Advertisement

Acta Mechanica Sinica

, Volume 11, Issue 4, pp 337–348 | Cite as

A method of interface inversion in inhomogeneous media

  • Ma Xingrui
  • Tao Liang
  • Huang Wenhu
Article

Abstract

First, an approximate solution of time domain interface scattering field is derived by extending the classical Born approximation in the problem of interface scattering. In accordance with the solution form, a projection density compensation (PDC) inversion method is developed according to the projection slice theorem, which is valid for the cases of inhomogeneous media and wave mode transformation. Finally, in the model of layered media, the calculation algorithm and the simulation inversion comparison results of point defect, crack, and crack on an interface, as well as the experiment method and results in the condition of acoustic wave, are given.

Key Words

inhomogeneous media interface inversion wave mode transform projection density compensation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Pao YH. Elastic waves in solids. ASME Trans.J Appl Mech, 1983, 50: 1152–1164zbMATHCrossRefGoogle Scholar
  2. [2]
    Rice JR, et al. Solid mechanics research trends and opportunities.Appl Mech Rev, 1985, 38(10): 1247–1308.Google Scholar
  3. [3]
    Huang WH, Ma XR, Zou ZZ, Tao L. Trends and opportunities on inverse problem in elastodynamics.Chinese Journal of Applied Mechanics, 1994, 11(3): 1–10 (in Chinese)MathSciNetzbMATHGoogle Scholar
  4. [4]
    Achenbach JD, et al. Diffraction of ultrasonic waves by penny-shaped cracks in metals: theory and experiment.J Acoust Soc Am, 1979, 66(6): 1848–1856 (in Chinese)CrossRefGoogle Scholar
  5. [5]
    Vidale J. Finite-difference calculation of travel-times.Bull Seis Soc Am, 1988, 78(6): 2062–2076Google Scholar
  6. [6]
    Qin FH, Luo Y, et al. Finite-difference solution of the eikonal equation along expanding wavefronts.Geophysics, 1992, 57(3): 478–487CrossRefGoogle Scholar
  7. [7]
    Asakawa E, Kawanaka T. Seismic ray tracing using linear traveltime interpolation.Geophysics Prospecting, 1993, 41: 99–111CrossRefGoogle Scholar
  8. [8]
    Muller RK, Kaveh M, Inverson RD. A new approach to acoustical tomography using diffraction technique. In: Metherell AF, ed.Acoustical Imaging. 1980, vol.8, 615–628Google Scholar
  9. [9]
    Devaney AJ. A filtered backpropagation algorithm for diffraction tomography.Ultrasonic Imaging. 1982. 4: 336–350CrossRefGoogle Scholar
  10. [10]
    Rose JH, Opsal JL. Inversion of ultrasonic scattering data. Review of Progress in QNDE, 1981. 187–195Google Scholar
  11. [11]
    Ma XR. Investigation on scattering of elastic waves by interface cracks and primary research on inverse problems in elastodynamics. Dissertation, Harbin: Harbin Institute of Technology, 1987. Chapter 5Google Scholar
  12. [12]
    Beylkin G. Imaging of discontinuities in the inverse scattering problem by inversion of a causal generalized Radon transform.J Math Phys, 1985, 26(1): 99–108MathSciNetCrossRefGoogle Scholar
  13. [13]
    Nagai K. Fourier domain reconstruction of ultrasonic 2-D and 3-D images using exact inverse scattering solution. IEEE Ultrasonics Symposium, 1985. 804–807Google Scholar
  14. [14]
    Wenzel F, Menges D. A comparison between Born inversion and frequency-wavenumber migration.Geophysics, 1989, 54(8): 1006–1011CrossRefGoogle Scholar
  15. [15]
    Thompson RB, Lakin KM, Rose JH. A comparison of the inverse Born and imaging techniques for reconstructing flaw shapes. IEEE Ultrasonics Symposium, 1981. 930–935Google Scholar
  16. [16]
    Teo TJ, Reid JM. Spatial/frequency diversity in inverse scattering. IEEE Ultrasonics Symposium, 1985. 800–803Google Scholar
  17. [17]
    Langenberg KJ. Introduction to the special issue on inverse problems.Wave Motion, 1989, 11: 99–112zbMATHCrossRefGoogle Scholar
  18. [18]
    Norton SJ, Linzer M. Ultrasonic reflectivity imaging in three dimensions: Exact inverse scattering solutions for plane, cylindrical, and spherical apertures. IEEE Trans, 1981, BME-28(2): 202–220Google Scholar
  19. [19]
    Norton SJ, Linzer M. Ultrasonic reflectivity tomography: Reconstruction with circular transducer arrays.Ultrasonic Imaging, 1979, 1: 154–184CrossRefGoogle Scholar
  20. [20]
    Harris JM. Diffraction tomography with arrays of discrete sources and receivers. IEEE Trans, 1987, GE-25(4): 448–455Google Scholar
  21. [21]
    Tao L. Research on the method and experiment of interface inversion in inhomogeneous media. Dissertation, Harbin: Harbin Institute of Technology, 1994. Chapter 6.Google Scholar
  22. [22]
    Tao L, Ma XR, Huang WH. Time-space domain incident angle compensation for ray inversion in an inhomogeneous medium.J Acoust Soc Am, 1995, 97(1): 410–413CrossRefGoogle Scholar

Copyright information

© Chinese Society of Theoretical and Applied Mechanics 1995

Authors and Affiliations

  • Ma Xingrui
    • 1
  • Tao Liang
    • 1
  • Huang Wenhu
    • 1
  1. 1.Harbin Institute of TechnologyHarbinChina

Personalised recommendations