1887
Volume 68, Issue 5
  • E-ISSN: 1365-2478
PDF

Abstract

ABSTRACT

Acoustic inversion in one‐dimension gives impedance as a function of travel time. Inverting the reflection response is a linear problem. Recursive methods, from top to bottom or vice versa, are known and use a fundamental wave field that is computed from the reflection response. An integral over the solution to the Marchenko equation, on the other hand, retrieves the impedance at any vertical travel time instant. It is a non‐recursive method, but requires the zero‐frequency value of the reflection response. These methods use the same fundamental wave field in different ways. Combining the two methods leads to a non‐recursive scheme that works with finite‐frequency bandwidth. This can be used for target‐oriented inversion. When a reflection response is available along a line over a horizontally layered medium, the thickness and wave velocity of any layer can be obtained together with the velocity of an adjacent layer and the density ratio of the two layers. Statistical analysis over 1000 noise realizations shows that the forward recursive method and the Marchenko‐type method perform well on computed noisy data.

Loading

Article metrics loading...

/content/journals/10.1111/1365-2478.12946
2020-03-17
2024-04-20
Loading full text...

Full text loading...

/deliver/fulltext/gpr/68/5/gpr12946.html?itemId=/content/journals/10.1111/1365-2478.12946&mimeType=html&fmt=ahah

References

  1. AbelesF.1946. *Optique ‐ Nouvelles formules relatives à la lumière réfléchie et transmise par un empilement de lames à faces parallèles, Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences223, 891–893.
    [Google Scholar]
  2. AgranovichZ.S. and MarchenkoV.A.1963. The Inverse Problem of Scattering Theory. Gordon and Breach, New York, NY.
    [Google Scholar]
  3. BackusM.M.1959. Water reverberations ‐ their nature and elimination. Geophysics24, 233–261.
    [Google Scholar]
  4. BardanV. and RobinsonE.A.2018. Inverse problem for Goupillaud‐layered earth model and dynamic deconvolution. Geophysical Prospecting66, 1441–1456.
    [Google Scholar]
  5. BerrymanJ.G. and GreeneR.R.1980. Discrete inverse methods for elastic waves in layered media. Geophysics45, 213–233.
    [Google Scholar]
  6. BrogginiF., SniederR. and WapenaarK.2012. Focusing the wavefield inside an unknown 1D medium: beyond seismic interferometry. Geophysics77, A25–A28.
    [Google Scholar]
  7. ClaerboutJ.F.1968. Synthesis of a layered medium from its acoustic transmission response. Geophysics33, 264–269.
    [Google Scholar]
  8. FinkM.1992. Time‐reversal of ultrasonic fields .1. Basic principles. IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control39, 555–566.
    [Google Scholar]
  9. GoupillaudP.L.1961. An approach to inverse filtering of near surface effects from seismic records. Geophysics26, 754–760.
    [Google Scholar]
  10. KunetzG.1964. Generalisation des operateurs d'anti‐resonance a un nombre quelconque de reflecteurs. Geophysical Prospecting12, 283–289.
    [Google Scholar]
  11. KunetzG. and d'ErcevilleI.1962. Sur certaines propriétés d'une onde acoustique plane de compression dans un milieu stratifié. Annales de Géophysique18, 351–359.
    [Google Scholar]
  12. LambG.L.1980. Elements of Soliton Theory. John Wiley & Sons, New York, NY.
    [Google Scholar]
  13. LomasA. and CurtisA.2019. An introduction to Marchenko methods for imaging. Geophysics84, F35–F45.
    [Google Scholar]
  14. NowackR.L. and KirazM.S.R. 2018. Virtual Green's functions using seismic interferometry and Marchenko redatuming. Seismological Research Letters89, 613–619.
    [Google Scholar]
  15. RavasiM.2017. Rayleigh‐Marchenko redatuming for target‐oriented, true‐amplitude imaging. Geophysics82, S439–S452.
    [Google Scholar]
  16. RobinsonE.A.1967. Multichannel Time Series Analysis with Digital Computer Programs. Holden‐Day, San Francisco, CA.
    [Google Scholar]
  17. RobinsonE.A. and TreitelS.1977. The spectral function of a layered system and the determination of the waveforms at depth. Geophysical Prospecting25, 434–459.
    [Google Scholar]
  18. RobinsonE.A. and TreitelS.1978. Fine‐structure of normal incidence synthetic seismogram. Geophysical Journal of the Royal Astronomical Society53, 289–309.
    [Google Scholar]
  19. RoseJ.H.2002. Single‐sided autofocusing of sound in layered materials. Inverse Problems18, 1923–1934.
    [Google Scholar]
  20. SinghS., SniederR., BehuraJ., van der NeutJ., WapenaarK. and SlobE.C.2015. Marchenko imaging: imaging with primaries, internal multiples, and free‐surface multiples. Geophysics80, S165–S174.
    [Google Scholar]
  21. SlobE., WapenaarK., BrogginiF. and SniederR.2014. Seismic reflector imaging using internal multiples with Marchenko‐type equations. Geophysics79, S63–S76.
    [Google Scholar]
  22. SlobE., WapenaarK. and TreitelS.2018. Fast non‐recursive 1D inversion by filtering acoustic reflection data. 88th SEG Annual International meeting, Expanded Abstracts, 5043–5047.
  23. WapenaarK., BrogginiF., SlobE. and SniederR.2013. Three‐dimensional single‐sided Marchenko inverse scattering, data‐driven focusing, Green's function retrieval, and their mutual relations. Physical Review Letters110, 084301.
    [Google Scholar]
  24. WapenaarK., ThorbeckeJ., van der NeutJ., BrogginiF., SlobE. and SniederR.2014. Marchenko imaging. Geophysics79, WA39–WA57.
    [Google Scholar]
  25. WapenaarK., ThorbeckeJ., van der NeutJ., SlobE. and SniederR.2017. Review paper: virtual sources and their responses, Part II: data‐driven single‐sided focusing. Geophysical Prospecting65, 1430–1451.
    [Google Scholar]
  26. WareJ.A. and AkiK.1969. Continuous and discrete inverse‐scattering problems in a stratified elastic medium. I. Plane waves at normal incidence. Journal of the Acoustical Society of America45, 911–921.
    [Google Scholar]
  27. ZhangL. and SlobE.2019. Free‐surface and internal multiple elimination in one step without adaptive subtraction. Geophysics84, A7–A11.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/1365-2478.12946
Loading
/content/journals/10.1111/1365-2478.12946
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): acoustic; inversion; numerical study

Most Cited This Month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error