On the discrepancy in measurement of Q using surface waves and normal modes

We revisit the decade-old unsolved problem of why measurements of the quality factor (Q) for fundamental mode propagating Rayleigh waves differs by up to 20% from that measured using normal modes, in the frequency band where both approaches are possible. Surface wave measurements consistently yield lower Q values than modes. Since it is unclear which measurement is more accurate, this is currently a limitation on the resolution of 1D average Q profiles in the Earth, compounded by the fact that the measurement bias may not only affect the region of the spectrum where both methods are available but every Q measurement that is based upon one or the other of the mentioned techniques. We investigate the effect of elastic focussing and defocussing on long time series using a spectral element method that we have shown to be accurate enough for the relevant period ranges and the necessarily long time series. While previous investigations are based upon approximate methods that are only valid for smooth 3D models and weak heterogeneities, the SEM allows us to estimate the effect of more realistic distributions of heterogeneities on amplitude measurements, and therefore Q. Our investigations show a bias towards lower Q in the first arriving surface wave trains and a bias towards higher Q in later arrivals which could explain the mode surface-wave discrepancy. Heuristically this can be explained by the fact that energy that has been scattered off the great circle path is brought back into the great circle after multiple-orbits, leading to increased amplitude in late arrivals. Further we reinvestigate the effects of noise that predominantly influences the later part of the seismogram, the effect of post-processing as well as mode amplitude modulations that could potentially bias the measurements. We plan to present preliminary results on applying our insights to debias real data and reduce the error bounds on 1D Q models from normal modes and surface waves.