Abstract
We develop a helioseismic inversion algorithm that can be used to recover sub-surface vertical profiles of 2-dimensional supergranular flows from surface measurements of synthetic wave travel times. We carry out seismic wave-propagation simulations through a 2-dimensional section of a flow profile that resembles an averaged supergranule, and a starting model that has flows only at the surface. We assume that the wave measurements are entirely without realization noise for the purpose of our test. We expand the vertical profile of the supergranule stream function on a basis of B-splines. We iteratively update the B-spline coefficients of the supergranule model to reduce the travel-times differences observed between the two simulations. We carry out the exercise for four different vertical profiles peaking at different depths below the solar surface. We are able to accurately recover depth profiles of four supergranule models at depths up to $8-10\,\text{Mm}$ below the solar surface using $f-p_4$ 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. A basis-resolved inversion performs significantly better than one where the flow field is inverted for 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.
Highlights
Convective flows on the solar surface exhibit several length scales (Nordlund et al 2009)
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
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
Summary
Convective flows on the solar surface exhibit several length scales (Nordlund et al 2009). DeGrave et al (2014) tried validating time-distance SOLA inversions with realistic solar simulations and found that they could recover horizontal flows down to 5 Mm below the solar surface; but, unlike Švanda et al (2011), DeGrave et al were unable to infer vertical flows accurately The authors attributed this to differences in measurement and analysis techniques. Hanasoge (2014) and Bhattacharya & Hanasoge (2016) tried a different appraoch, which used full-waveform inversion (Tromp et al 2010) to update iteratively a Cartesian two-dimensional flow profile to minimize the travel-time misfit computed with respect to a model similar to the average supergranule from Duvall & Birch (2010) These authors found that seismic waves in their simulations were primarily sensitive to flow updates close to the solar surface and inversions focused on updating these layers at the expense of deeper layers.
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