# Finite-frequency sensitivity kernels in spherical geometry for time-distance helioseismology

## TL;DR

This paper develops and validates finite-frequency sensitivity kernels in spherical geometry for time-distance helioseismology, enabling more accurate inference of the Sun's internal properties from surface wave travel times.

## Contribution

It introduces a method to compute finite-frequency sensitivity kernels in spherical geometry using parallelized Green's function calculations, improving speed and accuracy.

## Key findings

- Kernels produce travel time estimates within 0.47% of true values for uniform flows.
- Travel-time errors are less than 1 ms for flows similar to meridional circulation.
- Validated sensitivity kernels for sound-speed perturbations enhance helioseismic inferences.

## Abstract

The inference of internal properties of the Sun from surface measurements of wave travel times is the goal of time-distance helioseismology. A critical step toward the accurate interpretation of travel-time shifts is the computation of sensitivity functions linking seismic measurements to internal structure. Here we calculate finite-frequency sensitivity kernels in spherical geometry for two-point travel-time measurements. We numerically build Green's function by solving for it at each frequency and spherical-harmonic degree and summing over all these pieces. These computations are performed in parallel ("embarrassingly"), thereby achieving significant speedup in wall-clock time. Kernels are calculated by invoking the first-order Born approximation connecting deviations in the wavefield to perturbations in the operator. Validated flow kernels are shown to produce travel times within 0.47% of the true value for uniform flows up to 750 m/s. We find that travel-time can be obtained with errors of 1 millisecond or less for flows having magnitudes similar to meridional circulation. Alongside flows, we also compute and validate sensitivity kernel for sound-speed perturbations. These accurate sensitivity kernels might improve the current inferences of sub-surface flows significantly.