Helioseismology - Local Helioseismology

The goal of local helioseismology, a term first used in 1993, is to interpret the full wave field observed at the surface, not just the mode (more precisely, eigenmode) frequencies. Another way to look at it, is that global helioseismology studies standing waves of the entire Sun and local helioseismology studies propagating waves in parts of the Sun. A variety of solar phenomena are being studied, including sunspots, plage, supergranulation, giant cell convection, magnetically active region evolution, meridional circulation, and solar rotation. Local helioseismology provides a three-dimensional view of the solar interior, which is important to understand large-scale flows, magnetic structures, and their interactions in the solar interior.

There are many techniques used in this new and expanding field, which include:

• Fourier–Hankel spectral method, first introduced by Braun and Duvall, was originally used to search for wave absorption by sunspots.

• Ring-diagram analysis, first introduced by F. Hill, is used to infer the speed and direction of horizontal flows below the solar surface by observing the Doppler shifts of ambient acoustic waves from power spectra of solar oscillations computed over patches of the solar surface (typically 15° × 15°). Thus ring analysis is a generalization of global helioseismology applied to local areas on the Sun (as opposed to half of the Sun). For example, sound speed, and adiabatic index can be compared within magnetically active and inactive (quiet Sun) regions.

• Time-distance helioseismology, introduced by Duvall et al., aims to measure and interpret the travel times of solar waves between any two locations on the solar surface. A travel time anomaly contains the seismic signature of buried inhomogeneities within the proximity of the ray path that connects two surface locations. An inverse problem must then be solved to infer the local structure and dynamics of the solar interior.

• Helioseismic holography, introduced in detail by Lindsey and Braun for the purpose of far-side (magnetic) imaging, a special case of phase-sensitive holography. The idea is to use the wavefield on the visible disk to learn about active regions on the far side of the Sun. The basic idea in helioseismic holography is that the wavefield, e.g., the line-of-sight Doppler velocity observed at the solar surface, can be used to make an estimate of the wavefield at any location in the solar interior at any instant in time. In this sense, holography is much like seismic migration, a technique in geophysics that has been in use since the 1940s. As another example, this technique has been used to give a seismic image of a solar flare. Acoustic holography, applied to MDI data, is ideal for the detection of sources and sinks of acoustic waves on the Sun. Braun and Fan discovered a region of lower acoustic emission in the 3 – 4 mHz frequency band which extends far beyond the sunspots (the ‘acoustic moat’). Acoustic moats extend beyond magnetic regions into the quiet Sun. In addition, Braun and Lindsey discovered high-frequency emission (‘acoustic glories’) surrounding active regions.

• Direct modelling, after Woodard. Here the idea is to estimate subsurface flows from direct inversion of the frequency-wavenumber correlations seen in the wavefield in the Fourier domain. Woodard gave a practical demonstration of the ability of the technique to recover near-surface flows from the f-mode part of the spectrum.

This section is adapted from Laurent Gizon and Aaron C. Birch, "Local Helioseismology", Living Rev. Solar Phys. 2, (2005), 6. online article (cited on November 22, 2009).