A general formulation for computing spherical helioseismic sensitivity kernels while incorporating systematical effects

TL;DR

This paper introduces a comprehensive method for calculating spherical helioseismic sensitivity kernels that incorporate systematic effects, improving the accuracy and efficiency of helioseismic inversions.

Contribution

It presents a novel general formulation for tensor perturbations in spherical geometry, integrating line-of-sight and center-to-limb effects using quantum mechanics-inspired techniques.

Findings

Computed a travel-time sensitivity kernel for sound-speed perturbations.

Produced spherical harmonic coefficients for sensitivity kernels, enhancing inverse problem stability.

Demonstrated the method's efficiency and improved modeling of systematic effects.

Abstract

As helioseismology matures and turns into a precision science, modeling finite-frequency, geometric and systematical effects is becoming increasingly important. Here we introduce a general formulation for treating perturbations of arbitrary tensor rank in spherical geometry using fundamental ideas of quantum mechanics and their extensions in geophysics. We include line-of-sight projections and center-to-limb differences in line-formation heights in our analysis. We demonstrate the technique by computing a travel-time sensitivity kernel for sound-speed perturbations. The analysis produces the spherical harmonic coefficients of the sensitivity kernels, which leads to better-posed and computationally efficient inverse problems.