Investigating discrepancies among measurements of traveling and standing wave attenuation

In studies of long-period (150 s to 300 s) seismic wave attenuation, the mean decay reported for surface waves is generally 10 to 15% greater (lower quality factor Q) than that measured from equivalent fundamental modes of oscillation. Towards reconciling this inconsistency, we first establish through forward modeling that observed waveforms are more compatible with the rapid rate of decay inferred from traveling wave analyses. Second, we apply traveling and standing wave measurement techniques to a common set of predicted and observed seismograms and compare the inferred levels of surface wave attenuation. We demonstrate that the discrepancy documented in the literature is a consequence of the measurement techniques applied and not an effect of the individual data sets used in previous studies. Experiments with synthetically generated seismograms illustrate that the presence of noise elevates the mean Q inferred for the standing wave methods considered. This bias is related to the nonrandom influence of noise on the phase spectrum. However, for realistic noise levels, the experiment fails to reproduce the magnitude of the discrepancy present in the literature or observed in this study. The synthetic experiments motivate a new measurement approach based on the decrease of spectral power with time that incorporates the behavior of noise into the parameterization. When this technique is applied to data, the mean observed Q decreases from values consistent with normal mode studies to values consistent with traveling surface wave analysis. We thus conclude that noise is the dominant cause of the discrepancy.