Helioseismic Inversion for inferring the structure of the solar meridional flow

Accurate inference of solar meridional flow is of crucial importance for the understanding of solar dynamo process. Wave travel times, as measured on the surface, will change if the wave encounters perturbations e.g. in the sound speed or flows, as it passes through the solar interior. The perturbation that is causing that travel-time shift can be imaged using functions called sensitivity kernels that relate shifts in travel-time measurements to underlying anomalies. The inference of large-scale structures e.g meridional circulation requires computing sensitivity kernels in spherical geometry in the limit of the first-Born approximation. We earlier have developed a technique to compute such sensitivity function accurately. In this work, we perform an inversion for meridional circulation using travel-time measurements obtained from 6 years of SDO/HMI data with those sensitivity kernels. We enforce mass conservation by inverting for a stream function. The number of free parameters is reduced by projecting the solution on to 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 the return-flow occurring at depths below 0.8 solar radius.