mGal for the gravity model,and is 0.0019 nT for the magnetic model,and the reduction time is 975 s for a grid of 2048×2048 points by a notebook computer of which main frequency is 2.26 GHz.A field magnetic example demonstrates the validity of the approach.
【Fund】： 安徽省国土资源厅重点项目(08-g-16)和科研项目(2010-g-32);; 中国地质调查局项目(1212011220548)资助
【CateGory Index】： P631
CAJViewer7.0 supports all the CNKI file formats; AdobeReader only supports the PDF format.
 【Citations】
 Chinese Journal Full-text Database 10 Hits
 1 Du VE-BEN(The Geophysical Prospecting Co. Ministry of Metallurgical Industry);A NEW METHOD OF REDUCING FROM AN ARBITRARY SURFACE INTO A PLANE FOR THE THREE DIMENSIONAL MAGNETIC AND GRAVITY FIELD[J];Chinese Journal of Geophysics;1982-01 2 CHEN ZHONG-QI;PRINCIPLE AND COMPUTATIONAL METHOD OF CURVED SURFACE'S CONTINUATION OF POTENTIAL FIELD FOR EQUIVALENTLY DIPOLAR LAYER'S METHOD[J];Chinese Journal of Geophysics;1983-01 3 HOU CHONG-CHU CAI ZONG-XI LIU KUI-JUN (Beijing Computer Center, Ministry of Geology and Mineral Resources);INTERPRETATION SYSTEM OF POTENTIAL FIELDTRANSFORMATION ON AN UNEVEN SURFACEFROM THE POTENTIAL OF DOUBLE LAYER[J];Chinese Journal of Geophysics;1985-04 4 GuAN ZHI-NING AN YU-LIN (Beijing Graduate School of Wuhan Geological College)CHEN WEI-XIONG (Beijing Computer, Center Ministry of Geology and Mineral Resources);UPWARD CONTINUATION AND TRANSFORMATION OFCOMPONENT OF MAGNETIC FIELD ON AN UNDULATINGOBSERVED PROFILE OR SURFACE[J];Chinese Journal of Geophysics;1985-04 5 LIU Tian-You,YANG Yu-Shan,LI Yuan-Yuan,FENG Jie,WU Xiao-YangChina University of Geosciences,Wuhan 430074,China;The order-depression solution for large-scale integral equation and its application in the reduction of gravity data to a horizontal plane[J];Chinese Journal of Geophysics;2007-01 6 LIU Jin-Lan~1,WANG Wan-Yin~1,YU Chang-Chun~2 1 College of Geology Engineering and Geomatics,Chang'an University,Xi'an 710054,China2 China Aero Geophysical Survey & Remote Sensing Center for Land and Resources,Beijing 100083,China;Reduction of potential field data to a horizontal plane by a successive approximation procedure[J];Chinese Journal of Geophysics;2007-05 7 XU Shi-Zhe,YU Hai-LongDepartment of Earth Sciences,Zhejiang University,Hangzhou 310027,China;The interpolation-iteration method for potential field continuation from undulating surface to plane[J];Chinese Journal of Geophysics;2007-06 8 LIU Dong-Jia~1,HONG Tian-Qiu~1,JIA Zhi-Hai~1,LI Jian-She~2, LU San-Ming~2,SUN Xiao-Feng~2,XU Shi-Zhe~3 1 School of Resources and Environmental Engineering,Hefei University of Technology,Hefei 230009,China 2 Nonprofit Management Centre of Geological Survey in Anhui Province,Hefei 230001,China 3 Department of Earth Sciences,Zhejiang University,Hangzhou 310027,China;Wave number domain iteration method for downward continuation of potential fields and its convergence[J];Chinese Journal of Geophysics;2009-06 9 WANG Wan-Yin~(1,2),LIU Jin-Lan~(1,2),QIU Zhi-Yun~(1,2),YU Chang-Chun~3, HUANG Yi-Jian~(1,2)1 College of Geology Engineering and Geornatics,Chang an University, Xi'an 710054, China2 Key Laboratory of Western China's Mineral Resources and Geological Engineering , Ministry of Education,Chang an University , Xi'an 710054, China3 China AeroGeophysical Survey & Remote Sensing Center for Land and Resource , Beijing 100083, China;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;2009-10 10 Yang Zaichao:;The datuming of gravitational potential fields with the use of iteration method,[J];Oil Geophysical Prospecting;1989-02
