# Combined helioseismic inversions for 3D vector flows and sound-speed perturbations

## TL;DR

This paper presents an advanced helioseismic inversion method that simultaneously retrieves 3D vector flows and sound-speed perturbations in the solar interior, improving accuracy and reducing cross-talk effects.

## Contribution

The authors develop a novel inversion approach using SOLA with Born approximation kernels to recover full 3D flows and sound-speed variations simultaneously, validated on synthetic data.

## Key findings

- Successfully recover flows and sound-speed perturbations near the solar surface.
- The methodology is sensitive to the entire vertical velocity component.
- Cross-talk effects are negligible for horizontal flow inversions, but need minimization for vertical flows and sound-speed perturbations.

## Abstract

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. We introduce an improved methodology of the time-distance helioseismology which allows us to invert for a full 3D vector of flows and the sound-speed perturbations at once. Using this methodology one can also derive the mean value of the vertical component of flows and the cross-talk between the flows and the sound-speed perturbations. We used the SOLA 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. 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. 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.