Testing the volume integrals of travel-time sensitivity kernels for flows

Helioseismic inversions largely rely on sensitivity kernels, in which 3D spatial functions describe how the changes in the solar interior translate into the change in helioseismic observables. These sensitivity kernels in most cases come from the forward modelling that is used in the most advanced solar models. We aim to test the sensitivity kernels by comparing their volume integrals with measured values from helioseismic travel times. By manipulating the tracking rate, we mimicked the additional zonal velocity in the Dopplergram datacubes. These datacubes were then processed by a standard travel-time measurements pipeline. We investigated the dependence of the east-west travel time averaged over a box around the disc centre on the implanted tracking velocity. The slope of this dependence is directly proportional to the total volume integral of the sensitivity kernel that corresponds to the travel-time geometry that is used. The agreement between measurements and models for travel times that are computed with a ridge filtering is very good to acceptable. The dependence we sought to determine indeed resembles a linear function, and its slope agrees with the expected volume integral from the forward-modelled sensitivity kernel. The agreement is poorer for the phase-speed filtered datacubes. The disagreement is particularly strong for the slowest phase speeds (filters td1--td4). For the higher phase speeds, our result indicates that the measured kernel integrals are systematically larger than expected from the forward modelling. We admit our testing procedure may not be appropriate for high phase speeds and higher radial modes.