Helioseismologists study the acoustic oscillations visible on the surface of the sun to determine the sun's internal structure. The source function for the oscillations is stochastic, generated by turbulence in the convective region of the solar interior. To remove the effects of the stochastic source function, helioseismologists calculate time-distance curves by crosscorrelating passively observed seismograms.
In this chapter, I show how multi-dimensional spectral factorization can improve the spatial and temporal resolution of time-distance curves significantly. Time-distance curves calculated in this way have the same spatial and temporal bandwidth as the original data, rather than the decreased bandwidth obtained obtained by crosscorrelating traces. Additionally, the spectral factorization impulse response is minimum phase, as opposed to the zero phase time-distance curves produced by crosscorrelation.
In the final section, I show crosscorrelation and spectral factorization results from a small terrestrial passive 3-D survey, recorded in Long Beach, CA. In total, about four hours of 60-channel passive data were recorded and processed. Although no clear reflection events are visible, a coherent dispersive ground-roll event is visible, and the correlograms do resemble active source seismograms.