We have developed a new inversion method (OMD) suitable for helioseismology. OMD calculates the spatial resolution of the solution in order to build an optimal inversion mesh and select the smoothing criterion. The weight of such a smoothing function, at each tabular point, is given by the SVD analysis of the contribution of each point in the mesh to the solution. The method have been tested by applying it to artificial data. We have found that the solution fits the actual one within errors for all the cases considered. Also the behaviour of the averaging kernels illustrates the accuracy of the results.
Although the method is suitable for inversions of only one function, such as the rotational one used for test 1, it shows its advantage when two functions are inverted, especially because the weight of the smoothing function is applied in a different way for each radial point and each function to be inverted.
The fact that we are able to invert sound speed and density at the same time, is very important because the inversion is independent of the equation of state. Consequently, the solution obtained with OMD is more robust in this sense. Accuracy and precision are not the only advantages of OMD. Our method is also computationally faster than OLA or similar techniques.
Acknowledgements
We thank D.O. Gough for his help during the development of OMD technique. This work has been made possible thanks to the financial support of the Spanish DGICYT under grants ESP90-0969 and PB91-0530.