2.2 Local helioseismology

Not all acoustic waves (p-modes) in the Sun are resonant oscillations of the full sphere. Locally-excited waves interact with local variations in sound speed, flow fields, and magnetic activity which alter their propagation characteristics. Thus, a careful analysis of the acoustic wave field in a localized patch of the solar photosphere can potentially reveal a great deal about the subsurface dynamics. Extracting dynamical information from local wave fields can be more challenging than from global oscillations, primarily because the forward problem is more difficult; for a given structure and flow, what acoustic signal will be manifested on the solar surface? This depends to some degree on the source of the waves, which is complex and intermittent. A thorough understanding of this forward problem is necessary in order to devise reliable inversion techniques for inferring subsurface structure and dynamics from photospheric measurements.

Several related inversion techniques exist for local helioseismology, including ring-diagram analysis (Hill, 1988 ), time-distance methods (Kosovichev et al., 2000 ), and acoustic holography (Lindsey and Braun, 2000a ). All of these approaches are discussed in detail by Gizon and Birch (2005 ).

From the perspective of solar interior dynamics, the most important result to come from local helioseismology has been the mapping of horizontal flows in the surface layers of the Sun as shown in Figure 3 . Such mappings reveal meandering meridional and zonal circulation patterns as well as intricate smaller-scale flows associated with active regions and supergranulation. The investigation and monitoring of these flows has given rise to the new discipline of solar subsurface weather, SSW (Toomre, 2002 ). Local helioseismology has also been used to study the acoustic and flow structure underlying sunspots (Kosovichev et al., 2000 ; Braun and Lindsey, 2000 ; Zhao et al., 2001 ; Zhao and Kosovichev, 2003 ) and to image active regions on the far side of the Sun (Lindsey and Braun, 2000b ; Braun and Lindsey, 2001 ).

The probing of horizontal flows by local helioseismology has provided unpreceded insight into the structure and evolution of differential rotation (Section 3.3), meridional circulation (Section 3.4), and giant cells (Section 3.5). However, like any method, it has its limitations. Most notably, the small-wavelength acoustic waves, which local helioseismology is best suited to investigate, are confined principally to the near-surface layers, $r > 0.97Ro .$ . Some analyses have attempted to probe deeper (Giles et al., 1997 ; Braun and Fan, 1998 ) but the resolution is limited and the results are generally less reliable. There is much promise that with improved instrumentation and analysis techniques local helioseismology can do better and may soon provide information on flow structure, magnetic activity, and thermal asphericity as deep as the tachocline (Gizon and Birch, 2005 ).

Although local helioseismology can currently only provide detailed dynamical information for the outer few percent of the solar interior, the large-scale flow patterns it reveals may extend deeper into the convective envelope. For the same reason, surface observations are also relevant (Section 2.3).