Inversion of sonic waveforms with unknown source and receiver functions

A seismogram that is several times the length of the source-receiver wavelet is windowed into two parts-these may overlap-to obtain two seismograms with approximately the same source function but different Green's functions. A similarly windowed synthetic seismogram gives two corresponding synthetic seismograms. The spectral product of the window 1 data with the window 2 synthetic is equal to the spectral product of the window 1 synthetic with the window 2 data only if the correct earth model is used to compute the synthetic. This partition principle is applied to well-log sonic waveform data from Ocean Drilling Project hole 806B, a slow formation, and used there to estimate Poisson's ratio from a single seismogram whose transmitter and receiver functions are unknown. A multichannel extension of the algorithm gives even better results. The effective borehole radius R-b was included in the inversion procedure, because of waveform sensitivity to R-b. Inversion results for R-b agreed with the sonic caliper, but not the mechanical caliper; thus if R-b is not included in the inversion its value should be taken from the sonic caliper.