Close Search Advanced
Journals
Resources
About Us
Open Access

A Fast Local Level Set Method for Inverse Gravimetry

A Fast Local Level Set Method for Inverse Gravimetry
Preview
Add to basket

Year:    2011

Communications in Computational Physics, Vol. 10 (2011), Iss. 4 : pp. 1044–1070

Abstract

We propose a fast local level set method for the inverse problem of gravimetry. The theoretical foundation for our approach is based on the following uniqueness result: if an open set D is star-shaped or x3-convex with respect to its center of gravity, then its exterior potential uniquely determines the open set D. To achieve this purpose constructively, the first challenge is how to parametrize this open set D as its boundary may have a variety of possible shapes. To describe those different shapes we propose to use a level-set function to parametrize the unknown boundary of this open set. The second challenge is how to deal with the issue of partial data as gravimetric measurements are only made on a part of a given reference domain Ω. To overcome this difficulty, we propose a linear numerical continuation approach based on the single layer representation to find potentials on the boundary of some artificial domain containing the unknown set D. The third challenge is how to speed up the level set inversion process. Based on some features of the underlying inverse gravimetry problem such as the potential density being constant inside the unknown domain, we propose a novel numerical approach which is able to take advantage of these features so that the computational speed is accelerated by an order of magnitude. We carry out numerical experiments for both two- and three-dimensional cases to demonstrate the effectiveness of the new algorithm.

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.100710.021210a

Communications in Computational Physics, Vol. 10 (2011), Iss. 4 : pp. 1044–1070

Published online:    2011-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    27

Keywords:   

  1. A new non-iterative reconstruction method for the electrical impedance tomography problem

    Ferreira, A D | Novotny, A A

    Inverse Problems, Vol. 33 (2017), Iss. 3 P.035005

    https://doi.org/10.1088/1361-6420/aa54e4 [Citations: 24]

  2. An improved fast local level set method for three-dimensional inverse gravimetry

    Lu, Wangtao | Leung, Shingyu | Qian, Jianliang

    Inverse Problems & Imaging, Vol. 9 (2015), Iss. 2 P.479

    https://doi.org/10.3934/ipi.2015.9.479 [Citations: 16]
  3. Mathematical Methods in Image Processing and Inverse Problems

    An Adjoint State Method for An Schrödinger Inverse Problem

    Wei, Siyang | Leung, Shingyu

    2021

    https://doi.org/10.1007/978-981-16-2701-9_2 [Citations: 0]

  4. Reconstruction of a volumetric source domain

    Bin-Mohsin, B. | Lesnic, D.

    Journal of Computational Methods in Sciences and Engineering, Vol. 19 (2019), Iss. 2 P.367

    https://doi.org/10.3233/JCM-180878 [Citations: 0]

  5. Numerical method for solving the piecewise constant source inverse problem of an elliptic equation from a partial boundary observation data

    Ivanov, D Kh | Kolesov, A E | Vabishchevich, P N

    Journal of Physics: Conference Series, Vol. 2092 (2021), Iss. 1 P.012006

    https://doi.org/10.1088/1742-6596/2092/1/012006 [Citations: 1]

  6. Distance-regularized level set inversion of magnetic data

    Liu, Jin | Xiong, Shengqing | Wang, Wanyin

    GEOPHYSICS, Vol. 89 (2024), Iss. 6 P.G167

    https://doi.org/10.1190/geo2023-0329.1 [Citations: 0]

  7. A noniterative reconstruction method for solving a time-fractional inverse source problem from partial boundary measurements

    Prakash, R | Hrizi, M | Novotny, A A

    Inverse Problems, Vol. 38 (2022), Iss. 1 P.015002

    https://doi.org/10.1088/1361-6420/ac38b6 [Citations: 6]

  8. Joint inversion of surface and borehole magnetic data: A level-set approach

    Li, Wenbin | Qian, Jianliang | Li, Yaoguo

    GEOPHYSICS, Vol. 85 (2020), Iss. 1 P.J15

    https://doi.org/10.1190/geo2019-0139.1 [Citations: 10]

  9. Stochastic inversion of geophysical data by a conditional variational autoencoder

    McAliley, Wallace Anderson | Li, Yaoguo

    GEOPHYSICS, Vol. 89 (2024), Iss. 1 P.WA219

    https://doi.org/10.1190/geo2023-0147.1 [Citations: 4]

