Markus Roth, Jason Jackiewicz

We present the current status of an undergoing validation of a recently developed model for computing spherical Born approximation sensitivity functions for flows. In a first step, power spectra and reference cross-correlations from the model and a simulation of Hartlep et al. (2013) are matched. Some difficulties in obtaining such a match are discussed. In a second step, travel times from the forward model and from the simulation, which includes a standard meridional flow profile, are to be compared. The analysis procedure including the use of phase-speed filters is identical to the one employed in Jackiewicz et al. (2015). Furthermore, we present a novel approach for a fast computation of integrated sensitivity functions which can be used for interpreting rotationally symmetric flows such as differential rotation and meridional flow.

Markus Roth, Wolfgang Zima

We extend an existing Born approximation model for calculating the linear sensitivity of helioseismic travel-times to flows from plane-parallel to spherical geometry. This extension is necessary especially for dealing with deep flows. Furthermore, we present first results for the sensitivity kernels and validate our model with the help of artificial helioseismic data for a standard meridional flow pattern from Hartlep et al. (2013, ApJ).

Shukur Kholikov, Jason Jackiewicz, Markus Roth

In this study, we present first inversion results for deep meridional flow using spherical Born approximation kernels and time-distance helioseismology. The computation of Born approximation kernels for flows has only recently become available in spherical geometry. Compared to the ray approximation, the Born approximation is considered to provide a more realistic model of the advection and scattering processes in the solar interior, which are captured in travel time measurements. We first validate this method using artificial data from a linear 3D simulation of solar interior wave propagation. We find that the prediction of the Born approximation model coincides well with the simulated data. We then perform standard SOLA inversions of the solar meridional flow. First, inversion results of the simulated data are discussed and compared to the original flow profile included in the simulation. Finally, we apply the validated method to GONG data spanning periods of low, medium and high solar activity (2001-2003, 2004-2006, and 2007-2009). The results are discussed and compared to literature.

Markus Roth, Jason Jackiewicz, Shukur Kholikov

The solar meridional flow is a crucial ingredient to modern dynamo theory. Seismic estimates of this flow have, however, been contradictory in deeper layers below about 0.9Rsun. Results from time-distance helioseismology have so far been obtained using the ray approximation. Here, we perform inversions using the Born approximation. The initial result is similar to the result previously obtained using ray kernels by Jackiewicz et al. (2015), while using the same set of GONG data and the SOLA inversion technique. However, we show that the assumption of uncorrelated measurements used in earlier studies may lead to inversion errors being underestimated by a factor of about 2 - 4. In a second step, refined inversions are performed using the full covariance matrix and a regularization for cross-talk. As the results are found to depend on the threshold used in the singular value decomposition, they were obtained for a medium threshold (10^−7 to 10^−5 , about 50% of values used) and a threshold lower by a factor of 10 (about 70% of values used). The result obtained with the medium threshold is again similar to the original, with less latitudinal variation. However, using the lower threshold, the inverted flow in the southern hemisphere shows two or three cells stacked radially depending on the associated radial flows. Both the single-cell and the multi-cell profile are consistent with the measured travel times. All our results confirm a shallow return flow at about 0.9Rsun. Corresponding paper to appear in ApJ.