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. Due to 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 spatial resolutions of 7-10 Mm using generally 24 h 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.

Authors: J. Jackiewicz, L. Gizon, A.C. Birch
Projects: SoHO-MDI

Publication Status: Solar Physics (in press)
Last Modified: 2008-09-23 21:22

Time-distance helioseismology has shown that f-mode travel times contain information about horizontal flows in the Sun. The purpose of this study is to provide a simple interpretation of these travel times. We study the interaction of surface gravity waves with horizontal flows in an incompressible, plane-parallel solar atmosphere. We show that for uniform flows less than roughly 250 m s-1, the travel-time shifts are linear in the flow amplitude. For stronger flows, perturbation theory up to third order is needed to model waveforms. The case of small-amplitude spatially varying flows is treated using the first-order Born approximation. We derive two-dimensional Fr?chet kernels that give the sensitivity of travel-time shifts to local flows. We show that the effect of flows on travel times depends on wave damping and on the direction from which the observations are made. The main physical effect is the advection of the waves by the flow rather than the advection of wave sources or the effect of flows on wave damping. We compare the two-dimensional sensitivity kernels with simplified three-dimensional kernels that only account for wave advection and assume a vertical line of sight. We find that the three-dimensional f-mode kernels approximately separate in the horizontal and vertical coordinates, with the horizontal variations given by the simplified two-dimensional kernels. This consistency between quite different models gives us confidence in the usefulness of these kernels for interpreting quiet-Sun observations.

Authors: J. Jackiewicz, L. Gizon, A.C. Birch, T.L. Duvall Jr.
Projects: SoHO-MDI

Publication Status: ApJ (published 2007)
Last Modified: 2008-09-23 21:22

We perform a two-dimensional inversion of f-mode travel times to determine near-surface solar flows. The inversion is based on optimally localized averaging of travel times. We use finite-wavelength travel-time sensitivity functions and a realistic model of the data errors. We find that it is possible to obtain a spatial resolution of 2 Mm. The error in the resulting flow estimate ultimately depends on the observation time and the number of travel distances used in the inversion.

Authors: J. Jackiewicz, L. Gizon, A.C. Birch, M.J. Thompson
Projects: None

Publication Status: Astronomische Nachrichten (published 2007)
Last Modified: 2008-09-23 21:22

We perform a two-dimensional inversion of f-mode travel times to determine near-surface solar flows. The inversion is based on optimally localized averaging of travel times. We use finite-wavelength travel-time sensitivity functions and a realistic model of the data errors. We find that it is possible to obtain a spatial resolution of 2 Mm. The error in the resulting flow estimate ultimately depends on the observation time and the number of travel distances used in the inversion.

Authors: J. Jackiewicz, L. Gizon, A.C. Birch, M.J. Thompson
Projects: None

Publication Status: Astronomische Nachrichten (published)
Last Modified: 2008-09-23 21:22