Structure inversion Hare-and-Hounds

Abstract

We report some results of a hare-and-hounds exercise for the 1-D structure inversion of p-mode oscillation frequencies. The exercise was carried out to uncover possible uncertainties in the inversion results, and to test the reliability of the error estimates. The results have demonstrated numerically robust structure inversions for both the adiabatic and isothermal sound speeds. The most accurate results were obtained for the squared isothermal sound speed, u (≡p/ρ) using the optimally localized averages technique and the equation of state to constrain the variations of the adiabatic exponent". Without the additional constraint, the most accurate results were obtained for the adiabatic sound speed by the regularized least squares technique. The estimates of the density and the parameter of convective stability are less accurate than the estimates of the sound speeds. The variations of the adiabatic exponent, the temperature and the helium abundance in the radiative zone were not determined reliably. Additional constraints, such as the equation of state and the equations of thermal balance, are important for improving the diagnostic power of the structure inversions. Understanding the physics of the constraints theoretically and seismologically is essential for making robust inferences about solar properties by inversion. A detailed report is published elsewhere (Antia et al., 1996).