  10. A level-set algorithm for the inverse problem of full magnetic gradient tensor data

    Li, Wenbin | Qian, Jianliang

    Applied Mathematics Letters, Vol. 107 (2020), Iss. P.106416

    https://doi.org/10.1016/j.aml.2020.106416 [Citations: 1]

  11. Kantorovich-Rubinstein misfit for inverting gravity-gradient data by the level-set method

    Huang, Guanghui | Zhang, Xinming | Qian, Jianliang

    GEOPHYSICS, Vol. 84 (2019), Iss. 5 P.G55

    https://doi.org/10.1190/geo2018-0771.1 [Citations: 3]

  12. Damage identification in plate structures based on the topological derivative method

    da Silva, A. A. M. | Novotny, A. A.

    Structural and Multidisciplinary Optimization, Vol. 65 (2022), Iss. 1

    https://doi.org/10.1007/s00158-021-03145-1 [Citations: 4]

  13. Analysis of Regularized Kantorovich--Rubinstein Metric and Its Application to Inverse Gravity Problems

    Huang, Guanghui | Qian, Jianliang

    SIAM Journal on Imaging Sciences, Vol. 12 (2019), Iss. 3 P.1528

    https://doi.org/10.1137/18M1201275 [Citations: 2]

  14. A multiple level set method for three-dimensional inversion of magnetic data

    Li, Wenbin | Lu, Wangtao | Qian, Jianliang | Li, Yaoguo

    SEG Technical Program Expanded Abstracts 2017, (2017), P.1723

    https://doi.org/10.1190/segam2017-17729331.1 [Citations: 3]

  15. Learning on the correctness class for domain inverse problems of gravimetry

    Chen, Yihang | Li, Wenbin

    Machine Learning: Science and Technology, Vol. 5 (2024), Iss. 3 P.035072

    https://doi.org/10.1088/2632-2153/ad72cc [Citations: 0]

  16. Multiple level-set joint inversion of traveltime and gravity data with application to ore delineation: A synthetic study

    Zheglova, Polina | Lelièvre, Peter G. | Farquharson, Colin G.

    GEOPHYSICS, Vol. 83 (2018), Iss. 1 P.R13

    https://doi.org/10.1190/geo2016-0675.1 [Citations: 26]

  17. 3D multi-scale resistivity inversion method applied in the tunnel face to borehole observations for tunnel-ahead prospecting

    Pang, Yonghao | Liu, Zhengyu | Nie, Lichao | Zhang, Yongheng | Shao, Junyang | Bai, Peng | Dong, Zhao

    Journal of Applied Geophysics, Vol. 196 (2022), Iss. P.104510

    https://doi.org/10.1016/j.jappgeo.2021.104510 [Citations: 8]

  18. On the Kohn–Vogelius formulation for solving an inverse source problem

    Menoret, P. | Hrizi, M. | Novotny, A. A.

    Inverse Problems in Science and Engineering, Vol. 29 (2021), Iss. 1 P.56

    https://doi.org/10.1080/17415977.2020.1775201 [Citations: 5]

  19. Geometric and level set tomography using ensemble Kalman inversion

    Muir, Jack B | Tsai, Victor C

    Geophysical Journal International, Vol. 220 (2020), Iss. 2 P.967

    https://doi.org/10.1093/gji/ggz472 [Citations: 27]

  20. Mining and Geothermal Complete Session

    SEG Technical Program Expanded Abstracts 2016, (2016), P.1304

    https://doi.org/10.1190/segam2016-mg [Citations: 0]

  21. A new reconstruction method for the inverse source problem from partial boundary measurements

    Canelas, Alfredo | Laurain, Antoine | Novotny, Antonio A

    Inverse Problems, Vol. 31 (2015), Iss. 7 P.075009

    https://doi.org/10.1088/0266-5611/31/7/075009 [Citations: 30]

  22. Shape and location recovery of laser excitation sources in photoacoustic imaging using topological gradient optimization

    BenSalah, Mohamed

    Journal of Computational and Applied Mathematics, Vol. 451 (2024), Iss. P.116047

    https://doi.org/10.1016/j.cam.2024.116047 [Citations: 0]

  23. Recovery of inclusions in 2D and 3D domains for Poisson’s equation

    Ito, Kazufumi | Liu, Ji-Chuan

    Inverse Problems, Vol. 29 (2013), Iss. 7 P.075005

    https://doi.org/10.1088/0266-5611/29/7/075005 [Citations: 7]

  24. Topological asymptotic analysis of an optimal control problem modeled by a coupled system

    Fernandez, L. | Novotny, A.A. | Prakash, R.

