Combined helioseismic inversions for 3D vector flows and sound-speed perturbations
Astronomical Institute of Charles University, Faculty of Mathematics and Physics, V Holešovičkách 2, Praha 8 180 00, Czech Republic
2 Astronomical Institute of Czech Academy of Sciences, Fričova 298, Ondřejov 25165, Czech Republic
Accepted: 20 December 2018
Context. Time–distance helioseismology is the method of the study of the propagation of waves through the solar interior via the travel times of those waves. The travel times of wave packets contain information about the conditions in the interior integrated along the propagation path of the wave. The travel times are sensitive to perturbations of a variety of quantities. The usual task is to invert for the vector of plasma flows or the sound–speed perturbations separately. The separate inversions may be polluted by systematic bias, for instance, originating in the leakage of vector flows into the sound–speed perturbations and vice versa (called a cross-talk). Information about the cross-talk is necessary for a proper interpretation of results.
Aims. We introduce an improved methodology of the time-distance helioseismology which allows us to invert for a full 3D vector of plasma flows and the sound–speed perturbations at once. Using this methodology one can also derive the mean value of the vertical component of plasma flows and the cross-talk between the plasma flows and the sound–speed perturbations.
Methods. We used the Subtractive Optimally Localised Averaging method with a minimisation of the cross-talk as a tool for inverse modelling. In the forward model, we use Born approximation travel-time sensitivity kernels with the Model S as a background. The methodology was validated using forward-modelled travel times with both mean and difference point-to-annulus averaging geometries applied to a snapshot of fully self-consistent simulation of the convection.
Results. We tested the methodology on synthetic data. We demonstrate that we are able to recover flows and sound–speed perturbations in the near-surface layers. We have taken the advantage of the sensitivity of our methodology to entire vertical velocity, and not only to its variations as in other available methodologies. The cross-talk from both the vertical flow component and the sound–speed perturbation has only a negligible effect for inversions for the horizontal flow components. Furthermore, this cross-talk can be minimised if needed. The inversions for the vertical component of the vector flows or for the sound–speed perturbations are affected by the cross-talk from the horizontal components, which needs to be minimised in order to provide valid results. It seems that there is a nearly constant cross-talk between the vertical component of the vector flows and the sound–speed perturbations.
Key words: Sun: helioseismology / Sun: oscillations / Sun: interior
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