Validated helioseismic inversions for 3D vector flows^⋆

¹ Max-Planck-Institut für Sonnensystemforschung, Max-Planck-Straße 2, 37191 Katlenburg-Lindau, Germany
e-mail: svanda@mps.mpg.de; gizon@mps.mpg.de; hanasoge@mps.mpg.de
² Institut für Astrophysik, Georg-August-Universität Göttingen, 37077 Göttingen, Germany
³ Department of Geosciences, Princeton University, Princeton, NJ 08544, USA
⁴ Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya Sq. 4, 125047 Moscow, Russia

Received: 31 December 2010
Accepted: 20 April 2011

Abstract

Context. According to time-distance helioseismology, information about internal fluid motions is encoded in the travel times of solar waves. The inverse problem consists of inferring three-dimensional vector flows from a set of travel-time measurements. While only few tests of the inversions have been done, it is known that the retrieval of the small-amplitude vertical flow velocities is problematic. A thorough study of biases and noise has not been carried out in realistic conditions.

Aims. Here we investigate the potential of time-distance helioseismology to infer three-dimensional convective velocities in the near-surface layers of the Sun. We developed a new subtractive optimally localised averaging (SOLA) code suitable for pipeline pseudo-automatic processing. Compared to its predecessor, the code was improved by accounting for additional constraints in order to get the right answer within a given noise level. The main aim of this study is to validate results obtained by our inversion code.

Methods. We simulate travel-time maps using a snapshot from a numerical simulation of solar convective flows, realistic Born travel-time sensitivity kernels, and a realistic model of travel-time noise. These synthetic travel times are inverted for flows and the results compared with the known input flow field. Additional constraints are implemented in the inversion: cross-talk minimization between flow components and spatial localization of inversion coefficients.

Results. Using modes f, p₁ through p₄, we show that horizontal convective flow velocities can be inferred without bias, at a signal-to-noise ratio greater than one in the top 3.5 Mm, provided that observations span at least four days. The vertical component of velocity (v_z), if it were to be weak, is more difficult to infer and is seriously affected by cross-talk from horizontal velocity components. We emphasise that this cross-talk must be explicitly minimised in order to retrieve v_z in the top 1 Mm. We also show that statistical averaging over many different areas of the Sun allows for reliably measuring of average properties of all three flow components in the top 5.5 Mm of the convection zone.