倾斜台阶重力异常正演计算公式剖析
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摘要
规则地质体的正演异常是进行实际数据解释的依据,因此其正确性至关重要。现有教材和大部分论文中所列出的倾斜台阶重力异常正演公式在一定条件下会出现畸点,从而对构造模型的数据解释会产生困扰。笔者从台阶的重力积分表达式出发,重新推导了倾斜台阶模型的重力异常正演公式,模型试验表明笔者新推导公式不会出现畸点,这为数据解释提供更准确的基础数据。
The forward anomaly of regular geological bodies is the basis for the interpretation of actual data,so its correctness is crucial. Gradient step gravity anomaly forward formula listed in the existing textbooks and most of the papers have distortion points under certain conditions,which will cause trouble to the data interpretation of the structural model. Starting from the gravity integral expression of the step,the author re-derived the gravity anomaly forward formula of the inclined step model. The model test shows that the new derivation formula will not have distortion points,which provides more accurate basic data for data interpretation.
The forward anomaly of regular geological bodies is the basis for the interpretation of actual data,so its correctness is crucial. Gradient step gravity anomaly forward formula listed in the existing textbooks and most of the papers have distortion points under certain conditions,which will cause trouble to the data interpretation of the structural model. Starting from the gravity integral expression of the step,the author re-derived the gravity anomaly forward formula of the inclined step model. The model test shows that the new derivation formula will not have distortion points,which provides more accurate basic data for data interpretation.
引文
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[2] Hubbert M K. A line-integral method of computing the gravimetric effects of two-dimensional masses[J]. Geophysics,1948,13(2):215-225.
[3] Talwani M,Worzel J L,Landisman M. Rapid gravity computations for two-dimensional bodies with application to the Mendocino submarine fracture zone[J]. Journal of Geophysical Research-Atmospheres,1959,64(1):49-59.
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[6]蔡宗熹,姜兰.二维倾斜台阶断层重力异常的正反演[J].物化探计算技术,1986,8(1):20-41.CAI Zong-xi,JIANG Lan. Forward and inverse problems of gravity anomalies due to 2-D inclined faults[J].Computing Techniques for Geophysical and Geochemical Exploration(in Chinese),1986,8(1):20-41.
[7] Won I J,Bevis M. Computing the gravitational and magnetic anomalies due to a polygon:algorithms and fortransubroutine[J]. Geophysics,1987,52(2):232-238.
[8] Butler D K. Generalized gravity gradient analysis for 2-D inversion[J]. Geophysics, 1995, 60(4):1018-1028.
[9]郇恒飞,吴燕冈,管彦武,等.利用实测重力垂直梯度反演长白山地区一条剖面的深部构造[J].世界地质,2012,31(4):791-796.HUAN Heng-fei,WU Yan-gang,GUAN Yan-wu,et al.Deep structure inversion by measurement of vertical gradient of gravity for a profile of Changbai Mountain area[J]. Global Geology,2012,31(4):791-796.
[10]李丽丽,孟令顺,杜晓娟,等.一种断层重力异常定量解释方法[J].石油地球物理勘探,2012,47(4):665-667.LI Li-li,MENG Ling-shun,DU Xiao-juan,et al. A quantitative method for interpreting gravity anomaly of fault[J]. Oil Geophysical Prospecting, 2012, 47(4):665-667.
[11]张凤琴,朱洪英,张凤旭,等.基于DCT的重力归一化总梯度及相位在识别断裂构造中的研究与应用[J].世界地质,2008,27(1):83-88.ZHANG Feng-qin,ZHU Hong-ying,ZHANG Feng-xu,et al. Study and application of normalized full gradient of gravity anomalies and phase based on DCT in identifying fracture[J]. Global Geology,2008,27(1):83-88.
[12]冯兰天.台阶(断层)模型重力异常正演计算的一种新算法[J].世界地质,2014,33(2):477-483.FENG Lan-tian. A new algorithm for gravity anomaly forward calculation of stepped(fault)model[J].Global Geology,2014,33(2):477-483.
[13]苏和朋,李文尧,王荣华,等.倾斜台阶重力异常公式的改进[J].地球物理进展,2014,29(5):2066-2071.SU He-peng,LI Wen-yao,WANG Rong-hua, et al.Some improvements on the formula for inclined steps gravity anomaly[J]. Progress in Geophysics,2014,29(5):2066-2071.
[2] Hubbert M K. A line-integral method of computing the gravimetric effects of two-dimensional masses[J]. Geophysics,1948,13(2):215-225.
[3] Talwani M,Worzel J L,Landisman M. Rapid gravity computations for two-dimensional bodies with application to the Mendocino submarine fracture zone[J]. Journal of Geophysical Research-Atmospheres,1959,64(1):49-59.
[4] Grant F S. Interpretation theory in applied geophysics[J]. Geophysical Journal of the Royal Astronomical Society,2010,11(5):566-566.
[5] Stanley J M,Green R. Gravity gradients and its interpretation of the truncated plate[J]. Geophysics,1976,41:1370-1376.
[6]蔡宗熹,姜兰.二维倾斜台阶断层重力异常的正反演[J].物化探计算技术,1986,8(1):20-41.CAI Zong-xi,JIANG Lan. Forward and inverse problems of gravity anomalies due to 2-D inclined faults[J].Computing Techniques for Geophysical and Geochemical Exploration(in Chinese),1986,8(1):20-41.
[7] Won I J,Bevis M. Computing the gravitational and magnetic anomalies due to a polygon:algorithms and fortransubroutine[J]. Geophysics,1987,52(2):232-238.
[8] Butler D K. Generalized gravity gradient analysis for 2-D inversion[J]. Geophysics, 1995, 60(4):1018-1028.
[9]郇恒飞,吴燕冈,管彦武,等.利用实测重力垂直梯度反演长白山地区一条剖面的深部构造[J].世界地质,2012,31(4):791-796.HUAN Heng-fei,WU Yan-gang,GUAN Yan-wu,et al.Deep structure inversion by measurement of vertical gradient of gravity for a profile of Changbai Mountain area[J]. Global Geology,2012,31(4):791-796.
[10]李丽丽,孟令顺,杜晓娟,等.一种断层重力异常定量解释方法[J].石油地球物理勘探,2012,47(4):665-667.LI Li-li,MENG Ling-shun,DU Xiao-juan,et al. A quantitative method for interpreting gravity anomaly of fault[J]. Oil Geophysical Prospecting, 2012, 47(4):665-667.
[11]张凤琴,朱洪英,张凤旭,等.基于DCT的重力归一化总梯度及相位在识别断裂构造中的研究与应用[J].世界地质,2008,27(1):83-88.ZHANG Feng-qin,ZHU Hong-ying,ZHANG Feng-xu,et al. Study and application of normalized full gradient of gravity anomalies and phase based on DCT in identifying fracture[J]. Global Geology,2008,27(1):83-88.
[12]冯兰天.台阶(断层)模型重力异常正演计算的一种新算法[J].世界地质,2014,33(2):477-483.FENG Lan-tian. A new algorithm for gravity anomaly forward calculation of stepped(fault)model[J].Global Geology,2014,33(2):477-483.
[13]苏和朋,李文尧,王荣华,等.倾斜台阶重力异常公式的改进[J].地球物理进展,2014,29(5):2066-2071.SU He-peng,LI Wen-yao,WANG Rong-hua, et al.Some improvements on the formula for inclined steps gravity anomaly[J]. Progress in Geophysics,2014,29(5):2066-2071.