正则化方法在比值类位场边缘识别方法中的研究
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摘要
位场边缘识别方法有很多种,其中归一化标准差法(NSTD)、倾斜角法(Ta)和Theta Map(cosθ)等方法属于比值类方法。比值类方法在计算过程中会出现分母接近于0或者等于0这种情况,致使计算结果不稳定,并产生错误的边缘识别结果。为此,对比值类边缘识别方法计算公式中的分母加一个大于零的正则化因子,不但解决了比值类方法的数值计算稳定性问题,而且提高了部分比值类边缘识别方法识别结果的精度。通过理论模型和实际资料检验了新方法的稳定性、精度以及有效性。正则化因子的引入同样可以改善以比值类方法为基础构建的二阶导数类边缘识别方法的识别效果,如倾斜角总水平导数(Ta-THDR)的识别效果。正则化这一思想不但可以解决比值类位场边缘识别方法的数值计算问题,而且可以解决比值类方法的数值计算问题。
The ratio methods are one sort of edge recognition methods by using potential field,which contains the Normalized Standard Deviation method( NSTD),Tilt Angle method( Ta) and Theta Map( cosθ). If the denominator of ratio method closes or even equals to zero in the process of calculation,the result obtaining from ratio methods is unstable and may even bear little resemblance to the true geology. In order to relief this problem,a regularization factor,which is greater than zero,is added in the denominator of the ratio methods' formula,which not only enhances the numerical stability of the ratio methods but also improves the accuracy of some ratio edge recognition methods. The stability,accuracy and effectiveness of the new method is verified by testing synthetic models and calculating real data. Also,the introduction of the regularization factor also can improve the effect of recognizing edge by the second-derivative edge recognition methods,which is based on the ratio methods,such as the Total Horizontal Derivative of the Tilt Angle( TaTHDR). The idea of regularization can not only solve the numerical calculation problem of the ratio methods of edge recognition for potential field,but also solve the numerical calculation problem of all ratio methods.
The ratio methods are one sort of edge recognition methods by using potential field,which contains the Normalized Standard Deviation method( NSTD),Tilt Angle method( Ta) and Theta Map( cosθ). If the denominator of ratio method closes or even equals to zero in the process of calculation,the result obtaining from ratio methods is unstable and may even bear little resemblance to the true geology. In order to relief this problem,a regularization factor,which is greater than zero,is added in the denominator of the ratio methods' formula,which not only enhances the numerical stability of the ratio methods but also improves the accuracy of some ratio edge recognition methods. The stability,accuracy and effectiveness of the new method is verified by testing synthetic models and calculating real data. Also,the introduction of the regularization factor also can improve the effect of recognizing edge by the second-derivative edge recognition methods,which is based on the ratio methods,such as the Total Horizontal Derivative of the Tilt Angle( TaTHDR). The idea of regularization can not only solve the numerical calculation problem of the ratio methods of edge recognition for potential field,but also solve the numerical calculation problem of all ratio methods.
引文
[1] Miller H G,Singh V. Potential field tilt-a new concept for location of potential field sources[J]. Journal of Applied Geophysics,1994,32:213-217.
[2] Hood P,Mc Clure D J. Gradient measures in ground magnetic prospecting[J]. Geophysics,1965,30(3):403-410.
[3] Bhattacharyya B K. Two-dimensional harmonic analysis as a tool for magnetic interpretation[J]. Geosciences,1965,30(5):829-857.
[4] Cordell L. Gravimetric expression of graben faulting in Santa Fe Country and the Espanola Basin,New Mexico[C]//New Mexico Geol. Soc. Guidebook,1979,30th Field Conf:59-64.
[5] Wigns C,Perez C,Kowalczyk P. Theta map:Edge detection in magnetic data[J]. Geophysics,2005,70(4):L39-L43.
[6] Nabighian M N. The analytic signal of two-dimensional magnetic bodies with polygonal cross-section:its properties and use for automated anomaly interpretation[J]. Geophysics,1972,37(3):507-517.
[7] Coorper G R J,Cowan D R. Edge enhancement of potential-field data using normalized statistics[J]. Geophysics,2008,73(3):H1-H4.
[8]王万银.位场边缘识别技术研究[D].西安:长安大学,2009.Wang W Y. The research on the edge recognition methods and techniques for potential field[D]. Xi’an:Chang’an University,2009.
[9] Coorper G R J,Cowan D R. Enhancing potential field data using filters based on the local phase[J]. Computers&Geosciences,2006,32(10):1585-1591.
