5.7.5 Recovering velocity-delay maps from real data We have spent some effort transforming the BLR from configuration space into velocity-time-delay space. What we would really like to do is solve the inverse problem: we obtain experimentally a velocity-delay map from a spectroscopic monitoring program and transform this back into a unique solution for the BLR structure and kinematics. None of this is easy.
Inspection of the transfer equation (Equation (5.16)) would lead one immediately to think of Fourier inversion, i.e. the method of Fourier quotients. Indeed, this was the approach that was suggested in the seminal theoretical paper on reverberation mapping by Blandford & McKee (1982) nearly 25 years ago. The Fourier transform of the continuum light curve C(t) is
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