Time-distance helioseismology is a technique for measuring the time for waves to travel from one point on the solar surface to another. These wave travel times are affected by advection by subsurface flows. Inferences of plasma flows based on observe
d travel times depend critically on the ability to accurately model the effects of subsurface flows on time-distance measurements. We present a Born approximation based computation of the sensitivity of time distance travel times to weak, steady, inhomogeneous subsurface flows. Three sensitivity functions are obtained, one for each component of the 3D vector flow. We show that the depth sensitivity of travel times to horizontally uniform flows is given approximately by the kinetic energy density of the oscillation modes which contribute to the travel times. For flows with strong depth dependence, the Born approximation can give substantially different results than the ray approximation.
The Sun supports a rich spectrum of internal waves that are continuously excited by turbulent convection. The GONG network and the MDI/SOHO space instrument provide an exceptional data base of spatially-resolved observations of solar oscillations, co
vering an entire sunspot cycle (11 years). Local helioseismology is a set of tools for probing the solar interior in three dimensions using measurements of wave travel times and local mode frequencies. Local helioseismology has discovered (i) near-surface vector flows associated with convection (ii) 250 m/s subsurface horizontal outflows around sunspots (iii) ~50 m/s extended horizontal flows around active regions (converging near the surface and diverging below), (iv) the effect of the Coriolis force on convective flows and active region flows (v) the subsurface signature of the 15 m/s poleward meridional flow, (vi) a +/-5 m/s time-varying depth-dependent component of the meridional circulation around the mean latitude of activity, and (vii) magnetic activity on the far side of the Sun.
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{e}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.
