空间域和频率域平面位场延拓影响因素和稳定性分析
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摘要
位场延拓是重、磁位场数据处理的重要方法之一,高精度的位场延拓结果对后续的数据处理和解释尤为重要。笔者从平面位场延拓的基本公式出发,分析了空间域和频率域位场延拓结果精度的影响因素以及稳定性。通过理论模型测试比较了这些影响因素(场源体顶面埋深、剖面长度、扩边方法、窗口大小、点距和延拓高度)在空间域和频率域进行位场延拓时的异同性。经过测试表明,点距和延拓高度对延拓结果的影响最大,其次是剖面长度、扩边方法以及窗口大小,场源体的顶面埋深影响最小。随着顶面埋深的增大,会使延拓结果的精度降低;增大剖面长度和进行扩边会提高位场延拓结果的精度;选择合适滑动窗口可以提高计算效率,窗口越大延拓结果精度越高,窗口半径一般选择20倍延拓高度。空间域和频率域中位场延拓结果精度相当,但在空间域中,当延拓高度小于1倍点距时,延拓结果误差很大,此时需要用插值方法加密点距。
Potential field continuation is one of the important methods of gravity and magnetic potential field data processing,and obtaining high-precision continuation results is particularly important for subsequent data processing and interpretation. Starting with the basic formula of plane potential field continuation,the authors analyzed the factors and the stability that affect the accuracy of continuation results in space and frequency domains. Using the theory model,the authors investigated the buried depth of the top surface of the field source,the length of the section,the method of edge enlargement,the size of the window,the dot pitch and the continuation height,and compared the different influences of these factors in space domain and frequency domain. The theory model test shows that the dot pitch and continuation height have the greatest influence on the continuation results,followed by the section length,the method of edge enlargement and the size of window,with the top surface of the field source exhibiting minimal influence. With the increase of the top surface's depth,the continuation results accuracy is reduced. Increasing and expanding the length of the section will improve the accuracy of the field continuation results. Selecting the appropriate sliding window can improve the calculation efficiency,with the increasing window radius,the accuracy of the field continuation results is improved,and it can generally be chosen as 20 times of the continuation distance. The accuracy of the field continuation results have similarity in space domain and frequency domain; nevertheless,in space domain,the continuation error is very large when the continuation distance is less than 1 time of the dot pitch,so it needs to encrypt the dot pitch by using the interpolation method in this situation.
Potential field continuation is one of the important methods of gravity and magnetic potential field data processing,and obtaining high-precision continuation results is particularly important for subsequent data processing and interpretation. Starting with the basic formula of plane potential field continuation,the authors analyzed the factors and the stability that affect the accuracy of continuation results in space and frequency domains. Using the theory model,the authors investigated the buried depth of the top surface of the field source,the length of the section,the method of edge enlargement,the size of the window,the dot pitch and the continuation height,and compared the different influences of these factors in space domain and frequency domain. The theory model test shows that the dot pitch and continuation height have the greatest influence on the continuation results,followed by the section length,the method of edge enlargement and the size of window,with the top surface of the field source exhibiting minimal influence. With the increase of the top surface's depth,the continuation results accuracy is reduced. Increasing and expanding the length of the section will improve the accuracy of the field continuation results. Selecting the appropriate sliding window can improve the calculation efficiency,with the increasing window radius,the accuracy of the field continuation results is improved,and it can generally be chosen as 20 times of the continuation distance. The accuracy of the field continuation results have similarity in space domain and frequency domain; nevertheless,in space domain,the continuation error is very large when the continuation distance is less than 1 time of the dot pitch,so it needs to encrypt the dot pitch by using the interpolation method in this situation.
引文
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[10]王彦国.位场数据处理的高精度方法研究及应用[D].长春:吉林大学.2013.Wang Y G. Study and application of high-precision methods in potential-field data processing[D]. Changchun:Jilin University,2013.
