Skip to main content
SpringerLink
Log in
Book cover

Integral Methods in Science and Engineering, Volume 1 pp 21–28Cite as

Dyadic Elastic Scattering by Point Sources: Direct and Inverse Problems

  • Chapter
  • First Online:

  • 1160 Accesses

Abstract

This chapter is concerned with the scattering of elastic point sources by a bounded obstacle, as well as with a related near-field inverse problem for small scatterers. We consider the Dirichlet problem, where the displacement field is vanishing on the surface of the scatterer. A dyadic formulation for the aforementioned scattering problem is considered in order to gain the symmetry–compactness of the dyadic analysis [TAI94].

For acoustic and electromagnetic scattering, results on incident waves generated by a point source appear in [DK00], [AMS02]; see also references therein. In all these studies, scattering relations by point sources are established; related simple inversion algorithms for small scatterers can be found in [AMS01]. For elasticity, related problems such as the location and identification of a small three-dimensional elastic inclusion, using arrays of elastic source transmitters and receivers, are considered in [AK04], [ACI08].

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ammari, H., Kang, H.: Reconstruction of Small Inhomogeneities from Boundary Measurements, Springer, Berlin (2004).

    MATH  Google Scholar 

  2. Ammari, H., Calmon, P., Iakovleva, E.: Direct elastic imaging of a small inclusion. SIAM J. Imaging Sci., 1, 169–187 (2008).

    Article  MATH  MathSciNet  Google Scholar 

  3. Athanasiadis, C., Martin, P.A., Stratis, I.G.: On spherical-wave scattering by a spherical scatterer and related near-field inverse problems. IMA J. Appl. Math., 66, 539–549 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  4. Athanasiadis, C., Martin, P.A., Spyropoulos, A., Stratis, I.G.: Scattering relations for point sources: acoustic and electromagnetic waves. J. Math. Phys., 43, 5683–5697 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  5. Athanasiadis, E.C., Sevroglou, V., Stratis, I.G.: On the reconstruction of a small elastic sphere in the near field by point–sources, in Advanced Topics in Scattering and Biomedical Engineering, Charalambopoulos, A., Fotiadis, D.I., Polyzos, D., eds., World Scientific, Teaneck, NJ, 3–12 (2007).

    Google Scholar 

  6. Athanasiadis, E.C., Sevroglou, V., Stratis, I.G.: 3D-elastic scattering theorems for point-generated dyadic fields. Math. Methods Appl. Sci., 31, 987–1003 (2008).

    Article  MATH  MathSciNet  Google Scholar 

  7. Athanasiadis, E.C., Pelekanos, G., Sevroglou, V., Stratis, I.G.: On the scattering of 2D elastic point-sources and related near-field inverse problems for small disks. Proc. Royal Soc. Edinburgh (in press).

    Google Scholar 

  8. Ben–Menahem A., Singh, S.J.: Seismic Waves and Sources, Springer, New York (1981).

    MATH  Google Scholar 

  9. Dassios, G., Kleinman, R.: Low Frequency Scattering, Clarendon Press, Oxford (2000).

    MATH  Google Scholar 

  10. Gurtin, M.E.: The linear theory of elasticity, in Handbuch der Physik, Vol. VIa/2, Truesdell, C., ed., Springer, Berlin, 1–295 (1972).

    Google Scholar 

  11. Hsiao, G.C., Wendland, W.L.:Boundary Integral Equations, Springer, Berlin (2008).

    Book  MATH  Google Scholar 

  12. Kupradze, V.D.: Potential Methods in the Theory of Elasticity, Israel Program for Scientific Translations, Jerusalem (1965).

    MATH  Google Scholar 

  13. Kupradze, V.D., Gegelia, T.G., Basheleishvili, M.O., Burchuladze, T.V.: Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity, North-Holland, Amsterdam (1979).

    MATH  Google Scholar 

  14. Tai, C.T.: Dyadic Green Functions in Electromagnetic Theory, IEEE Press, New York (1994).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National and Kapodistrian University of Athens, Athens, Greece

    C. E. Athanasiadis & I. G. Stratis

  2. University of Piraeus, Piraeus, Greece

    V. Sevroglou

Authors
  1. C. E. Athanasiadis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. Sevroglou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. I. G. Stratis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. E. Athanasiadis .

Editor information

Editors and Affiliations

  1. Department of Mathematical , University of Tulsa, South Tucker Drive 800, Tulsa, 74104, U.S.A.

    Christian Constanda

  2. Departamento de Matematica Aplicada, Universidad Cantabria, Santander, 39005, Spain

    M.E. Pérez

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Birkhäuser Boston, a part of Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Athanasiadis, C.E., Sevroglou, V., Stratis, I.G. (2010). Dyadic Elastic Scattering by Point Sources: Direct and Inverse Problems. In: Constanda, C., Pérez, M. (eds) Integral Methods in Science and Engineering, Volume 1. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4899-2_3

Download citation

Publish with us

Policies and ethics

Search

Navigation