利用重/磁场梯度比值函数计算地质体深度
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摘要
本文定义了一种函数,即重力场或磁力场的一阶水平导数与原始异常的比值,利用该函数值可直接推导地质体的位置。对于不同类型地质体,其梯度比值函数均表现出极值点间水平距离等于地质体深度2倍的特征,从而无须任何先验信息即可计算异常体深度。为了降低倾斜磁化对磁数据处理结果的影响,磁异常解释采用解析信号水平导数与解析信号的比值。梯度比值函数仅计算异常的一阶水平导数,因此不会明显地增大噪声。此外,对梯度比值函数计算多个上延高度、求取其平均值,并对上半空间极值成像,可获得更加准确的地质体深度。理论模型试验和实测剖面磁数据的解释结果都证明梯度比值函数能快速、准确地获得地质体深度,且具有较强的抗噪性。
This paper defines a gradient ratio function of gravity and magnetic data,which is the ratio of first-order horizontal derivative to original anomaly.This function can directly obtain the location of geological body.The gradient ratio function has the relationship for different types of bodies,that is the horizontal distance of extremes equal to two times the depth of geological body.So this method can realize the depth calculation without any priori information.In order to low the interference of oblique magnetization,we use the ratio of analytic signal derivative to analytic signal for magnetic anomaly interpretation.The gradient ratio function calculates only the first-order horizontal derivative of anomaly,so it will not increase the interference of noise.In addition,we provide the average value of multiple upward continuation heights and upperhalf space extreme imaging based on the gradient ratio function to get more accurate results.Theoretical model tests prove that the gradient ratio function can quickly and correctly calculate geological body depth,and have stronger anti-noise capability.We apply this proposed method to real magnetic data,and obtain the depth of geological bodies.
This paper defines a gradient ratio function of gravity and magnetic data,which is the ratio of first-order horizontal derivative to original anomaly.This function can directly obtain the location of geological body.The gradient ratio function has the relationship for different types of bodies,that is the horizontal distance of extremes equal to two times the depth of geological body.So this method can realize the depth calculation without any priori information.In order to low the interference of oblique magnetization,we use the ratio of analytic signal derivative to analytic signal for magnetic anomaly interpretation.The gradient ratio function calculates only the first-order horizontal derivative of anomaly,so it will not increase the interference of noise.In addition,we provide the average value of multiple upward continuation heights and upperhalf space extreme imaging based on the gradient ratio function to get more accurate results.Theoretical model tests prove that the gradient ratio function can quickly and correctly calculate geological body depth,and have stronger anti-noise capability.We apply this proposed method to real magnetic data,and obtain the depth of geological bodies.
引文
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[9] 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.
[10] Nabighian M N.Additional comments on the analytic signal of two-dimensional magnetic bodies with poly-gonal cross-section[J].Geophysics,1974,39(1):85-92.
[11] Nabighian M N.Toward a three-dimensional automa-tic interpretation of potential-field data via generalized Hilbert transforms: Fundamental relations[J]. Geophysics,1984,49(5):780-786.
[12] Roest W R,Verhoef J and Pilkington M.Magnetic interpretation using 3-D analytic signal[J].Geophy-sics,1992,57(1):116-125.
[13] Thurston J B and Smith R S.Automatic conversion of magnetic data to depth,dip,and susceptibility contrast using the SPI method[J].Geophysics,1997,62(3):807-813.
[14] Thurston J B,Smith R S and Guillon J.A multi-model method for depth estimation from magnetic data[J].Geophysics,2002,67(2):555-561.
[15] Salem A,Ravat D,Gamey T J,et al.Analytic signal approach and its applicability in environmental magnetic investigations[J].Journal of Applied Geophy-sics,2002,49(4):231-244.
[16] Hsu S K,Sibuet J C and Shyu C T.High-resolution detection of geologic boundaries from potential ano-malies: An enhanced analytic signal technique[J]. Geophysics,1996,61(2):373-386.
[17] Hsu S K,Coppens D and Shyu C T.Depth to magne-tic source using the generalized analytic signal[J].Geophysics,1998,63(6):1947-1957.
[18] Bastani M and Pedersen L B.Automatic interpretation of magnetic dike parameters using the analytic signal technique[J].Geophysics,2001,66(2):551-561.
[19] Smith R S,Thurston J B,Dai T F,et al.ISPI: the improved source parameters imaging method[J].Geophysical Prospecting,1998,46(2):141-151.
[20] Salem A,Ravat D,Mushayandebvu M F,et al.Linea-rized least-squares method for interpretation of potential-field data from sources of simple geometry[J]. Geophysics,2004,69(3):783-788.