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[13]吴姿颖,邓居智,王彦国,等.重力向下延拓的迭代法对比分析研究[J].物探与化探计算技术,2018,40(2):189-196Wu Z Y,Den J Z,Wang Y G,et al.Comparative analysis on the iterative methods for downward continuation of gravity field[J].Computing Techniques for Geophysical and Geochemical Exploration,2018,40(2):189-196.
[14]栾文贵.位场解析延拓的稳定化算法[J].地球物理学报,1983,26(3):263-274.Luan W G.The stabilized algorithm of the analytic continuation for the potential field[J]. Chinese J. Geophys.,1983,26(3):263-274.
[15]毛小平,吴蓉元,曲赞.频率域位场下延的振荡机制及消除方法[J].石油地球物理勘探,1998,33(2):230-237.Mao X P,Wu R Y,Qu Z. Oscillation mechanism of potential field downward continuation in frequency domain and its elimination[J]. OGP,1998,33(2):230-237.
[16]张辉,陈龙伟,任治新,等.位场向下延拓迭代法收敛性分析及稳健向下延拓方法研究[J].地球物理学报,2009,52(4):1107-1113.Zhang H,Chen L W,Ren Z X,et al. Analysis on convergence of iteration method for potential fields downward continuation and research on robust downward continuation method[J]. Chinese J.Geophys.,2009,52(4):1107-1113.
[17]于波,翟国君,刘燕春,等.噪声对磁场向下延拓迭代法的计算误差影响分析[J].地球物理学报,2009,52(8):2182-2188.Yu B,Zhai G J. Liu Y C,et al. Analysis of noise effect on the calculation error of downward continuation with iteration Method[J].Chinese J. Geophys.,2009,52(8):2182-2188.
[18]陆正立.频率域向上延拓的误差分析[J].桂林冶金地质学院学报,1981,(1):62-68.Lu Z L.Error analysis of upward continuation in frequency domain[J]. Journal of Guilin Institute of Metallurgical Geology,1981,(1):62-68.
[19]熊光楚.在地球物理测量的数据处理中值得进一步研究的一些问题[J].物探与化探,1985,9(2):100-107.Xiong G C. Some problems worthy of further study in geophysical data processing[J]. Geophysical and Geochemical Exploration,1985,9(2):100-107.
[20]熊光楚.矿产预测中重磁异常变换的若干问题——二、向上延拓的作用及问题[J].物探与化探,1992,16(5):358-455.Xiong G Z.Some problems in the transformation of gravity and magnetic anomalies in mineral prediction-two. The role and problems of upward continuation[J].Geophysical and Geochemical Exploration,1992,16(5):358-455.
[21]王建明.重磁异常变换中的延拓问题[J].新疆有色金属,2006(2):11-16.Wang J M. Continuation in the transformation of gravity and magnetic anomalies[J].Xinjiang Nonferrous Metals,2006(2):11-16.
[22]曾华霖.重力场与重力勘探[M].北京:地质出版社,2004.Zemg H L. Gravity field and gravity exploration[M]. Beijing:Geological Publishing Press,2004.
[23]王万银,邱之云,刘金兰,等.位场数据处理中的最小曲率扩边和补空方法研究[J].地球物理学进展,2009,24(4):1327-1338.Wang W Y,Qiu Z Y,Liu J L,et al.There research to the extending edge and interpolation based on the minimum curvature method in potential field data processing[J]. Progress in Geophys.,2009,24(4):1327-1338.
[24]马国庆,孟令顺,杜小娟,等.磁法数据处理中的扩边和优化中值滤波方法的研究[J].物探与化探计算技术,2010,32(2):194-199.Ma G Q,Meng L S,Du X J,et al.The study of edge expansion and optim ization median filtering method in magnetic data processing[J].Computing Techniques for Geophysical and Geochemical Exploration,2010,32(2):194-199.
[25]张志厚,徐世浙,余海龙,等.位场向下延拓的迭代法的扩边方法[J].浙江大学学报,2013,47(5):918-924.Zhang Z H,Xu S Z,Yu H L,et al.Study of extending methods of iteration of downward continuation in potential field[J]. Journal of Zhejiang University,2013,47(5):918-924.