 【Co-citations】
 Chinese Journal Full-text Database 10 Hits
 1 Liu Xiaohua Zou Xinmin(Department of Geophysics);THE THEORY OF DIFFERENTIAL REDUCTION TO THE POLE OF MAGNETIC ANOMALIES[J];;1993-01 2 LU Peng-yu College of GeoExploration Science and Technology,Jilin University,Changchun 130026,China;Two-dimensional Microgravity Measurement and Target Detection Rate[J];Journal of Jilin University(Earth Science Edition);2010-S1 3 ZHAI Guojun1,BIAN Guanglang1,2,HUANG Motao1 1.Naval Institute of Hydrographic Surveying and Charting,Tianjin 300061,China;2.Department of Hydrography and Cartography,Dalian Naval Academy,Dalian 116018,China;A New Method to Calculate the Vertical Derivatives of Total Field Magnetic Anomaly[J];Acta Geodaetica et Cartographica Sinica;2011-06 4 SUI Su-wen, YU Chang-chun, XIONG Sheng-qing(China Aero geophysical Survey and Remote Sensing center for Land and Resources, Beijing 100083, China);Apparent magnetization mapping from high resolution aero magnetic data in the region of high topographic relief[J];Progress In Geophysics;2004-02 5 CHEN Shi,ZHANG Jian(Laboratory of Computational Geodynamics,Graduate School of Chinese Academy of Sciences,Beijing 100039,China);The view of the spectral analysis method of gravity potential field[J];Progress in Geophysics;2006-04 6 TANG Jing-tian,REN Zheng-yong,HUA Xi-rui(1.School of Info-physics and Geomatics Engineering,Central South University, Changsha 400083,China);Triangle and tetrahedral finite element meshing from arbitrary geophysical model data[J];Progress in Geophysics;2006-04 7 YU Chang-Chun,FAN Zheng-Guo,WANG Nai-Dong,XIONG Sheng-Qing,WAN Jian-Hua,ZHANG Hong-Rui(China Aero geophysical Survey and Remote Sensing center for Land and Resources,Beijing 100083,China);High-resolution aeromagnetic exploration methods and their application in daye iron mines[J];Progress in Geophysics;2007-03 8 XU Tian-he1,GAN Yue-hong2(1 Xi'an Research Institute of Surveying and Mapping,Xi'an 710054,China;2 Nanchang Institute of Aeronautical Technology,Nanchang 330036,China);CHAMP Gravity field recovery based on the improved energy conservation approach[J];Progress in Geophysics;2008-01 9 SUN Gang1,XU Bing1,HAN Yan2(1.Institute of Mineral Resources Prediction of Synthetic Information,Jilin University,Changchun 130026,China;2.Mathematics School & Institute,Jilin University,Changchun 130026,China);Research and application on the method of restricted kriging in geology[J];Progress in Geophysics;2008-02 10 XIAO Zhong-xiang1,XU Rui2(1.College of Petroleum Resources,Xi′an Shiyou University,Xi′an 710065,China;2.Tuha Business Division,China Petroleum Logging CO.LTD.,Shanshan 838202,China);Study of the method to extract oil-water interface automatically from MDT data[J];Progress in Geophysics;2008-06