[10]马国庆,黄大年,于平,等.改进的均衡滤波器在位场数据边界识别中的应用[J].地球物理学报,2012,55(12):4288-4295.Ma G Q,Huang D N,Yu P,et al. Application of improved balancing filters to edge identification of potential field data[J]. Chinese Journal of Geophysics,2012,55(12):4288-4295.
[11]王明,郭志宏,骆遥.扩展的倾斜角与倾斜角总水平导数[J].地球物理学进展,2013,28(3),1453-1463.Wang M,Guo Z H,Luo Y,et al. Extended tilt angle and total horizontal derivatives[J]. Progress in Geophysic,2013,28(3):1453-1463.
[12] Coorper G R J. Reply to a discussion about the“Hyperbolic tilt angle method”by Zhou et al[J]Computers&Geosciences,2013,52:496-497.
[13]马国庆,杜晓娟,李丽丽.位场边缘识别的新方法—增强型水平导数法[J].地球物理学进展,2013,28(1):402-408.Ma G Q,Du X J,Li L L. New edge detection method of potential field data-enhanced horizontal derivative method[J]. Progress in Geophysics,2013,28(1):402-408.
[14] Li L L,Huang D N,Han L G,et al. Optimised edge detection filters in the interpretation of potential field data[J]. Exploration Geophysics,2014,45(3):171-176.
[15]顾廷杰,吴燕冈,袁园,等.应用加强解析信号倾斜角进行位场数据的边界检测[J].地球物理学报,2016,59(7),2694-2702.Gu T J,Wu Y G,Yuan Y,et al. Edge detection of potential field data using an enhanced analytic signal tilt angle[J]. Chinese Journal of Geophysics,2016,59(7):2694-2702.
[16] Yuan Y,Huang D N,Yu Q L. Edge detection of potential field data with improved structure tensor methods[J]. Journal of Applied Geophysical,2014,172(2):461-472.
[17]袁园,黄大年,余青露.利用加强水平方向总水平导数对位场全张量数据进行边界识别[J].地球物理学报,2015,58(7):2556-2565.Yuan Y,Huang D N,Yu Q L. Using enhanced directional total horizontal derivatives to detect the edges of potential field full tensor data:Chinese Journal of Geophysics,2015,58(7):2556-2565.
[18] Tikhonov A N,Glasko V B.Using of the regularization method in non-linear problems[J]. Zh. Vychislit. Matem. i matem. fiz.,1965,5(N):463-473.
[19] Pa?teka R,Richter F P,Karcol R,et al. Regularized derivatives of potential and their role in semi-automated interpretation methods[J].Geophysical Prospecting,2009,57:507-516.
[20]曾小牛,李夕海,贾维敏,等.位场各阶垂向导数换算的新正则化方法[J].地球物理学报,2015,58(4):1400-1410.Zeng X N,Li X H,Su J. An adaptive iteration method for downward continuation of potential-field data from a horizontal plane:Geophysics,2015,58(4):1400-1410.
[21]栾文贵.场位解析延拓的稳定化算法[J].地球物理学报,1983,26(3):263-273.Luan W G. Stabilization algorithm for analytical continuation of potential field[J]. Chinese Journal of Geophysics,1983,26(3):263-273.
[22]梁锦文.位场向下延拓的正则化方法[J].地球物理学报,1989,33(5):600-608.Liang J W. Regularization method for downward continuation of potential field[J]. Chinese Journal of Geophysics,1989,33(5):600-608.
[23] Pa?teka R,Karcol R,Ku nirák D,et al. Regcont:A Matlab based program for stable downward continuation of geophysical potential fields using Tikhonov regularization[J]. Computers&Geosciences,2012(49):278-289.
[24] Abedi M,Gholami A,Norouzi G H. A stable downward continuation of airborne magnetic data:A case study for mineral prospectivity mapping in Central Iran[J]. Computers&Geosciences,2013,(52):269-280.
[25] Li Y G,Sarah G R D,Richard A K,et al. Enhancemant of magnetic data by stable downward continuation for UXO application[J]. IEEE transactions on Geoscience and Remote Sensing,2013,51(6):3605-3614.
[26]赵亚博,刘天佑.迭代Tikhonov正则化位场向下延拓方法及其在尕林铁矿的应用[J].物探与化探,2015,39(4):743-748.Zhao Y B,Liu T Y. The iterative regularization method for downward continuation of potential fields and its application to the Galinge iron deposit[J]. Geophysical and Geochemical Exploration,2015,39(4):743-748.
[27] Verduzco B,Fairhead J D,Green C M,Mackenzie C. The meter reader-New insights into magnetic derivatives for structural mapping[J]. The Leading Edge,2004,23(2):116-119.
