Skip to main content
SpringerLink
Log in

Inverting helioseismic data

  • Published:
Solar Physics Aims and scope Submit manuscript

Abstract

Methods by which the observed frequencies of solar oscillations can be, and in some cases have been used to infer the internal structure of the Sun are discussed. Attention is confined to so-called inverse methods that identify and extract the information that is actually contained in the data. Because only a finite quantity of data can ever be acquired, the functions describing the interior stratification of the Sun can never be established completely without the acceptance of certain assumptions. Nevertheless, the assumptions that are required are simple to understand, and the results do not depend on the complicated and uncertain theory of stellar evolution which has traditionally been used to construct solar models. First results of the inversions have given us an estimate of the sound speed and the angular velocity throughout much of the solar interior. These estimates have already stimulated speculation which hopefully will encourage further theoretical and observational research that will improve our understanding of the Sun.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Backus, G. and Gilbert, F.: 1967, Geophys. J. Roy. Astron. Soc. 13, 247.

    Google Scholar 

  • Backus, G. and Gilbert, F.: 1968, Geophys. J. Roy. Astron. Soc. 16, 169.

    Google Scholar 

  • Backus, G. and Gilbert, F.: 1970, Phil. Trans. 266A, 123.

    Google Scholar 

  • Berthomieu, G. and Provost, J.: Astron. Astrophys., submitted.

  • Brown, T. M.: 1985a, Nature, in press.

  • Brown, T. M.: 1985b, in D. O. Gough (ed.), Seismology of the Sun and the Distant Stars, D. Reidel Publ. Co., Dordrecht, Holland, in press.

    Google Scholar 

  • Christensen-Dalsgaard, J.: 1982, Monthly Notices Roy. Astron. Soc. 199, 735.

    Google Scholar 

  • Christensen-Dalsgaard, J.: 1984, in A. Noels and M. Gabriel (eds.), Theoretical Problems in Stellar Stability and Oscillations, Univ. Liège, p. 155.

  • Christensen-Dalsgaard, J.: 1985, in D. O. Gough (ed.), Seismology of the Sun and the Distant Stars, D. Reidel Publ. Co., Dordrecht, Holland, in press.

    Google Scholar 

  • Christensen-Dalsgaard, J. and Frandsen, S.: 1983, Solar Phys. 82, 165.

    Google Scholar 

  • Christensen-Dalsgaard, J. and Gough, D. O.: 1984a, in R. K. Ulrich, J. W. Harvey, E. J. Rhodes, Jr., and J. Toomre (eds.), Solar Seismology from Space, Jet Propulsion Laboratory Publication 84-84, Pasadena, p. 199.

  • Christensen-Dalsgaard, J. and Gough, D. O.: 1984b, in R. K. Ulrich, J. W. Harvey, E. J. Rhodes, Jr., and J. Toomre (eds.), Solar Seismology from Space, Jet Propulsion Laboratory Publication 84-84, Pasadena, p. 79.

  • Christensen-Dalsgaard, J., Dziembowski, W. A., and Gough, D. O.: 1980, in H. A. Hill and W. A. Dziembowski (eds.), Nonradial and Nonlinear Stellar Pulsation, Springer, Heidelberg, p. 313.

    Google Scholar 

  • Christensen-Dalsgaard, J., Duvall Jr, T. L., Gough, D. O., Harvey, J. W., and Rhodes Jr., E. J.: 1985, Nature 315, 378.

    Google Scholar 

  • Cox, J. P.: 1980, Theory of Stellar Pulsation, Princeton Univ. Press.

  • Däppen, W. and Gough, D. O.: 1985, in D. O. Gough (ed.), Seismology of the Sun and the Distant Stars, D. Reidel Publ. Co., Dordrecht, Holland, in press.

    Google Scholar 

  • Denis, A. I. and Denis, C.: 1984, in A. Noels and M. Gabriel (eds.), Theoretical Problems in Stellar Stability and Oscillations, Univ. Liège, p. 270.

