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Abstract

Aims. We develop a helioseismic inversion algorithm that can be used to recover subsurface vertical profiles of two-dimensional supergranular flows from surface measurements of synthetic wave travel times. Methods. We carried out seismic wave-propagation simulations with a two-dimensional section of a flow profile that resembles an average supergranule and a starting model that only has flows at the surface. We assumed that the wave measurements are entirely without realization noise for the purpose of our test. We expanded the vertical profile of the supergranule stream function on a basis of B-splines. We iteratively updated the B-spline coefficients of the supergranule model to reduce the travel-time differences observed between the two simulations. We performed the exercise for four different vertical profiles peaking at different depths below the solar surface. Results. We are able to accurately recover depth profiles of four supergranule models at depths up to 8−10 Mm below the solar surface using f−p4 modes under the assumption that there is no realization noise. We are able to obtain the peak depth and the depth of the return flow for each model. Conclusions. A basis-resolved inversion performs significantly better than an inversion in which the flow field is inverted at each point in the radial grid. This is an encouraging result and might act as a guide in developing more realistic inversion strategies that can be applied to supergranular flows in the Sun.