A new strategy for helioseismic inversions

Helioseismic inversion techniques have been revealed as powerful tools for inferring the internal structure and dynamics of the Sun. One of the most popular techniques is Regularized Least Squares. When it is used, it is necessary to define an inversion mesh and a penalty function, without an a priori knowledge of the behaviour of the solution. In addition, this penalty function is weighted by a trade-off parameter that must be fixed in order to obtain the solution. We present here a new technique, developed in order to find the optimal mesh and smoothing function by means of a deep analysis of the basis functions of the inversion problem. We have found that the method is suitable in particular for obtaining the sound speed and density profiles simultaneously, without any reference to the equation of state.