On the effect of error correlation on linear inversions

We have examined the effect on linear helioseismic inversions of correlations in data errors, taking an example from one-dimensional rotational splitting inversion. Artificial data with correlated errors were generated and then inverted with or without using the proper covariance matrix. The effects of using incorrect covariance matrices, on solutions as well as on trade-offs, are discussed. It is found that improper account of the correlations can be deleterious to the faithfulness of the inversions, and yields incorrect error estimates, which under some circumstances can lead to misleading inferences.