[21] Salem A.Interpretation of magnetic data using analy-tic signal derivatives[J]. Geophysical Prospecting,2005,53(1):75-82.
[22] Thompson D T.EULDPH: A new technique for ma-king computer-assisted depth estimates from magnetic data[J].Geophysics,1982,47(1):31-37.
[23] Reid A N,Allsop J M,Granser H.Magnetic interpretation in three dimensions using Euler deconvolution[J].Geophysics,1990,55(1):80-91.
[24] Ma G and Du X.An improved analytic signal technique for the depth and structural index from 2D magnetic anomaly data[J].Pure and Applied Geophysics,2012,169(8):2193-2200.
[25] Cooper G R J.The automatic determination of the location and depth of contacts and dykes from aeromagnetic data[J].Pure and Applied Geophysics,2014,171(9):2417-2423.
[26] Cooper G R J.Using the analytic signal amplitude to determine the location and depth of thin dykes from magnetic data[J].Geophysics,2015,80 (1):J1-J6.
[27] 马国庆,黄大年,李丽丽,等.重磁异常解释的归一化局部波数法[J].地球物理学报,2014,57(4):1300-1309.MA Guoqing,HUANG Danian,LI Lili,et al.A normalized local wave number method for interpretation of gravity and magnetic anomalies[J].Chinese Journal of Geophysics,2014,57(4):1300-1309.
[28] 马国庆,杜晓娟,李丽丽.改进的位场相关成像方法[J].地球科学——中国地质大学学报,2013,38(5):1121-1127.MA Guoqing,DU Xiaojuan,LI Lili.Improved potential field correlation imaging method[J].Earth Science:Journal of China University of Geosciences,2013,38(5):1121-1127.
[29] Ma Guoqing,Liu Cai,Xu Jiashu,et al.Correlation ima-ging method based on local wave number for interpreting magnetic data[J].Journal of Applied Geophysics,2017,138(1):17-22.
[30] Ma Guoqing,Liu Cai,Li Lili.Balanced horizontal derivative of potential field data to recognize the edges and estimate location parameters of the source[J]. Journal of Applied Geophysics,2014,108(9):12-18.
[31] Salem A and Ravat D.A combined analytic signal and Euler method (AN-EUL) for automatic interpretation of magnetic data[J].Geophysics,2003,68(6):1952-1961.
[32] Wen B D,Hsu S K and Yeh Y C.A derivative-based interpretation approach to estimating source parameters of simple 2D magnetic sources from Euler deconvolution,the analytic-signal method and analytical expressions of the anomalies[J].Geophysical Prospecting,2007,55(1):255-264.
[33] Stavrev P and Reid A.Degrees of homogeneity of potential fields and structural indices of Euler deconvolution[J].Geophysics,2007,72(1):L1-L12.
[2] Blakely R J.Potential Theory in Gravity and Magnetic Applications[M].Cambridge University Press,1995.
[3] Debeglia N and Corpel J.Automatic 3-D interpretation of potential field data using analytic signal derivatives[J].Geophysics,1997,62(1):87-96.
[4] MacLeod I N,Jones K and Dai T F.3-D analytic signal in the interpretation of total magnetic field data at low magnetic latitudes[J].Exploration Geophysics,1993,24(3):679-688.
[5] 谷文彬,陈清礼,王余泉,等.饶阳凹陷虎8北潜山重力三维松约束反演[J].石油地球物理勘探,2016,51(6):1219-1226.GU Wenbin,CHEN Qingli,WANG Yuquan,et al.Part-constrained 3D gravity inversion for the Hubabei buried hill in Raoyang Sag[J].Oil Geophysical Prospecting,2016,51(6):1219-1226.
[6] 李婧,崔永谦,宋景明,等.重力—地震联合建模正演技术在SH地区潜山勘探中的应用[J].石油地球物理勘探,2016,51(增刊1):152-160.LI Jing,CUI Yongqian,SONG Jingming,et al.Gravity forward modeling with model built based on drilling and seismic data: an example of buried hill exploration in area SH[J].Oil Geophysical Prospecting,2016,51(S1): 152-160.
[7] 耿美霞,杨庆节.应用RBF神经网络反演二维重力密度分布[J].石油地球物理勘探,2013,48(4):651-657.GENG Meixia,YANG Qingjie.2D density inversion with the RBF neural network method[J].Oil Geophysical Prospecting,2013,48(4):651-657.
[8] 林宝泽,肖锋,王明常.二维重力数据径向反演及应用[J].石油地球物理勘探,2018,53(2):403-409.LIN Baoze,XIAO Feng,WANG Mingchang.2D gravity data radial inversion[J].Oil Geophysical Prospecting,2018,53(2):403-409.
[9] 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.