[28]王万银,邱之云,杨永,等.位场边缘识别方法研究进展[J].地球物理学进展,2010,25(1):196-210.Wang W Y,Qiu Z Y,Yang Y,et al. Some advances in the edge recognition of the potential field[J]. Progress in Geophysics,2010,25(1):196-210.
[29] Ma G Q,Huang D N,Cai Liu. Step-edge detection filters for the Interpretation of potential field data[J]. Pure and Applied Geophysics,2016,173:795-803.
[30] Ma,G. Q. Edge detection of potential field data using improved local phase filter[J]. Exploration Geophysics,2013,44:36-41.
[31]周帅,黄大年,焦健.基于三维构造张量的位场边界识别滤波器[J].地球物理学报,2016,59(10):3847-3858.Zhou S,Huang D N,Jiao J.Construction of potential Field Boundary recognition filter based on three-dimensional Construction of Zhang Liang[J]. Journal of Geophysics,2016,59(10):3847-3858.
[32]颜廷杰,吴燕冈,袁园,等.应用加强解析信号倾斜角进行位场数据的边界检测[J].地球物理学报,2016,59(7):2694-2702.Yan T J,Wu Y G,Yuan Y,et al.Boundary Detection of potential Field data by strengthening the inclination Angle of Analytic signal[J].Journal of Geophysics,2016,59(7):2694-2702.
[33]陈国强,马国庆.位场数据解释的Theta-Depth法[J].地球物理学报,2016,59(6):2225-2231.Chen G Q,Ma G Q. Theta-Depth method for potential Field data interpretation[J]. Journal of Geophysics,2016,59(6):2225-2231.
[2] Hood P,Mc Clure D J. Gradient measures in ground magnetic prospecting[J]. Geophysics,1965,30(3):403-410.
[3] Bhattacharyya B K. Two-dimensional harmonic analysis as a tool for magnetic interpretation[J]. Geosciences,1965,30(5):829-857.
[4] Cordell L. Gravimetric expression of graben faulting in Santa Fe Country and the Espanola Basin,New Mexico[C]//New Mexico Geol. Soc. Guidebook,1979,30th Field Conf:59-64.
[5] Wigns C,Perez C,Kowalczyk P. Theta map:Edge detection in magnetic data[J]. Geophysics,2005,70(4):L39-L43.
[6] Nabighian M N. The analytic signal of two-dimensional magnetic bodies with polygonal cross-section:its properties and use for automated anomaly interpretation[J]. Geophysics,1972,37(3):507-517.
[7] Coorper G R J,Cowan D R. Edge enhancement of potential-field data using normalized statistics[J]. Geophysics,2008,73(3):H1-H4.
[8]王万银.位场边缘识别技术研究[D].西安:长安大学,2009.Wang W Y. The research on the edge recognition methods and techniques for potential field[D]. Xi’an:Chang’an University,2009.
[9] Coorper G R J,Cowan D R. Enhancing potential field data using filters based on the local phase[J]. Computers&Geosciences,2006,32(10):1585-1591.
[10]马国庆,黄大年,于平,等.改进的均衡滤波器在位场数据边界识别中的应用[J].地球物理学报,2012,55(12):4288-4295.Ma G Q,Huang D N,Yu P,et al. Application of improved balancing filters to edge identification of potential field data[J]. Chinese Journal of Geophysics,2012,55(12):4288-4295.
[11]王明,郭志宏,骆遥.扩展的倾斜角与倾斜角总水平导数[J].地球物理学进展,2013,28(3),1453-1463.Wang M,Guo Z H,Luo Y,et al. Extended tilt angle and total horizontal derivatives[J]. Progress in Geophysic,2013,28(3):1453-1463.
[12] Coorper G R J. Reply to a discussion about the“Hyperbolic tilt angle method”by Zhou et al[J]Computers&Geosciences,2013,52:496-497.
[13]马国庆,杜晓娟,李丽丽.位场边缘识别的新方法—增强型水平导数法[J].地球物理学进展,2013,28(1):402-408.Ma G Q,Du X J,Li L L. New edge detection method of potential field data-enhanced horizontal derivative method[J]. Progress in Geophysics,2013,28(1):402-408.
[14] Li L L,Huang D N,Han L G,et al. Optimised edge detection filters in the interpretation of potential field data[J]. Exploration Geophysics,2014,45(3):171-176.
[15]顾廷杰,吴燕冈,袁园,等.应用加强解析信号倾斜角进行位场数据的边界检测[J].地球物理学报,2016,59(7),2694-2702.Gu T J,Wu Y G,Yuan Y,et al. Edge detection of potential field data using an enhanced analytic signal tilt angle[J]. Chinese Journal of Geophysics,2016,59(7):2694-2702.
