基于起伏地层的曲面重力场快速高精度正演
|
摘要
Parker公式在起伏地层重力场正演方面以其简洁、快速等优点被广泛应用于地形改正以及界面反演等,但传统的Parker公式正演方法存在一定的缺陷,在起伏地层模型重力场的正演计算中,由于正演式中e的指数项数值稳定性较差,导致正演结果精度不高。在前人研究的基础上,对Parker公式进行了改进,通过增加上、下界面平均值的方法,提高正演的数值稳定性,改进后的正演精度得到大幅提升。在此基础上,提出了一种曲面观测算法,将观测面由传统的水平面推广到任意起伏面,实现了上下界面起伏地层在起伏观测面上的快速高精度重力正演计算和带地形的密度界面起伏模型的快速高精度重力正演模拟。为了保障数值精度,采用了Gauss-FFT算法,模型实验均取得很好效果。
In the aspects of undulating structure forward, Parker put forward a famous formula in 1972. Parker's formula is widely used in terrain correction and interface inversion for it's succinct and efficient. However, the original Parker's formular have some deficiencies innumerical stability, which is caused by the exponent term of e in the formula. In this paper, Parker formula has been re-derived based on the previous research work, the numerical stability has been increased by adding interface averages. The improved formula accuracy also has been greatly improved. In addition, a surface observation method algorithm is proposed based on this improved forward algorithm. This method can extend the observation surface from the traditional horizontal plane to any undulating plane, and has high computational accuracy and efficiency. In order to ensure the numerical accuracy, a new algorithm-Gauss-FFT method has been adopted.
In the aspects of undulating structure forward, Parker put forward a famous formula in 1972. Parker's formula is widely used in terrain correction and interface inversion for it's succinct and efficient. However, the original Parker's formular have some deficiencies innumerical stability, which is caused by the exponent term of e in the formula. In this paper, Parker formula has been re-derived based on the previous research work, the numerical stability has been increased by adding interface averages. The improved formula accuracy also has been greatly improved. In addition, a surface observation method algorithm is proposed based on this improved forward algorithm. This method can extend the observation surface from the traditional horizontal plane to any undulating plane, and has high computational accuracy and efficiency. In order to ensure the numerical accuracy, a new algorithm-Gauss-FFT method has been adopted.
引文
[1] 曾华霖.重力场与重力勘探[M].北京:地质出版社,2005.ZENG H L.Gravity field and gravity exploration[M].Beijing:Geological Publishing House,2005.(In Chinese)
[2] MANIK TALWANI,J LAMAR WORZEL,MARK LANDISMAN.Rapid gravity computations for two-dimensional bodies with application to the mendocino submarine fracture zone[J].Journal of Geophysical Research,1959,64(1):49-59.
[3] DEZSO NAGY.The gravitational attraction of a right rectangular prism[J].Geophysics,1966,31(2):362-371.
[4] MK PAUL.The gravity effect of a homogeneous polyhedron for three-dimensional interpretation[J] Pure and Applied Geophysics,1974,112(3):553-561.
[5] DONALD PLOUFF.Gravity and magnetic fields of polygonal prisms and application to magnetic terrain corrections[J].Geophysics,1976,41(4):727-741.
[6] MANIK TAIWANI,MAURICE EWING.Rapid computation of gravitational attraction of three-dimensional bodies of arbitrary shape[J].Geophysics,1960,25(1):203-225.
[7] X.LI,M.CHOUTEAU.Three-dimensional gravity modeling in all space [J].Surveys In Geophysics,July 1998,19(4):339-368.
[8] DEZSO NAGY,GABOR PAPP,JUDIT BENEDEK.The gravitational potential and its derivatives for the prism [J].Journal of Geodesy,2000,74(7-8):552-560.
[9] J.GARCIA-ABDESLEM.The gravitational attraction of a right rectangular prism with density varying with depth following a cubic polynomial [J].Geophysics,2005,70(6):39-42.
[10] J.GARCIA-ABDESLEM.Gravitational attraction of a rectangular prism with depth-dependent density [J].Geophysics,1992,57(3):470-473.
