Conclusions

Under assumptions of translational invariance, a white source function, and a minimum-phase impulse response, I have shown that estimation of the sun's acoustic time-distance impulse response amounts to multi-dimensional spectral factorization.

I performed the spectral factorization by transforming the entire multi-dimensional helioseismic wavefield into a one-dimensional super-trace, which could be factored efficiently with Kolmogorov's frequency domain method. I showed that time-distance curves obtained by spectral factorization have a broader temporal and spatial bandwidth equivalent curves calculated by crosscorrelation.

In the final section, I calculated the 3-D autocorrelation and spectral factorization of a small passive dataset collected in Long Beach, CA. The seismograms resemble active-source seismograms with a clearly visible ground-roll event.