On the use of the error correlation function in helioseismic inversions

A diagnostic of helioseismic inversions that has not so far been greatly used is the correlation function describing how the errors in the solutions at different points in the solar interior are correlated. Even if the errors in the input data are uncorrelated, the solution errors will in general be correlated. We investigate the correlation functions for a variety of inversion methods commonly used in helioseismology, using the estimation of a one-dimensional rotation profile as a prototypical example. As we demonstrate, there are characteristic length scales over which the errors are correlated, which are similar among different inversion methods. However, there can also be dramatic differences in the error correlations among otherwise similar-looking inversions if the parameters are chosen inappropriately. It is therefore advisable to consider the correlation function, as well as other diagnostics, when assessing the reliability of an inversion solution.