 【Secondary Citations】
 Chinese Journal Full-text Database 10 Hits
 1 CHENG Qiu-ming 1,2 (1.Laboratory of Earth Systems and Mineral Resources Engineering, China University of Geosciences, Wuhan430074, China; 2.Department of Earth and Atmospheric Science, York University, Toronto, CanadaM3J1P3);Non-Linear Mineralization Model and Information Processing Methods for Prediction of Unconventional Mineral Resources[J];;2003-04 2 CHENG Qiu-ming~(1,2) 1.Key Lab of Lithosphere Evolution and Mineral Resources, China University of Geosciences, Wuhan430074,China 2.Department of Earth and Space Science and Department of Geography, York University, Toronto-M3J 1P3 Canada;Quantifying the Generalized Self-Similarity of Spatial Patterns for Mineral Resource Assessment[J];;2004-06 3 CHEN ZHONG-QI;PRINCIPLE AND COMPUTATIONAL METHOD OF CURVED SURFACE'S CONTINUATION OF POTENTIAL FIELD FOR EQUIVALENTLY DIPOLAR LAYER'S METHOD[J];Chinese Journal of Geophysics;1983-01 4 HOU CHONG-CHU CAI ZONG-XI LIU KUI-JUN (Beijing Computer Center, Ministry of Geology and Mineral Resources);POTENTIAL TRANSFORMATION TECHNIQUES ON AN UNDULATING OBSERVED PROFILE[J];Chinese Journal of Geophysics;1984-06 5 HOU CHONG-CHU CAI ZONG-XI LIU KUI-JUN (Beijing Computer Center, Ministry of Geology and Mineral Resources);INTERPRETATION SYSTEM OF POTENTIAL FIELDTRANSFORMATION ON AN UNEVEN SURFACEFROM THE POTENTIAL OF DOUBLE LAYER[J];Chinese Journal of Geophysics;1985-04 6 GuAN ZHI-NING AN YU-LIN (Beijing Graduate School of Wuhan Geological College)CHEN WEI-XIONG (Beijing Computer, Center Ministry of Geology and Mineral Resources);UPWARD CONTINUATION AND TRANSFORMATION OFCOMPONENT OF MAGNETIC FIELD ON AN UNDULATINGOBSERVED PROFILE OR SURFACE[J];Chinese Journal of Geophysics;1985-04 7 LIANG JIN-WEN(Guilin College of Geology);DOWNWARD CONTINUATION OF REGULARIZATION METHODS FOR POTENTIAL FIELDS[J];Chinese Journal of Geophysics;1989-05 8 WANG Xing-Tao XIA Zhe-Ren SHI Pan SUN Zhong-Miao Xi'an Research Institute of Surveying and Mapping, Xi'an 710054, China;A COMPARISON OF DIFFERENT DOWNWARD CONTINUATION METHODS FOR AIRBORNE GRAVITY DATA[J];Chinese Journal of Geophysics;2004-06 9 XU Shi-Zhe 1 SHEN Xiao-Hua 1 ZOU Le-Jun 1 YANG Hua 2 1 Department of Geosciences,Zhejiang University,Hangzhou 310027,China 2 Aero-Geophysical and Remote Sensing Center,China Geology Survey,Beijing 100083,China;DOWNWARD CONTINUATION OF AEROMAGNETIC ANOMALY FROM FLYING ALTITUDE TO TERRAIN[J];Chinese Journal of Geophysics;2004-06 10 XU Shi-ZheDepartment of Earth Sciences,Zhejiang University,Hangzhou 310027,China;The integral-iteration method for continuation of potential fields[J];Chinese Journal of Geophysics;2006-04
Similar Journals
 > Acta Scientiarum Naturalium Universitatis Pekinensis > Journal of Lanzhou University(Natural Sciences) > Acta Physica Sinica > Journal of University of Science and Technology Beijing > Journal of Sichuan University(Natural Science Edition) > Journal of Northeastern University(Natural Science) > Journal of Jilin University(Science Edition) > Chinese Science Bulletin > Acta Mathematica Sinica > Advances In Mathematics