Reference frequency of teleseismic body waves

Anelasticity of the Earth causes physical dispersion of seismic waves. The appropriate choice of reference frequency is important to determine arrival times of body waves, especially later arrival times, from broadband seismograms by fitting observed to synthetic waveforms. Our question is how to choose the reference frequency of physical dispersion, f_o, consistent with the extensive data sets of hand-picked body wave arrival times compiled through the long history of seismology. Setting the reference frequency to be the conventional 1 Hz, we measured S-P differential travel times by waveform fitting. We found a systematic discrepancy between the measured and hand-picked S-P times that can be removed by changing f_o from 1 to 2 Hz. This change of f_o requires a correction in Q of the PREM model: (1 if Q is strictly frequency-independent, we need a 15% increase in Q value or (2) if Q is fixed to the value given by PREM at a period of 200 s, we need to introduce a small frequency dependence in Q, where the dependence is expressed by the power law with an exponent of 0.04.