Time-distance helioseismology: Inversion of noisy correlated data

In time-distance helioseismology most inversion procedures ignore the correlations in the data errors. Here we simulate the travel-time perturbations of wavepackets that result from known distributions of sound speed inhomogeneities. The forward and inverse problems are carried out using recently developed Born approximation sensitivity kernels. A realistic solar noise component, with the correct statistics, is added to the data. We then apply a three-dimensional inversion procedure based on an improved multichannel deconvolution algorithm that includes the full covariance matrix of the simulated data and constrains the solution both in the vertical and horizontal directions. The validation of the inversion is achieved through comparison of the inferred sound speed distributions with the exact solutions. We show that including the covariance matrix matters for sound speed inhomogeneities varying on a length scale smaller than the correlation length. We also find that the inversion procedure is improved by adding horizontal regularization.