[11] 相鹏,刘展.基于Parker算法的磁性双界面模式正反演研究[J].石油天然气学报(江汉石油学院报),2008,30(3):78-82.XIANG P,LIU Z.Magnetic interfacial inversion using dual interface pattern based on Parker algorithm [J].Journal of Oil and Gas Technology,2008,30(3):78-82.(In Chinese)
[12] 冯娟,孟小红,陈召曦,等.三维密度界面的正反演研究和应用[J].地球物理学报,2014,57(1):287-294.FENG J,MENG X H,CHEN Z X,et al.The investigation and application of three-dimensional density interface[J].Chinese Journal of geophysics,2014,57(1):287-284.(In Chinese)
[13] 姜永涛,张永志,王帅,等.考虑沉积层重力改正的中国西部Moho面深度反演[J].地震研究,2015,38(2):257-261.JIANG Y T,ZHANG Y Z,WANG S,et al.Inversion of Moho Depth in western China considering gravity correction of deposition layer[J].Journal of Seismological Research,2015,38(2):257-261.(In Chinese)
[14] 卢鹏羽,马国庆.基于重力全张量数据的Parker-Oldenburg算法研究[J].世界地质,2016,35(1):216-222.LU P Y,MA G Q.Parker-Oldenburg algorithm based on full tensor gravity data[J].Global Geology,2016,35(1):216-222.(In Chinese)
[15] BK BHATTACHARYYA.Continuous spectrum of the total-magnetic-field anomaly due to a rectangular prismatic body [J].Geophysics,1966,31(1):97-121.
[16] JAN ARNOLDUS SCHOUTEN.A fundamental analysis of magnetic anomalies over oceanic ridges[J].Marine Geophysical Researches,1971,1(2):111-144.
[17] HANS SCHOUTEN,KEITH MCCAMY.Filtering marine magnetic anomalies [J].Journal of Geophysical Research,1972,77(35):7089-7099.
[18] RL PARKER.The rapid calculation of potential anomalies[J].Geophysical Journal of the Royal Astronomical Society,1973,31(4):447-455.
[19] RENE FORSBERG.Gravity field terrain effect computations by fft[J].Bulletin geode sique,1985,59(4):342-360.
[20] 冯锐.三维物性分布的位场计算[J].地球物理学报,1986,29(04):399-406.FENG R.A computation method of potential field with three-dimensional density and magnetization distributions[J].Acta Geophysica Sinica,1986,29(4):399-406.(In Chinese)
[21] XIA,J.H.& SPROWL,D.R.Moho depths in Kansas from gravity inversion assuming exponential density contrast[J].Comput.Geosci,1995,21(2):237-244.
[22] YUFU CHAI,WILLIAM J HINZE.Gravity inversion of an interface above which the density contrast varies exponentially with depth [J].Geophysics,1988,53(6):837-845.
[23] 柴玉璞,贾继军.Parker公式的一系列推广及其在石油重力勘探中的应用前景[J].石油地球物理勘探,1990,25(3):321-332.CHAI Y P,JIA J J.Parker’s formulas in different forms and their applications to oil gravity survey[J].OGP,1990,25(3):321-332.(In Chinese)
[24] 陈中林.Dft理论及其新算法研究[J].地球物理学报,1986,3(3):255-272.CHEN Z L.The investigations of DFT theory and its new computing method[J].Acta Geophysica Sinica,1986,29(3):255-272.(In Chinese)
[25] 柴玉璞.偏移抽样理论及其应用[M].北京:石油工业出版社,1997.CHAI Y P.Shift sampling theory and its application [M].Beijing:Petroleum Industry Press,1997.(In Chinese)
[26] WU,L.& TIAN,G.High-precision Fourier forward modeling of potential fields[J].Geophysics,2014,79(5):59-68.
[27] BLAKELY,R.J.Potential theory in gravity and magnetic applications[M].Cambridge Univ.Press,Cambridge,U.K.1995.
[28] BRACEWELL,R.The Fourier transform and its applications[M].McGraw-Hill,New York,1965.
[2] MANIK TALWANI,J LAMAR WORZEL,MARK LANDISMAN.Rapid gravity computations for two-dimensional bodies with application to the mendocino submarine fracture zone[J].Journal of Geophysical Research,1959,64(1):49-59.
[3] DEZSO NAGY.The gravitational attraction of a right rectangular prism[J].Geophysics,1966,31(2):362-371.
[4] MK PAUL.The gravity effect of a homogeneous polyhedron for three-dimensional interpretation[J] Pure and Applied Geophysics,1974,112(3):553-561.
[5] DONALD PLOUFF.Gravity and magnetic fields of polygonal prisms and application to magnetic terrain corrections[J].Geophysics,1976,41(4):727-741.
[6] MANIK TAIWANI,MAURICE EWING.Rapid computation of gravitational attraction of three-dimensional bodies of arbitrary shape[J].Geophysics,1960,25(1):203-225.
[7] X.LI,M.CHOUTEAU.Three-dimensional gravity modeling in all space [J].Surveys In Geophysics,July 1998,19(4):339-368.