    Asymptotic Analysis, Vol. 109 (2018), Iss. 1-2 P.1

    https://doi.org/10.3233/ASY-181465 [Citations: 2]

  25. A reconstruction method for the inverse gravimetric problem

    Gerber-Roth, Anthony | Munnier, Alexandre | Ramdani, Karim

    The SMAI Journal of computational mathematics, Vol. 9 (2023), Iss. P.197

    https://doi.org/10.5802/smai-jcm.99 [Citations: 0]

  26. One-iteration reconstruction algorithm for geometric inverse source problem

    Hrizi, Mourad | Hassine, Maatoug

    Journal of Elliptic and Parabolic Equations, Vol. 4 (2018), Iss. 1 P.177

    https://doi.org/10.1007/s41808-018-0015-4 [Citations: 6]

  27. Noniterative Reconstruction Method for an Inverse Potential Problem Modeled by a Modified Helmholtz Equation

    Fernandez, L. | Novotny, A. A. | Prakash, R.

    Numerical Functional Analysis and Optimization, Vol. 39 (2018), Iss. 9 P.937

    https://doi.org/10.1080/01630563.2018.1432645 [Citations: 12]

  28. A fast local level set adjoint state method for first arrival transmission traveltime tomography with discontinuous slowness

    Li, Wenbin | Leung, Shingyu

    Geophysical Journal International, Vol. 195 (2013), Iss. 1 P.582

    https://doi.org/10.1093/gji/ggt244 [Citations: 25]

  29. Kantorovich-Rubinstein metric based level-set methods for inverting modulus of gravity-force data

    Li, Wenbin | Qian, Jianliang

    Inverse Problems and Imaging, Vol. 16 (2022), Iss. 6 P.1643

    https://doi.org/10.3934/ipi.2022053 [Citations: 2]

  30. A multiple level-set method for 3D inversion of magnetic data

    Li, Wenbin | Lu, Wangtao | Qian, Jianliang | Li, Yaoguo

    GEOPHYSICS, Vol. 82 (2017), Iss. 5 P.J61

    https://doi.org/10.1190/geo2016-0530.1 [Citations: 22]

  31. A noniterative reconstruction method for the inverse potential problem with partial boundary measurements

    Fernandez, Lucas | Novotny, Antonio A. | Prakash, Ravi

    Mathematical Methods in the Applied Sciences, Vol. 42 (2019), Iss. 7 P.2256

    https://doi.org/10.1002/mma.5504 [Citations: 7]

  32. Imaging of mass distributions from partial domain measurement

    Hrizi, Mourad | Novotny, Antonio Andre | Hassine, Maatoug

    Journal of Inverse and Ill-posed Problems, Vol. 0 (2022), Iss. 0

    https://doi.org/10.1515/jiip-2020-0143 [Citations: 0]

  33. A new reconstruction method for the inverse potential problem

    Canelas, Alfredo | Laurain, Antoine | Novotny, Antonio A.

    Journal of Computational Physics, Vol. 268 (2014), Iss. P.417

    https://doi.org/10.1016/j.jcp.2013.10.020 [Citations: 33]

  34. Piecewise Acoustic Source Imaging with Unknown Speed of Sound Using a Level-Set Method

    Huang, Guanghui | Qian, Jianliang | Yang, Yang

    Communications on Applied Mathematics and Computation, Vol. 6 (2024), Iss. 2 P.1070

    https://doi.org/10.1007/s42967-023-00291-9 [Citations: 0]

  35. Joint level set inversion of gravity and travel time data: Application to mineral exploration

    Zheglova, Polina | Farquharson, Colin

    SEG Technical Program Expanded Abstracts 2016, (2016), P.2165

    https://doi.org/10.1190/segam2016-13864508.1 [Citations: 3]

  36. Simultaneously recovering both domain and varying density in inverse gravimetry by efficient level-set methods

    Li, Wenbin | Qian, Jianliang

    Inverse Problems & Imaging, Vol. 15 (2021), Iss. 3 P.387

    https://doi.org/10.3934/ipi.2020073 [Citations: 5]

  37. Reconstruction of a source domain from boundary measurements

    Bin-Mohsin, B. | Lesnic, D.

