# Sensitivity of Helioseismic Measurements of Normal-mode Coupling to Flows and Sound-speed Perturbations

## TL;DR

This paper derives the sensitivity kernels for helioseismic normal-mode coupling to flows and sound-speed perturbations, enabling more accurate inferences of solar interior dynamics using first-Born perturbation theory.

## Contribution

It provides a detailed derivation and correction of the sensitivity kernels for mode coupling, including sound-speed effects, based on the formalism of Lavely and Ritzwoller (1992).

## Key findings

- Derived and computed mode coupling sensitivity kernels to flows.
- Reformulated the fluid-continuity condition for accuracy.
- Established kernels for sound-speed perturbations.

## Abstract

In this article, we derive and compute the sensitivity of measurements of coupling between normal modes of oscillation in the Sun to underlying flows. The theory is based on first-Born perturbation theory, and the analysis is carried out using the formalism described by \citet{lavely92}. Albeit tedious, we detail the derivation and compute the sensitivity of specific pairs of coupled normal modes to anomalies in the interior. Indeed, these kernels are critical for the accurate inference of convective flow amplitudes and large-scale circulations in the solar interior. We resolve some inconsistencies in the derivation of \citet{lavely92} and reformulate the fluid-continuity condition. We also derive and compute sound-speed kernels, paving the way for inverting for thermal anomalies alongside flows.