have been developed. They do not rely on the global resonant-mode nature of the observed oscillations: rather, the observations of wave motions are interpreted in terms of their local properties. Three methods in particular are widely used. Ring analysis (or ring-diagram analysis) works within a freqeuncy-wavenumber framework for analysing the oscillations, albeit on localized patches of the solar surface, and may therefore be considered the local-helioseismic analogue of global-mode helioseismology. Time-distance helioseismology (or helioseismic tomography), and the closely related method of acoustic holography, work rather in the framework of interpreting the effect of heterogeneities and flows on propagating waves in terms of travel-time shifts or equivalently phase shifts. These two basically distinct approaches will be described briefly below.

In ring analysis [@1989ApJ...343L..69H], measurements of wave properties are made in localized regions (“tiles”) on the surface of the Sun. The observable - typically the Doppler velocity - over the pixels within the region are Fourier transformed in the two spatial horizontal directions and in time to give wave power as a function of spatial wavenumbers $k_x$, $k_y$ and frequency. In cuts through the 3-D power spectrum at fixed frequency, the power is found to lie in rings corresponding to the different 