    Applied Mathematical Modelling, Vol. 45 (2017), Iss. P.925

    https://doi.org/10.1016/j.apm.2017.01.021 [Citations: 6]

  38. A new one‐shot pointwise source reconstruction method

    Machado, Thiago J. | Angelo, Jaqueline S. | Novotny, Antonio A.

    Mathematical Methods in the Applied Sciences, Vol. 40 (2017), Iss. 5 P.1367

    https://doi.org/10.1002/mma.4059 [Citations: 17]

  39. A level-set method for imaging salt structures using gravity data

    Li, Wenbin | Lu, Wangtao | Qian, Jianliang

    GEOPHYSICS, Vol. 81 (2016), Iss. 2 P.G27

    https://doi.org/10.1190/geo2015-0295.1 [Citations: 26]

  40. Generalization of level-set inversion to an arbitrary number of geologic units in a regularized least-squares framework

    Giraud, Jérémie | Lindsay, Mark | Jessell, Mark

    GEOPHYSICS, Vol. 86 (2021), Iss. 4 P.R623

    https://doi.org/10.1190/geo2020-0263.1 [Citations: 14]

  41. Topological Derivatives of Shape Functionals. Part III: Second-Order Method and Applications

    Novotny, Antonio André | Sokołowski, Jan | Żochowski, Antoni

    Journal of Optimization Theory and Applications, Vol. 181 (2019), Iss. 1 P.1

    https://doi.org/10.1007/s10957-018-1420-4 [Citations: 15]

  42. A local level-set method for 3D inversion of gravity-gradient data

    Lu, Wangtao | Qian, Jianliang

    GEOPHYSICS, Vol. 80 (2015), Iss. 1 P.G35

    https://doi.org/10.1190/geo2014-0188.1 [Citations: 30]
  43. Inverse Problems

    Regularization of Nonlinear Inverse Problems

    Richter, Mathias

    2020

    https://doi.org/10.1007/978-3-030-59317-9_4 [Citations: 0]

  44. Numerical method for recovering the piecewise constant right-hand side function of an elliptic equation from a boundary overdetermination data

    Kh Ivanov, D | Kolesov, A E | Vabishchevich, P N

    Journal of Physics: Conference Series, Vol. 1392 (2019), Iss. 1 P.012081

    https://doi.org/10.1088/1742-6596/1392/1/012081 [Citations: 0]

  45. Pollution Sources Reconstruction Based on the Topological Derivative Method

    Fernandez, L. | Novotny, A. A. | Prakash, R. | Sokołowski, J.

    Applied Mathematics & Optimization, Vol. 84 (2021), Iss. 2 P.1493

    https://doi.org/10.1007/s00245-020-09685-0 [Citations: 4]

  46. A level-set approach for joint inversion of surface and borehole magnetic data

    Li, Wenbin | Qian, Jianliang | Li, Yaoguo

    SEG Technical Program Expanded Abstracts 2018, (2018), P.1404

    https://doi.org/10.1190/segam2018-2996911.1 [Citations: 1]

  47. Joint inversion of gravity and traveltime data using a level-set-based structural parameterization

    Li, Wenbin | Qian, Jianliang

    GEOPHYSICS, Vol. 81 (2016), Iss. 6 P.G107

    https://doi.org/10.1190/geo2015-0547.1 [Citations: 30]

  48. Gravity and Magnetics Complete Session

    SEG Technical Program Expanded Abstracts 2017, (2017), P.1708

    https://doi.org/10.1190/segam2017-gm [Citations: 0]

  49. A stability analysis of the harmonic continuation

    Elcrat, A | Isakov, V | Kropf, E | Stewart, D

    Inverse Problems, Vol. 28 (2012), Iss. 7 P.075016

    https://doi.org/10.1088/0266-5611/28/7/075016 [Citations: 5]

  50. A Factorization Method for Multifrequency Inverse Source Problems with Sparse Far Field Measurements

    Griesmaier, Roland | Schmiedecke, Christian

    SIAM Journal on Imaging Sciences, Vol. 10 (2017), Iss. 4 P.2119

    https://doi.org/10.1137/17M111290X [Citations: 30]

  51. Technical Program in full - Part I (ACQ 1 - PS P1)

    SEG Technical Program Expanded Abstracts 2016, (2016), P.1

    https://doi.org/10.1190/segam2016-full [Citations: 0]