[10] Nabighian M N.Additional comments on the analytic signal of two-dimensional magnetic bodies with poly-gonal cross-section[J].Geophysics,1974,39(1):85-92.
[11] Nabighian M N.Toward a three-dimensional automa-tic interpretation of potential-field data via generalized Hilbert transforms: Fundamental relations[J]. Geophysics,1984,49(5):780-786.
[12] Roest W R,Verhoef J and Pilkington M.Magnetic interpretation using 3-D analytic signal[J].Geophy-sics,1992,57(1):116-125.
[13] Thurston J B and Smith R S.Automatic conversion of magnetic data to depth,dip,and susceptibility contrast using the SPI method[J].Geophysics,1997,62(3):807-813.
[14] Thurston J B,Smith R S and Guillon J.A multi-model method for depth estimation from magnetic data[J].Geophysics,2002,67(2):555-561.
[15] Salem A,Ravat D,Gamey T J,et al.Analytic signal approach and its applicability in environmental magnetic investigations[J].Journal of Applied Geophy-sics,2002,49(4):231-244.
[16] Hsu S K,Sibuet J C and Shyu C T.High-resolution detection of geologic boundaries from potential ano-malies: An enhanced analytic signal technique[J]. Geophysics,1996,61(2):373-386.
[17] Hsu S K,Coppens D and Shyu C T.Depth to magne-tic source using the generalized analytic signal[J].Geophysics,1998,63(6):1947-1957.
[18] Bastani M and Pedersen L B.Automatic interpretation of magnetic dike parameters using the analytic signal technique[J].Geophysics,2001,66(2):551-561.
[19] Smith R S,Thurston J B,Dai T F,et al.ISPI: the improved source parameters imaging method[J].Geophysical Prospecting,1998,46(2):141-151.
[20] Salem A,Ravat D,Mushayandebvu M F,et al.Linea-rized least-squares method for interpretation of potential-field data from sources of simple geometry[J]. Geophysics,2004,69(3):783-788.
[21] Salem A.Interpretation of magnetic data using analy-tic signal derivatives[J]. Geophysical Prospecting,2005,53(1):75-82.
[22] Thompson D T.EULDPH: A new technique for ma-king computer-assisted depth estimates from magnetic data[J].Geophysics,1982,47(1):31-37.
[23] Reid A N,Allsop J M,Granser H.Magnetic interpretation in three dimensions using Euler deconvolution[J].Geophysics,1990,55(1):80-91.
[24] Ma G and Du X.An improved analytic signal technique for the depth and structural index from 2D magnetic anomaly data[J].Pure and Applied Geophysics,2012,169(8):2193-2200.
[25] Cooper G R J.The automatic determination of the location and depth of contacts and dykes from aeromagnetic data[J].Pure and Applied Geophysics,2014,171(9):2417-2423.
[26] Cooper G R J.Using the analytic signal amplitude to determine the location and depth of thin dykes from magnetic data[J].Geophysics,2015,80 (1):J1-J6.
[27] 马国庆,黄大年,李丽丽,等.重磁异常解释的归一化局部波数法[J].地球物理学报,2014,57(4):1300-1309.MA Guoqing,HUANG Danian,LI Lili,et al.A normalized local wave number method for interpretation of gravity and magnetic anomalies[J].Chinese Journal of Geophysics,2014,57(4):1300-1309.
[28] 马国庆,杜晓娟,李丽丽.改进的位场相关成像方法[J].地球科学——中国地质大学学报,2013,38(5):1121-1127.MA Guoqing,DU Xiaojuan,LI Lili.Improved potential field correlation imaging method[J].Earth Science:Journal of China University of Geosciences,2013,38(5):1121-1127.
[29] Ma Guoqing,Liu Cai,Xu Jiashu,et al.Correlation ima-ging method based on local wave number for interpreting magnetic data[J].Journal of Applied Geophysics,2017,138(1):17-22.
[30] Ma Guoqing,Liu Cai,Li Lili.Balanced horizontal derivative of potential field data to recognize the edges and estimate location parameters of the source[J]. Journal of Applied Geophysics,2014,108(9):12-18.
[31] Salem A and Ravat D.A combined analytic signal and Euler method (AN-EUL) for automatic interpretation of magnetic data[J].Geophysics,2003,68(6):1952-1961.
[32] Wen B D,Hsu S K and Yeh Y C.A derivative-based interpretation approach to estimating source parameters of simple 2D magnetic sources from Euler deconvolution,the analytic-signal method and analytical expressions of the anomalies[J].Geophysical Prospecting,2007,55(1):255-264.
[33] Stavrev P and Reid A.Degrees of homogeneity of potential fields and structural indices of Euler deconvolution[J].Geophysics,2007,72(1):L1-L12.