Research Note

Issues with time–distance inversions for supergranular flows

¹ Astronomical Institute, Academy of Sciences of the Czech Republic (v. v. i.), Fričova 298, 25165 Ondřejov, Czech Republic
e-mail: michal@astronomie.cz
² Astronomical Institute, Faculty of Mathematics and Physics, Charles University in Prague, V Holešovičkách 2, 18000 Prague 8, Czech Republic

Received: 23 October 2014
Accepted: 22 January 2015

Abstract

Aims. Recent studies have shown that time–distance inversions for flows start to be dominated by a random noise at a depth of only a few Mm. It was proposed that the ensemble averaging might be a solution for learning about the structure of the convective flows, e.g. about the depth structure of supergranulation.

Methods. Time–distance inversion is applied to the statistical sample of ∼ 10⁴ supergranules, which allows the inversion cost function to be regularised weakly about the random-noise term and thus provides a much better localisation in space. We compare these inversions at four depths (1.9, 2.9, 4.3, and 6.2 Mm) when using different spatio-temporal filtering schemes in order to gain confidence about these inferences.

Results. The flows inferred by using different spatio-temporal filtering schemes are different (even by the sign) even though the formal averaging kernels and the random-noise levels are very similar. The inverted flows changes its sign several times with depth. I suggest that this is due to the inaccuracies in the forward problem that are possibly amplified by the inversion. It is also possible that other time–distance inversions are affected by this.