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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 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.

** Next:** Model of stochastic oscillations
** Up:** Introduction to helioseismology
** Previous:** Introduction to helioseismology
Stanford Exploration Project

5/27/2001