Message Board

Respected readers, authors and reviewers, you can add comments to this page on any questions about the contribution, review,        editing and publication of this journal. We will give you an answer as soon as possible. Thank you for your support!

Name
E-mail
Phone
Title
Content
Verification Code
Turn off MathJax
Article Contents

DENG Kailiang, HUANG Motao, WU Taiqi, WANG Weiping, OUYANG Yongzhong, CHEN Xin, XIONG Xiong, LIU Min, WANG Xu. Downward Continuation of Gravity Using the Band-Limited Models for High-Order Radial Derivatives of Gravity Anomaly[J]. Geomatics and Information Science of Wuhan University. doi: 10.13203/j.whugis20210630
Citation: DENG Kailiang, HUANG Motao, WU Taiqi, WANG Weiping, OUYANG Yongzhong, CHEN Xin, XIONG Xiong, LIU Min, WANG Xu. Downward Continuation of Gravity Using the Band-Limited Models for High-Order Radial Derivatives of Gravity Anomaly[J]. Geomatics and Information Science of Wuhan University. doi: 10.13203/j.whugis20210630

Downward Continuation of Gravity Using the Band-Limited Models for High-Order Radial Derivatives of Gravity Anomaly

doi: 10.13203/j.whugis20210630
Funds:

The National Natural Science Foundation of China, Nos.42174013, 41804011, 41774021

  • Received Date: 2022-05-22
    Available Online: 2022-06-17
  • Taylor series expansion is often used in the downward continuation of potential field, and its performance depends on the accuracy and reliability of the vertical or radial partial derivatives (VPDs or RPDs) of potential field parameters. In order to avoid the singularity on spherical boundary and the uncertainty to the computational results by using the closed analytic kernel function to solve the partial derivative, considering the fact that all kinds of gravity observations behave as a type of limited spectrum bandwidth signal after being filtered, this research proposes to express the kernel function of the Poisson integral for the external gravity anomaly by a spherical harmonic series expansion, which is then truncated into a band-limited summation that has the same spectrum range as the gravity observation. After that, we derive a set of band-limited formulas to calculate the high-order RPDs, which are modified and applied to the downward continuation of the gravity anomaly by Taylor series expansion. The formulas are validated using the ultra-high-degree geopotential model EGM2008 by a two-stage procedure. The numerical tests of the band-limited formulas and the Taylor series expansion downward continuation model show that the proposed band-limited formulas have good reliability and validity, and are superior to other models in terms of stability and accuracy.
  • [1] Moritz H. Advanced Physical Geodesy[M]. Karlsruhe:Herbert Wichmann Verlag, 1980
    [2] Sebera J, Šprlák M, Novák P, et al. Iterative Spherical Downward Continuation Applied to Magnetic and Gravitational Data from Satellite[J]. Surveys in Geophysics, 2014, 35(4):941-958
    [3] Pitoňák M, Novák P, Eshagh M, et al. Downward Continuation of Gravitational Field Quantities to an Irregular Surface by Spectral Weighting[J]. Journal of Geodesy, 2020, 94(7):1-26
    [4] Leão J W D, Silva J B C. Discrete Linear Transformations of Potential Field Data[J]. GEOPHYSICS, 1989, 54(4):497-507
    [5] Pawlowski R S. Preferential Continuation for Potential-Field Anomaly Enhancement[J]. GEOPHYSICS, 1995, 60(2):390-398
    [6] Fedi M, Florio G. A Stable Downward Continuation by Using the ISVD Method[J]. Geophysical Journal International, 2002, 151(1):146-156
    [7] Trompat H, Boschetti F, Hornby P. Improved Downward Continuation of Potential Field Data[J]. Exploration Geophysics, 2003, 34(4):249-256
    [8] Heiskanen W A, Moritz H. Physical Geodesy[M]. San Francisco:Freeman and Company, 1967
    [9] Martinec Z. Stability Investigations of a Discrete Downward Continuation Problem for Geoid Determination in the Canadian Rocky Mountains[J]. Journal of Geodesy, 1996, 70(11):805-828
    [10] Novák P, Heck B. Downward Continuation and Geoid Determination Based on Band-Limited Airborne Gravity Data[J]. Journal of Geodesy, 2002, 76(5):269-278
    [11] SansòF, Sideris M. Geoid Determination:Theory and Methods[M]. Berlin:Springer, 2013
    [12] Xu P L. Truncated SVD Methods for Discrete Linear Ill-Posed Problems[J]. Geophysical Journal International, 1998, 135(2):505-514
    [13] Hansen P C, O'Leary D P. The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems[J]. SIAM Journal on Scientific Computing, 1993, 14(6):1487-1503
    [14] Kern M. An Analysis of the Combination and Downward Continuation of Satellite, Airborne and Terrestrial Gravity Data[D]. Calgary:University of Calgary, 2003
    [15] Alberts B, Klees R. A Comparison of Methods for the Inversion of Airborne Gravity Data[J]. Journal of Geodesy, 2004, 78(1/2):55-65
    [16] Hwang C, Hsiao Y S, Shih H C, et al. Geodetic and Geophysical Results from a Taiwan Airborne Gravity Survey:Data Reduction and Accuracy Assessment[J]. Journal of Geophysical Research:Solid Earth, 2007, 112(B4):93-101
    [17] Bjerhammar A. A New Theory of Geodetic Gravity[M]. Stockholm:Tekniska Hogskolan, 1964
    [18] Dampney C N G. The Equivalent Source Technique[J]. GEOPHYSICS, 1969, 34(1):39-53
    [19] Sünkel H. The Generation of a Mass Point Model from Surface Gravity Data[R]. Ohio:Ohio State University, 1983
    [20] Boschetti F, Therond V, Hornby P. Feature Removal and Isolation in Potential Field Data[J]. Geophysical Journal International, 2004, 159(3):833-841
    [21] Novák P, Kern M, Schwarz K. Numerical Studies on the Harmonic Downward Continuation of Band-Limited Airborne Gravity[J]. Studia Geophysica et Geodaetica, 2001, 45:327-345
    [22] Novák P, Kern M, Schwarz K P, et al. On Geoid Determination from Airborne Gravity[J]. Journal of Geodesy, 2003, 76(9/10):510-522
    [23] Kern M, Schwarz K K P P, Sneeuw N. A Study on the Combination of Satellite, Airborne, and Terrestrial Gravity Data[J]. Journal of Geodesy, 2003, 77(3/4):217-225
    [24] Mansi A H, Capponi M, Sampietro D. Downward Continuation of Airborne Gravity Data by Means of the Change of Boundary Approach[J]. Pure and Applied Geophysics, 2018, 175(3):977-988
    [25] Ma G Q, Liu C, Huang D N, et al. A Stable Iterative Downward Continuation of Potential Field Data[J]. Journal of Applied Geophysics, 2013, 98:205-211
    [26] Zhang C, Lü Q, Yan J Y, et al. Numerical Solutions of the Mean-Value Theorem:New Methods for Downward Continuation of Potential Fields[J]. Geophysical Research Letters, 2018, 45(8):3461-3470
    [27] Tran K V, Nguyen T N. A Novel Method for Computing the Vertical Gradients of the Potential Field:Application to Downward Continuation[J]. Geophysical Journal International, 2019, 220(2):1316-1329
    [28] Wei Ziqing. High-Order Radial Derivatives of Harmonic Function and Gravity Anomaly[J]. Journal of Physical Science and Application, 2014, 4(7):454-467
    [29] Wong L, Gore R. Accuracy of Geoid Heights from Modified Stokes Kernels[J]. Geophysical Journal International, 1969, 18(1):81-91
    [30] Vaníček P, Featherstone W E. Performance of Three Types of Stokes's Kernel in the Combined Solution for the Geoid[J]. Journal of Geodesy, 1998, 72(12):684-697
    [31] Wang Y M, Saleh J, Li X, et al. The US Gravimetric Geoid of 2009(USGG2009):Model Development and Evaluation[J]. Journal of Geodesy, 2012, 86(3):165-180
    [32] Pavlis N K, Holmes S A, Kenyon S C, et al. The Development and Evaluation of the Earth Gravitational Model 2008(EGM2008)[J]. Journal of Geophysical Research:Solid Earth, 2012, 117(B4)
  • 加载中
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Article Metrics

