Abstract
To recover the flow information encoded in travel-time data of time – distance helioseismology, accurate forward modeling and a robust inversion of the travel times are required. We accomplish this using three-dimensional finite-frequency travel-time sensitivity kernels for flows along with a (2+1)-dimensional (2+1D) optimally localized averaging (OLA) inversion scheme. Travel times are measured by ridge filtering MDI full-disk Doppler data and the corresponding Born sensitivity kernels are computed for these particular travel times. We also utilize the full noise-covariance properties of the travel times, which allow us to accurately estimate the errors for all inversions. The whole procedure is thus fully consistent. Because of ridge filtering, the kernel functions separate in the horizontal and vertical directions, motivating our choice of a 2+1D inversion implementation. The inversion procedure also minimizes cross-talk effects among the three flow components, and the averaging kernels resulting from the inversion show very small amounts of cross-talk. We obtain three-dimensional maps of vector solar flows in the quiet Sun at horizontal spatial resolutions of 7−10 Mm using generally 24 hours of data. For all of the flow maps we provide averaging kernels and the noise estimates. We present examples to test the inferred flows, such as a comparison with Doppler data, in which we find a correlation of 0.9. We also present results for quiet-Sun supergranular flows at different depths in the upper convection zone. Our estimation of the vertical velocity shows good qualitative agreement with the horizontal vector flows. We also show vertical flows measured solely from f-mode travel times. In addition, we demonstrate how to directly invert for the horizontal divergence and flow vorticity. Finally we study inferred flow-map correlations at different depths and find a rapid decrease in this correlation with depth, consistent with other recent local helioseismic analyses.
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