Comparison between Time-domain and Frequency-domain Measurement Techniques for Mantle Shear-wave Attenuation

We study the frequency- and time-domain techniques which have been used to measure shear attenuation in the mantle using long-period body waveforms. In the time-domain technique, waveform modeling is carried out and the attenuation model that best fits the data is chosen. In the frequency-domain technique, we solve for the attenuation model that best fits the spectra of the seismic waveforms. Though theoretically both these techniques are equivalent, modeling assumptions and measurement biases associated with each technique can give rise to different results. In this study, we compare these two techniques in terms of their accuracy in obtaining mantle shear attenuation. Specifically, we estimate the biases in constraining attenuation from differential SS S and absolute S waveforms. We carry out these tests using realistic synthetic seismograms and we follow this with an analysis of recorded data to verify the results from the synthetic tests. For the SS S waveforms, the primary biasing factors are interference with seismic phases due to mantle discontinuities and due to crustal reverberation under the SS bounce point. These factors can affect the t* measurements by up to 0.5 s in the frequency domain and more than 1.5 s in the time domain. For the S waveforms, the frequency-domain measurements are accurate to 0.3 s while the time-domain measurements can vary by more than 2.0 s from the predicted values. These errors are also manifested in the t* measurements made using teleseismically recorded waveforms and lead to comparatively larger noise levels in the time-domain measurements. Based on these results, we propose that in long-period body-wave attenuation studies, frequency-domain techniques should be the method of choice.