Three‐dimensional Inversion of Sound Speed below a Sunspot in the Born Approximation

Abstract

We revise the inversion of acoustic travel times for the three-dimensional sound-speed structure below the solar NOAA Active Region 8243 of 1998 June. We benefit from recent progress in time-distance helioseismology that provides us with more reliable tools to infer subsurface solar properties. Among the improvements we implement here are the use of Born approximation-based travel-time sensitivity kernels that take into account finite-wavelength effects and thus are more accurate than the previously employed ray-path kernels, the inclusion of solar noise statistical properties in the inversion procedure through the noise covariance matrix, and the use of the actual variance of the noise in the temporal cross-covariances in the travel-time fitting procedure. Of these three improvements, the most significant is the application of the Born approximation to time-distance helioseismology. This puts the results of this discipline at the same level of confidence as those of global helioseismology based on inversion of normal-mode frequencies. Also, we compare inversion results based on ray-path and Born approximation kernels. We show that both approximations return a similar two-region structure for sunspots. However, the depth of inverted structures may be offset by 1 or 2 Mm, and the spatial resolution of the results is more accurately estimated with the more realistic Born sensitivity kernels. Finally, using artificial realizations of Doppler velocities of the quiet Sun, we are now able to estimate the statistical uncertainties of these inversion results.

Validating Time‐Distance Far‐Side Imaging of Solar Active Regions through Numerical Simulations

“…The profile has been derived by inversions of the time-distance measurements of an actual sunspot ( Kosovichev et al 2000), and confirmed by a number of other local helioseismology inversions (Jensen et al 2001;Sun et al 2002;Basu et al 2004;Couvidat et al 2006;Zharkov et al 2007). Some of these studies have shown that the significant sound speed perturbation associated with the sunspot structure probably extends deeper than what was originally inferred.…”

Advances in Global and Local Helioseismology: An Introductory Review

“…That means that the inversion results based on the ray theory may underestimate the strength of the small-scale perturbations. The comparison of the inversion results for sub-surface sound-speed structures beneath sunspots have showed a very good agreement between the ray-paths and Born theories [158]. …”

“…Similarly to global helioseismology, these relations are expressed in the form linear integral equations with sensitivity kernels. Two basic types of the sensitivity kernels have been used: ray-path kernels [50] and Born-approximation kernels [156][157][158]. The raypath kernels are based on a simple and generally robust theoretical ray approximation, but they do not take into account finite wavelength effects and thus are not sufficiently accurate for diagnostics of small-scale structures.…”

Damping rates of p-modes by an ensemble of randomly distributed thin magnetic flux tubes

“…This scattering of p-modes has been well observed using various helioseismic techniques (see Braun et al 1988;Couvidat et al 2006). Braun & Birch (2008) found that sunspots can absorb over half of incident p-mode power and plage regions can absorb around 20%.…”