Helioseismic Inversion to Infer the Depth Profile of Solar Meridional Flow Using Spherical Born Kernels

Abstract

Accurate inferences of solar meridional flow are crucial for understanding solar dynamo processes. Wave travel times, as measured on the surface, will change if the waves encounter perturbations, e.g., in the sound speed or flows, as they propagate through the solar interior. Using functions called sensitivity kernels, we can image the underlying anomalies that cause measured shifts in travel times. The inference of large-scale structures, e.g., meridional circulation, requires computing sensitivity kernels in spherical geometry. Mandal et al. have computed such spherical kernels in the limit of the first-Born approximation. In this work, we perform an inversion for meridional circulation using travel-time measurements obtained from 6 years of Solar Dynamics Observatory /Helioseismic and Magnetic Imager data and those sensitivity kernels. We enforce mass conservation by inverting for a stream function. The number of free parameters is reduced by projecting the solution onto cubic B-splines in radius and derivatives of the Legendre-polynomial basis in latitude, thereby improving the condition number of the inverse problem. We validate our approach for synthetic observations before performing the actual inversion. The inversion suggests a single-cell profile with a return flow occurring at depths below 0.78 R ⊙ .