[8] DEZSO NAGY,GABOR PAPP,JUDIT BENEDEK.The gravitational potential and its derivatives for the prism [J].Journal of Geodesy,2000,74(7-8):552-560.
[9] J.GARCIA-ABDESLEM.The gravitational attraction of a right rectangular prism with density varying with depth following a cubic polynomial [J].Geophysics,2005,70(6):39-42.
[10] J.GARCIA-ABDESLEM.Gravitational attraction of a rectangular prism with depth-dependent density [J].Geophysics,1992,57(3):470-473.
[11] 相鹏,刘展.基于Parker算法的磁性双界面模式正反演研究[J].石油天然气学报(江汉石油学院报),2008,30(3):78-82.XIANG P,LIU Z.Magnetic interfacial inversion using dual interface pattern based on Parker algorithm [J].Journal of Oil and Gas Technology,2008,30(3):78-82.(In Chinese)
[12] 冯娟,孟小红,陈召曦,等.三维密度界面的正反演研究和应用[J].地球物理学报,2014,57(1):287-294.FENG J,MENG X H,CHEN Z X,et al.The investigation and application of three-dimensional density interface[J].Chinese Journal of geophysics,2014,57(1):287-284.(In Chinese)
[13] 姜永涛,张永志,王帅,等.考虑沉积层重力改正的中国西部Moho面深度反演[J].地震研究,2015,38(2):257-261.JIANG Y T,ZHANG Y Z,WANG S,et al.Inversion of Moho Depth in western China considering gravity correction of deposition layer[J].Journal of Seismological Research,2015,38(2):257-261.(In Chinese)
[14] 卢鹏羽,马国庆.基于重力全张量数据的Parker-Oldenburg算法研究[J].世界地质,2016,35(1):216-222.LU P Y,MA G Q.Parker-Oldenburg algorithm based on full tensor gravity data[J].Global Geology,2016,35(1):216-222.(In Chinese)
[15] BK BHATTACHARYYA.Continuous spectrum of the total-magnetic-field anomaly due to a rectangular prismatic body [J].Geophysics,1966,31(1):97-121.
[16] JAN ARNOLDUS SCHOUTEN.A fundamental analysis of magnetic anomalies over oceanic ridges[J].Marine Geophysical Researches,1971,1(2):111-144.
[17] HANS SCHOUTEN,KEITH MCCAMY.Filtering marine magnetic anomalies [J].Journal of Geophysical Research,1972,77(35):7089-7099.
[18] RL PARKER.The rapid calculation of potential anomalies[J].Geophysical Journal of the Royal Astronomical Society,1973,31(4):447-455.
[19] RENE FORSBERG.Gravity field terrain effect computations by fft[J].Bulletin geode sique,1985,59(4):342-360.
[20] 冯锐.三维物性分布的位场计算[J].地球物理学报,1986,29(04):399-406.FENG R.A computation method of potential field with three-dimensional density and magnetization distributions[J].Acta Geophysica Sinica,1986,29(4):399-406.(In Chinese)
[21] XIA,J.H.& SPROWL,D.R.Moho depths in Kansas from gravity inversion assuming exponential density contrast[J].Comput.Geosci,1995,21(2):237-244.
[22] YUFU CHAI,WILLIAM J HINZE.Gravity inversion of an interface above which the density contrast varies exponentially with depth [J].Geophysics,1988,53(6):837-845.
[23] 柴玉璞,贾继军.Parker公式的一系列推广及其在石油重力勘探中的应用前景[J].石油地球物理勘探,1990,25(3):321-332.CHAI Y P,JIA J J.Parker’s formulas in different forms and their applications to oil gravity survey[J].OGP,1990,25(3):321-332.(In Chinese)
[24] 陈中林.Dft理论及其新算法研究[J].地球物理学报,1986,3(3):255-272.CHEN Z L.The investigations of DFT theory and its new computing method[J].Acta Geophysica Sinica,1986,29(3):255-272.(In Chinese)
[25] 柴玉璞.偏移抽样理论及其应用[M].北京:石油工业出版社,1997.CHAI Y P.Shift sampling theory and its application [M].Beijing:Petroleum Industry Press,1997.(In Chinese)
[26] WU,L.& TIAN,G.High-precision Fourier forward modeling of potential fields[J].Geophysics,2014,79(5):59-68.
[27] BLAKELY,R.J.Potential theory in gravity and magnetic applications[M].Cambridge Univ.Press,Cambridge,U.K.1995.
[28] BRACEWELL,R.The Fourier transform and its applications[M].McGraw-Hill,New York,1965.