ABSTRACT
Helioseismology has become a unique diagnostic observational tool in the field of solar physics to study the solar interior. The photospheric surface oscillations were discovered in 1960 by spectro-scopic methods as Doppler velocity fluctuations. They were interpreted to result from superposition of millions of standing modes trapped in acoustic cavities of varying depths in solar interior. This chapter discusses the basic physics and formalism of the trapped global modes, and derives the properties of p- and g-modes using local or asymptotic treatment. This is followed by observational requirements for frequency, temporal and spatial resolutions, and helioseismic observations over long time spans using ground-based observing networks and from space. The direct and inversion techniques are described which help in obtaining profiles of physical parameters in the solar interior, such as, the density, sound speed or temperature, rotation, depth of convection zone, etc. Helio-seismology inversions have led to the discovery of shear layer, or tachocline, located at the base of the convection zone, where transition from differential to solid-body rotation occurs. Local helio-seismology of active region has developed as another important field which deals with the birth of sunspots, and far-side imaging of the Sun. Extension of helioseismology to other stars has also been successful in providing information about the otherwise difficult problem about their interior. There are still several problems related to various types of stars and detection of the elusive g-modes that need to be followed up in the coming years.
