A. E-Darwich and F. Perez Hernandez

Abstract. Helioseismic inversion techniques have been revealed as powerful tools for inferring the internal struc-ture and dynamics of the Sun. One of the most popular techniques is Regularized Least Squares. When it is used, it is necessary to dene 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-o parameter that must be xed in order to ob-tain the solution. We present here a new technique, developed in order to nd 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 pro-les simultaneously, without any reference to the equation of state