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Astron. Astrophys. 324, 298-310 (1997)

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1. Introduction

One of the main interests of helioseismology is the description of the Sun's internal rotation rate versus depth and latitude. Over the past decade, increasingly accurate observational data have become available from ground based observations (e.g. Chaplin et al. 1996; Harvey et al. 1996; Lazrek et al. 1996; Woodard & Libbrecht 1993; Appourchaux et al. 1994; Tomczyk et al. 1995a). These and other datasets have allowed several teams to infer the solar internal rotation profile using 1D (Duvall et al. 1984), 1.5D (Christensen-Dalsgaard & Schou 1988; Dziembowski et al. 1989) and 2D (Sekii 1990, Schou 1991) inversion codes (see Schou et al. (1994) for a more complete list of historical references). All these inversions tend to show a rotation profile which is approximately constant on radii throughout the convection zone, with a sharp transition to a latitudinal independent rotation rate below the base of the convection zone.

One of the objectives of the Global Oscillations at Low Frequency (GOLF, Gabriel et al. 1995), Michelson Doppler Imager (MDI, Scherrer et al. 1995) and Variability of solar IRadiance and Gravity Oscillations (VIRGO, Fröhlich et al. 1995) experiments aboard the SOlar and Heliospheric Observatory (SOHO) satellite is to obtain a more accurate set of measurements of low- and high-degree acoustic modes in order to specify what happens in the deep interior [FORMULA], near the surface [FORMULA] and in the transition zone below the convection zone. Nevertheless, ground-based experiments have been operating for many years and can provide spectra obtained over much longer time periods than are currently available to the SOHO experiments. In particular, in this paper we use data from the LOWL experiment covering a two year period of observation on which we apply a 2D RLS inversion code using an approximation of the rotation rate by piecewise polynomials projected on a B-splines tensorial product.

We briefly present the well known forward problem in Sect. 2 and discuss the relevant hypothesis and the boundary conditions for the rotation rate. In Sect. 3 we recall basic principles for the 2D RLS method. We present the LOWL data and discuss the choice of inversion parameters for this particular dataset in Sect. 4. The results of inverting the observed frequency splittings are presented in Sect. 5, and our conclusions are presented in Sect. 6. In addition, Appendices A and B give some details about splines basis and the minimization process and Appendix C recalls the concept of averaging kernels for a linear inversion.

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© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998