Time-distance helioseismology

Time-distance helioseismology is based upon crosscorrelating oscillatory dopplergram traces from different locations on the surface of the sun Duvall et al. (1993). The crosscorrelation between two such traces provides information about the ray-paths that propagate energy between the two locations. This allows helioseismologists to study the kinematics of acoustic waves traveling between the two trace locations, facilitating a family of techniques that are proving very successful for studying a range of solar phenomena at a large range of scales. For example, time-distance measurements can be used to estimate both near surface flow velocities associated with super-granulation Kosovichev and Duvall (1997), which are very difficult to resolve with spherical harmonic analysis, and meridional circulation deep within the convective zone Giles et al. (1997).

The process of picking traveltimes from time-distance curves is a critical element of these studies. Both signal-to-noise levels and signal bandwidth can limit the resolution of traveltime picks. Signal-to-noise can be increased by stacking individual crosscorrelelograms with similar offsets. This amounts to taking the multi-dimensional autocorrelation of the original data, and unfortunately, has the side-effect that it reduces the spatial and temporal bandwidth of the derived impulse response, by essentially squaring the $(\omega,k_x,k_y)$ amplitude spectrum.

I show that this problem can be avoided by looking at the multi-dimensional minimum-phase factor of the autocorrelogram rather than the autocorrelogram itself. The minimum phase time-distance impulse response has the same spectra as the original data, as opposed to its square.