# Validation of Spherical Born Approximation Sensitivity Functions for Measuring Deep Solar Meridional Flow

## TL;DR

This study validates the use of the spherical Born approximation for accurately measuring deep solar meridional flows, demonstrating its effectiveness in modeling observational data and recovering flow profiles through numerical and inversion techniques.

## Contribution

The paper introduces a validated method using the Born approximation in spherical geometry for sensitivity function computation, improving the accuracy of deep solar flow measurements.

## Key findings

- Born approximation accurately models travel times with observed power spectra.
- Radial flow contributes up to 20% of total travel time at large distances.
- 2D SOLA inversion successfully recovers input flow profiles.

## Abstract

Accurate measurements of deep solar meridional flow are of vital interest for understanding the solar dynamo. In this paper, we validate a recently developed method for obtaining sensitivity functions (kernels) for travel-time measurements to solar interior flows using the Born approximation in spherical geometry, which is expected to be more accurate than the classical ray approximation. Furthermore, we develop a numerical approach to efficiently compute a large number of kernels based on the separability of the eigenfunctions into their horizontal and radial dependence. The validation is performed using a hydrodynamic simulation of linear wave propagation in the Sun, which includes a standard single-cell meridional flow profile. We show that, using the Born approximation, it is possible to accurately model observational quantities relevant for time-distance helioseismology such as the mean power spectrum, disc-averaged cross-covariance functions, and travel times in the presence of a flow field. In order to closely match the model to observations, we show that it is beneficial to use mode frequencies and damping rates which were extracted from the measured power spectrum. Furthermore, the contribution of the radial flow to the total travel time is found to reach 20% of the contribution of the horizontal flow at travel distances over $40^\circ$. Using the Born kernels and a 2D SOLA inversion of travel times, we can recover most features of the input meridional flow profile. The Born approximation is thus a promising method for inferring large-scale solar interior flows.