On the inference of supergranular flows by time-distance helioseismology

We have attempted to derive the internal flow fields of supergranules by inverting time-distance helioseismology measurements based on the ray theoretical approximation. Due to the "cross-talk" effect between the contributions of the vertical flows and horizontal divergent flows and also due to the measurement errors propagation in the inversion, we can derive reliably only the horizontal velocity distribution in the supergranules, but the vertical velocity which is much smaller than the horizontal velocity is rather uncertain. The preliminary results from our inversion show that the divergent flows extend to a few megameters below solar surface, and also present evidence of converging flows at the depth of ∼10 Mm. A simple estimation gives the average depth of supergranules is approximately 15 Mm. Another inversion technique Multi-Channel Deconvolution is also developed. The subsurface flow fields of a sunspot derived from this technique are compared with the results from algorithm LSQR, and a correlation of 95% and above is found.