Article views(101) PDF downloads(3) Cited by()

Related
Proportional views

Downward Continuation of Gravity Using the Band-Limited Models for High-Order Radial Derivatives of Gravity Anomaly

doi: 10.13203/j.whugis20210630
Funds:

The National Natural Science Foundation of China, Nos.42174013, 41804011, 41774021

Abstract: Taylor series expansion is often used in the downward continuation of potential field, and its performance depends on the accuracy and reliability of the vertical or radial partial derivatives (VPDs or RPDs) of potential field parameters. In order to avoid the singularity on spherical boundary and the uncertainty to the computational results by using the closed analytic kernel function to solve the partial derivative, considering the fact that all kinds of gravity observations behave as a type of limited spectrum bandwidth signal after being filtered, this research proposes to express the kernel function of the Poisson integral for the external gravity anomaly by a spherical harmonic series expansion, which is then truncated into a band-limited summation that has the same spectrum range as the gravity observation. After that, we derive a set of band-limited formulas to calculate the high-order RPDs, which are modified and applied to the downward continuation of the gravity anomaly by Taylor series expansion. The formulas are validated using the ultra-high-degree geopotential model EGM2008 by a two-stage procedure. The numerical tests of the band-limited formulas and the Taylor series expansion downward continuation model show that the proposed band-limited formulas have good reliability and validity, and are superior to other models in terms of stability and accuracy.

DENG Kailiang, HUANG Motao, WU Taiqi, WANG Weiping, OUYANG Yongzhong, CHEN Xin, XIONG Xiong, LIU Min, WANG Xu. Downward Continuation of Gravity Using the Band-Limited Models for High-Order Radial Derivatives of Gravity Anomaly[J]. Geomatics and Information Science of Wuhan University. doi: 10.13203/j.whugis20210630
Citation: DENG Kailiang, HUANG Motao, WU Taiqi, WANG Weiping, OUYANG Yongzhong, CHEN Xin, XIONG Xiong, LIU Min, WANG Xu. Downward Continuation of Gravity Using the Band-Limited Models for High-Order Radial Derivatives of Gravity Anomaly[J]. Geomatics and Information Science of Wuhan University. doi: 10.13203/j.whugis20210630
Reference (32)

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return