[16] Yuan Y,Huang D N,Yu Q L. Edge detection of potential field data with improved structure tensor methods[J]. Journal of Applied Geophysical,2014,172(2):461-472.
[17]袁园,黄大年,余青露.利用加强水平方向总水平导数对位场全张量数据进行边界识别[J].地球物理学报,2015,58(7):2556-2565.Yuan Y,Huang D N,Yu Q L. Using enhanced directional total horizontal derivatives to detect the edges of potential field full tensor data:Chinese Journal of Geophysics,2015,58(7):2556-2565.
[18] Tikhonov A N,Glasko V B.Using of the regularization method in non-linear problems[J]. Zh. Vychislit. Matem. i matem. fiz.,1965,5(N):463-473.
[19] Pa?teka R,Richter F P,Karcol R,et al. Regularized derivatives of potential and their role in semi-automated interpretation methods[J].Geophysical Prospecting,2009,57:507-516.
[20]曾小牛,李夕海,贾维敏,等.位场各阶垂向导数换算的新正则化方法[J].地球物理学报,2015,58(4):1400-1410.Zeng X N,Li X H,Su J. An adaptive iteration method for downward continuation of potential-field data from a horizontal plane:Geophysics,2015,58(4):1400-1410.
[21]栾文贵.场位解析延拓的稳定化算法[J].地球物理学报,1983,26(3):263-273.Luan W G. Stabilization algorithm for analytical continuation of potential field[J]. Chinese Journal of Geophysics,1983,26(3):263-273.
[22]梁锦文.位场向下延拓的正则化方法[J].地球物理学报,1989,33(5):600-608.Liang J W. Regularization method for downward continuation of potential field[J]. Chinese Journal of Geophysics,1989,33(5):600-608.
[23] Pa?teka R,Karcol R,Ku nirák D,et al. Regcont:A Matlab based program for stable downward continuation of geophysical potential fields using Tikhonov regularization[J]. Computers&Geosciences,2012(49):278-289.
[24] Abedi M,Gholami A,Norouzi G H. A stable downward continuation of airborne magnetic data:A case study for mineral prospectivity mapping in Central Iran[J]. Computers&Geosciences,2013,(52):269-280.
[25] Li Y G,Sarah G R D,Richard A K,et al. Enhancemant of magnetic data by stable downward continuation for UXO application[J]. IEEE transactions on Geoscience and Remote Sensing,2013,51(6):3605-3614.
[26]赵亚博,刘天佑.迭代Tikhonov正则化位场向下延拓方法及其在尕林铁矿的应用[J].物探与化探,2015,39(4):743-748.Zhao Y B,Liu T Y. The iterative regularization method for downward continuation of potential fields and its application to the Galinge iron deposit[J]. Geophysical and Geochemical Exploration,2015,39(4):743-748.
[27] Verduzco B,Fairhead J D,Green C M,Mackenzie C. The meter reader-New insights into magnetic derivatives for structural mapping[J]. The Leading Edge,2004,23(2):116-119.
[28]王万银,邱之云,杨永,等.位场边缘识别方法研究进展[J].地球物理学进展,2010,25(1):196-210.Wang W Y,Qiu Z Y,Yang Y,et al. Some advances in the edge recognition of the potential field[J]. Progress in Geophysics,2010,25(1):196-210.
[29] Ma G Q,Huang D N,Cai Liu. Step-edge detection filters for the Interpretation of potential field data[J]. Pure and Applied Geophysics,2016,173:795-803.
[30] Ma,G. Q. Edge detection of potential field data using improved local phase filter[J]. Exploration Geophysics,2013,44:36-41.
[31]周帅,黄大年,焦健.基于三维构造张量的位场边界识别滤波器[J].地球物理学报,2016,59(10):3847-3858.Zhou S,Huang D N,Jiao J.Construction of potential Field Boundary recognition filter based on three-dimensional Construction of Zhang Liang[J]. Journal of Geophysics,2016,59(10):3847-3858.
[32]颜廷杰,吴燕冈,袁园,等.应用加强解析信号倾斜角进行位场数据的边界检测[J].地球物理学报,2016,59(7):2694-2702.Yan T J,Wu Y G,Yuan Y,et al.Boundary Detection of potential Field data by strengthening the inclination Angle of Analytic signal[J].Journal of Geophysics,2016,59(7):2694-2702.
[33]陈国强,马国庆.位场数据解释的Theta-Depth法[J].地球物理学报,2016,59(6):2225-2231.Chen G Q,Ma G Q. Theta-Depth method for potential Field data interpretation[J]. Journal of Geophysics,2016,59(6):2225-2231.
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