Delineation of detailed mantle structure frequently requires the separ
ation of source signature and structural response from seismograms rec
orded at teleseismic distances. This deconvolution problem can be pose
d in a log-spectral domain where the operation of time-domain convolut
ion is reduced to an additive form. The introduction of multiple event
s recorded at many stations leads to a system of consistency equations
that must be honoured by both the source time functions and the impul
se responses associated with propagation paths between sources and rec
eivers. The system is inherently singular, and stabilization is accomp
lished through the supply of an initial estimate of the source time fu
nction. Although alternative choices exist, an effective estimate is d
erived from the eigenimage associated with the largest eigenvalue in a
singular-value decomposition of the suite of aligned seismograms corr
esponding to a given event. The relation of the deconvolution scheme t
o simultaneous least-squares deconvolution is examined. Application of
the methodology to broadband teleseismic P waveforms recorded on the
Canadian National Seismograph Network demonstrates the retrieval of ef
fective Green's functions including secondary phases associated with u
pper-mantle structure.