[26]段本春,徐世浙.重磁局部场区域场分量处理中的扩边方法研究[J].物探与化探计算技术,1997,19(4):298-304.Duan B C,Xu S Z,et al.A study of the scheme of extending in the processing of separating local field from regional field for magnetic/gravity anomaly[J]. Computing Techniques for Geophysical and Geochemical Exploration,1997,19(4):298-304
[2]王兴涛,夏哲仁,石磐,等.航空重力测量数据向下延拓方法比较[J].地球物理学报,2004,47(6):1017-1022.Wang X T,Xia Z R,Shi P,et al. A Comparison of different downward continuation methods for airborne gravity data[J].Chinese J.Geophys.,2004,47(6):1017-1022
[3]陈生昌,肖鹏飞.位场向下延拓的波数域广义逆算法[J].地球物理学报,2007,50(6):1816-1822.Chen S C,Xiao P F.Wavenumber domain generalized inverse algorithm for potential field downward continuation[J].Chinese J. Geophys,2007,50(6):1816-1822.
[4]徐世浙.位场延拓的积分—迭代法[J].地球物理学报,2006,49(4):1176-1182.Xu S Z. The integral-iteration method for continuation of potential fields[J]. Chinese J Geophys,2006,49(4):1176-1182.
[5]徐世浙.位场大深度向下延拓[J].物探与化探计算技术,2006,28(s):29-31.Xu S Z. A great depth downward continuation of potential field.Computing techniques for geophysical and geochemical exploration,2006,28(s):29-31.
[6]曾小牛,李夕海,韩绍卿,等.位场向下延拓三种迭代方法之比较[J].地球物理学进展,2011,26(3):908-915.Zeng X N,Li X H,Han S Q,et al. A comparison of three iteration methods for downward continuation of potential fields[J]. Progress in Geophys,2011,26(3):908-915.
[7]陈龙伟,徐世浙,胡小平,等.位场向下延拓的迭代最小二乘法[J].地球物理学进展,2011,26(3):894-901.Chen L W,Xu S Z,Hu X P,et al.The iterative least square method for downward continuation of potential fields[J]. Progress in Geophys,2011,26(3):894-901.
[8] Dmitriev V I. Iterative method for analytical continuation of the gravity field[J].Computational Mathematics and Modeling,2012,23(1):67-73.
[9]刘东甲,洪天求,贾海,等.位场向下延拓的波数域迭代法及其收敛性[J].地球物理学报,2009,52(6):1599-1605.Liu D J,Hong T Q,Jia Z H,et al. Wave number domain iteration method for downward continuation of Potential fields and its convergence.Chinese J. Geophys.,,2009,52(6):1599-1605.
[10]王彦国.位场数据处理的高精度方法研究及应用[D].长春:吉林大学.2013.Wang Y G. Study and application of high-precision methods in potential-field data processing[D]. Changchun:Jilin University,2013.
[11]安玉林,管志宁.滤除高频干扰的正则化稳定因子[J].物探与化探计算技术,1985,7(1):13-23.An Y L,Guan Z N.The regularized stable factors of removing high frequency disturbances[J]. Computing Techniques for Geophysical and Geochemical exploration,1985,7(1):13-23.
[12]姚长利,李宏伟,郑元满,等.重磁位场转换计算中迭代法的综合分析与研究[J].地球物理学报,2012,55(6):2062-2078.Yao C L,Li H W,Zhen Y M,et al.Research on iteration method using in potential field transformation[J]. Chinese J. Geophys.,2012,55(6):2062-2078.
[13]吴姿颖,邓居智,王彦国,等.重力向下延拓的迭代法对比分析研究[J].物探与化探计算技术,2018,40(2):189-196Wu Z Y,Den J Z,Wang Y G,et al.Comparative analysis on the iterative methods for downward continuation of gravity field[J].Computing Techniques for Geophysical and Geochemical Exploration,2018,40(2):189-196.
[14]栾文贵.位场解析延拓的稳定化算法[J].地球物理学报,1983,26(3):263-274.Luan W G.The stabilized algorithm of the analytic continuation for the potential field[J]. Chinese J. Geophys.,1983,26(3):263-274.
