Helioseismic Finite-frequency Sensitivity Kernels for Flows in Spherical Geometry including Systematic Effects

Helioseismic inferences of large-scale flows in the solar interior necessitate accounting for the curvature of the Sun, both in interpreting systematic trends introduced in measurements as well as the sensitivity kernel that relates photospheric measurements to subsurface flow velocities. Additionally, the inverse problem that relates measurements to model parameters needs to be well posed to obtain accurate inferences, which necessitates a sparse set of parameters. Further, the sensitivity functions need to be computationally easy to evaluate. In this work, we address these issues by demonstrating that the sensitivity kernels for flow velocities may be computed efficiently on the basis of vector spherical harmonics. We are also able to account for line-of-sight projections in Doppler measurements, as well as center-to-limb differences in line-formation heights. We show that given the assumed spherical symmetry of the background model, it is often cheap to simultaneously compute the kernels for pairs of observation points that are related by a rotation. Such an approach is therefore particularly well suited to inverse problems for large-scale flows in the Sun, such as meridional circulation.