  • Deubner, F.-L. and Gough, D. O.: 1984, Ann. Rev. Astron. Astrophys. 22, 593.

    Google Scholar 

  • Duvall, Jr, T. L.: 1982, Nature 300, 242.

    Google Scholar 

  • Duvall, Jr, T. L. and Harvey, J. W.: 1983, Nature 302, 24.

    Google Scholar 

  • Duvall, Jr, T. L. and Harvey, J. W.: 1984, Nature 310, 19.

    Google Scholar 

  • Duvall, Jr, T. L., Dziembowski, W. A., Goode, P. R., Gough, D. O., Harvey, J. W., and Liebacher, J. W.: 1984, Nature 310, 22.

    Google Scholar 

  • Dziembowski, W. A. and Goode, P. R.: 1984, Mem. Soc. Astr. Italiana 55, 185.

    Google Scholar 

  • Dziembowski, W. A. and Pamjatnykh, A. A.: 1978, in Rösch (ed.), Pleins Feux sur la Physique Solaire, Centre National de la Recherche Scientifique, Paris, p. 135.

    Google Scholar 

  • Ellis, A. N.: 1984, in A. Noels and M. Gabriel (eds.), Theoretical Problems in Stellar Evolution and Oscillations, Univ. Liège, p. 290.

  • Ellis, A. N.: 1985, Monthly Notices Roy. Astron. Soc., submitted.

  • Fossat, E.: 1985, in E. Rolfe and B. Battrick (eds.), Future Missions in Solar, Heliospheric and Space Plasma Physics, ESA SP-235, European Space Agency, Noordwijk, p. 209.

    Google Scholar 

  • Gabriel, M.: 1985, in D. O. Gough (ed.), Seismology of the Sun and the Distant Stars, D. Reidel Publ. Co., Dordrecht, Holland, in press.

    Google Scholar 

  • Gough, D. O.: 1978, in G. Belvedere and L. Paternò (eds.), Proc. Workshop on Solar Rotation, Univ. Catania Press, p. 255.

  • Gough, D. O.: 1981, Monthly Notices Roy. Astron. Soc. 196, 731.

    Google Scholar 

  • Gough, D. O.: 1982, Nature 298, 334.

    Google Scholar 

  • Gough, D. O.: 1983, in P. A. Shaver, D. Kunth, and K. Kjär (eds.), Proc. Primordial Helium Workshop, European Southern Observatory, Garching, p. 117.

    Google Scholar 

  • Gough, D. O.: 1984a, Adv. Space Res. 4, 85.

    Google Scholar 

  • Gough, D. O.: 1984b, Phil. Trans. 313A, 27.

    Google Scholar 

  • Gough, D. O.: 1984c, in R. K. Ulrich, J. W. Harvey, E. J. Rhodes, Jr., and J. Toomre (eds.), Solar Seismology from Space, Jet Propulsion Laboratory Publication 84-84, Pasadena, p. 49.

  • Gough, D. O.: 1985a, in B. Chen and C. de Jager (eds.), Proc. International Workshop on Solar Physics and interplanetary Travelling Phenomena, Kunming, November 1983, in press.

  • Gough, D. O.: 1985b, in E. Rolfe and B. Battrick (eds.), Future Missions in Solar, Heliospheric and Space Plasma Physics, ESA SP-235, European Space Agency, Noordwijk, p. 183.

    Google Scholar 

  • Gough, D. O. and Taylor, P. P.: 1984, Mem. Soc. Astron. Italiana 55, 215.

    Google Scholar 

  • Hansen, D. J., Cox, J. P., and Van Horn, J. H.: 1977, Astrophys. J. 217, 151.

    Google Scholar 

  • Harvey, J. W. and Duvall, Jr., T. L.: 1984, in R. K. Ulrich, J. W. Harvey, E. J. Rhodes, Jr., and J. Toomre (eds.), Solar Seismology from Space, Jet Propulsion Laboratory Publication 84-84, Pasadena, p. 165.

  • Hill, F., Gough, D. O., and Toomre, J.: 1984a, Mem. Soc. Astron. Italiana 55, 153.

