Spectral factorization of seismic wavefields

The first part (Chapter ) covers the multidimensional spectral factorization of passive seismic wavefields. I show that calculating the 3-D spectral factorization of a passive seismic wavefield amounts to estimating the medium's 3-D impulse response. Helioseismic dopplergrams provide a high-quality passive seismic dataset that has uniquely dense spatial coverage. This enables me to compare the solar impulse response from derived by spectral factorization with that derived by cross-correlation. The spectral factorization results contain significantly higher bandwidth, both temporally and spatially. I then show it is possible to derive active-source seismograms from terrestrial passive seismic data by crosscorrelating and factorizing data collected during a small passive seismic experiment conducted in Long Beach, CA.