Two-dimensional inversion of rotational splitting data

  • Takashi Sekii
Part V Inverse Problems of Solar Oscillations
Part of the Lecture Notes in Physics book series (LNP, volume 367)


We solve a two-dimensional inverse problem of the rotational frequency splitting to infer the rotation rate in the sun as a function of both the radius and the latitude. We use Libbrecht's (1989) observational data of the solar p-mode frequency splitting. We discretize a set of linear integral equations for rotational splittings and reduce them a set of linear algebraic equations. We solve the resultant algebraic equations by imposing an error-weighted least squares condition cooperated with boundary constraint at the surface. In order to stabilize the solution to observational and numerical errors, we discard small singular values of the coefficient matrix, and this keeps some parameters undetermined. To determine these parameters we impose a flatness condition. The inverted results show the solar internal rotation becomes slower at low latitudes and faster at high latitudes with increasing depth. The most significant deviation from this trend is that rotation is slow at low latitudes in the convection zone.


Rotation Rate Convection Zone Frequency Splitting Flatness Condition Inverted Result 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Christensen-Dalsgaard, J., and Schou, J. 1988, in Seismology of the Sun and Sun-lake Stars, ed. E. Rolfe, ESA SP-286 (ESA Publication Division, Noordwijk), p.149.Google Scholar
  2. Dziembowski, W.A., Goode, P.R., and Libbrecht, K.G. 1989, Astrophys. J. Letters, 337, L53.CrossRefGoogle Scholar
  3. Hansen, C.J., Cox, J.P., and van Horn, H.M. 1977, Astrophys. J., 217, 151.CrossRefGoogle Scholar
  4. Libbrecht, K.G. 1989, Astrophys. J., 336, 1092.CrossRefGoogle Scholar
  5. Sekii, T., and Shibahashi, H. 1988, in Seismology of the Sun and Sun-like Stars, ed. E. Rolfe, ESA SP-286 (ESA Publication Division, Noordwijk), p.521.Google Scholar
  6. Shibahashi, H., Noels, A., and Gabriel, M. 1983, Astron. Astrophys., 123, 283.Google Scholar
  7. Snodgrass, H.B. 1983, Astrophys. J., 270, 288.Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Takashi Sekii
    • 1
  1. 1.Department of AstronomyUniversity of TokyoTokyoJapan

Personalised recommendations