    Google Scholar 

  • Hill, F., Gough, D. O., and Toomre, J.: 1984b, in R. K. Ulrich, J. W. Harvey, E. J. Rhodes Jr., and J. Toomre (eds.), Solar Seismology from Space, Jet Propulsion Laboratory Publication 84-84, Pasadena, p. 95.

  • Hill, H. A., Bos, R. J., and Goode, P. R.: 1982, Phys. Rev. Letters 49, 1794.

    Google Scholar 

  • Isaak, G. R.: 1985, in D. O. Gough (ed.), Seismology of the Sun and the Distant Stars, D. Reidel Publ. Co., Dordrecht, in press.

    Google Scholar 

  • Jackson, D. D.: 1972, Geophys. J. Roy. Astron. Soc. 28, 97.

    Google Scholar 

  • Jackson, D. D.: 1973, Geophys. J. Roy. Astron. Soc. 35, 121.

    Google Scholar 

  • Keller, J. B. and Rubinow, S. I.: 1960, Ann. Phys. 9, 24.

    Google Scholar 

  • Lamb, H.: 1908, Proc. London Math. Soc. 7, 122.

    Google Scholar 

  • Lamb, H.: 1932, Hydrodynamics, Cambridge Univ. Press.

  • Lanczos, C.: 1961, Linear Differential Equations, Van Nostrand, London.

    Google Scholar 

  • Ledoux, P. and Walraven, T.: 1958, Handb. Physik 51, 353.

    Google Scholar 

  • Leibacher, J. W.: 1984, in A. Noels and M. Gabriel (eds.), Theoretical Problems in Stellar Evolution and Oscillations, Univ. Liège, p. 298.

  • Lynden-Bell, D. and Ostriker, J.: 1967, Monthly Notices Roy. Astron. Soc. 136, 293.

    Google Scholar 

  • Parker, R. L.: 1977a, Ann. Rev. Earth Planet Sci. 5, 35.

    Google Scholar 

  • Parker, R. L.: 1977b, Rev. Geophys. Space Phys. 15, 446.

    Google Scholar 

  • Perdang, J.: 1985, in D. O. Gough (ed.), Seismology of the Sun and the Distant Stars, D. Reidel Publ. Co., Dordrecht, Holland, in press.

    Google Scholar 

  • Provost, J.: 1984, in A. Maeder and A. Renzini (eds.), ‘Observational Tests of Stellar Evolution Theory’, IAU Symp. 105, 47.

  • Rosner, R. and Weiss, N. O.: 1985, Nature, submitted.

  • Tassoul, M.: 1980, Astrophys. J. Suppl. 43, 469.

    Google Scholar 

  • Ulrich, R. K., Harvey, J. W., Rhodes, Jr., E. J., and Toomre, J. (eds.): 1984, Solar Seismology from Space, Jet Propulsion Laboratory Publication 84-84, Pasadena.

  • Unno, W., Osaki, Y., Ando, H., and Shibahashi, H.: 1979, Nonradial Oscillations of Stars, Univ. Tokyo Press.

  • Vandakurov, Yu. V.: 1967, Astron. Zh. 44, 786.

    Google Scholar 

  • van der Raay, H. B., Palle, P. L., and Roca Cortes, T.: 1985, in D. O. Gough (ed.), Seismology of the Sun and the Distant Stars, D. Reidel Publ. Co., Dordrecht, in press.

    Google Scholar 

  • Wiggins, R. A.: 1972, Rev. Geophys. Space Phys. 10, 251.

    Google Scholar 

  • Zahn, J.-P.: 1970, Astron. Astrophys. 4, 452.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Astronomy and Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, U.K.

    Douglas Gough

  2. Observatoires du Pic-du-Midi et de Toulouse, Université Paul Sabatier, France

    Douglas Gough

Authors
  1. Douglas Gough
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gough, D. Inverting helioseismic data. Sol Phys 100, 65–99 (1985). https://doi.org/10.1007/BF00158422

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00158422

Keywords

Search

Navigation