[15]毛小平,吴蓉元,曲赞.频率域位场下延的振荡机制及消除方法[J].石油地球物理勘探,1998,33(2):230-237.Mao X P,Wu R Y,Qu Z. Oscillation mechanism of potential field downward continuation in frequency domain and its elimination[J]. OGP,1998,33(2):230-237.
[16]张辉,陈龙伟,任治新,等.位场向下延拓迭代法收敛性分析及稳健向下延拓方法研究[J].地球物理学报,2009,52(4):1107-1113.Zhang H,Chen L W,Ren Z X,et al. Analysis on convergence of iteration method for potential fields downward continuation and research on robust downward continuation method[J]. Chinese J.Geophys.,2009,52(4):1107-1113.
[17]于波,翟国君,刘燕春,等.噪声对磁场向下延拓迭代法的计算误差影响分析[J].地球物理学报,2009,52(8):2182-2188.Yu B,Zhai G J. Liu Y C,et al. Analysis of noise effect on the calculation error of downward continuation with iteration Method[J].Chinese J. Geophys.,2009,52(8):2182-2188.
[18]陆正立.频率域向上延拓的误差分析[J].桂林冶金地质学院学报,1981,(1):62-68.Lu Z L.Error analysis of upward continuation in frequency domain[J]. Journal of Guilin Institute of Metallurgical Geology,1981,(1):62-68.
[19]熊光楚.在地球物理测量的数据处理中值得进一步研究的一些问题[J].物探与化探,1985,9(2):100-107.Xiong G C. Some problems worthy of further study in geophysical data processing[J]. Geophysical and Geochemical Exploration,1985,9(2):100-107.
[20]熊光楚.矿产预测中重磁异常变换的若干问题——二、向上延拓的作用及问题[J].物探与化探,1992,16(5):358-455.Xiong G Z.Some problems in the transformation of gravity and magnetic anomalies in mineral prediction-two. The role and problems of upward continuation[J].Geophysical and Geochemical Exploration,1992,16(5):358-455.
[21]王建明.重磁异常变换中的延拓问题[J].新疆有色金属,2006(2):11-16.Wang J M. Continuation in the transformation of gravity and magnetic anomalies[J].Xinjiang Nonferrous Metals,2006(2):11-16.
[22]曾华霖.重力场与重力勘探[M].北京:地质出版社,2004.Zemg H L. Gravity field and gravity exploration[M]. Beijing:Geological Publishing Press,2004.
[23]王万银,邱之云,刘金兰,等.位场数据处理中的最小曲率扩边和补空方法研究[J].地球物理学进展,2009,24(4):1327-1338.Wang W Y,Qiu Z Y,Liu J L,et al.There research to the extending edge and interpolation based on the minimum curvature method in potential field data processing[J]. Progress in Geophys.,2009,24(4):1327-1338.
[24]马国庆,孟令顺,杜小娟,等.磁法数据处理中的扩边和优化中值滤波方法的研究[J].物探与化探计算技术,2010,32(2):194-199.Ma G Q,Meng L S,Du X J,et al.The study of edge expansion and optim ization median filtering method in magnetic data processing[J].Computing Techniques for Geophysical and Geochemical Exploration,2010,32(2):194-199.
[25]张志厚,徐世浙,余海龙,等.位场向下延拓的迭代法的扩边方法[J].浙江大学学报,2013,47(5):918-924.Zhang Z H,Xu S Z,Yu H L,et al.Study of extending methods of iteration of downward continuation in potential field[J]. Journal of Zhejiang University,2013,47(5):918-924.
[26]段本春,徐世浙.重磁局部场区域场分量处理中的扩边方法研究[J].物探与化探计算技术,1997,19(4):298-304.Duan B C,Xu S Z,et al.A study of the scheme of extending in the processing of separating local field from regional field for magnetic/gravity anomaly[J]. Computing Techniques for Geophysical and Geochemical Exploration,1997,19(4):298-304