2014 Articles

A comparison of approaches to the prediction of surface wave amplitude

Dalton, Colleen A.; Hjorleifsdottir, Vala; Ekström, Göran

A controlled experiment is performed to investigate how assumptions and simplifications in the measurement and analysis of surface wave amplitudes affect inferred attenuation variations in the mantle. Synthetic seismograms are generated using a spectral-element method for 42 earthquakes, 134 receiver locations and two earth models, both of which contain 3-D elastic properties and 1-D anelastic properties. Fundamental-mode Rayleigh-wave amplitudes are measured at periods of 50, 75 and 125 s for 4749 paths. The amplitudes are measured with respect to a reference waveform based on 1-D Earth structure, and thus amplitude observations that are not equal to unity can be attributed to differences in the computation of the spectral-element and reference waveforms or to uncertainties in the amplitude measurements themselves. Calculation of earthquake source excitation in the 3-D earth model versus the 1-D earth model has a significant effect on the amplitudes, especially at shorter periods, and variations in the average amplitude for each event are well explained by the effect of Earth structure at the event location on the source excitation. The effect of local Earth structure at the receiver location on the amplitude is, for most paths, much smaller than for the source amplitude. After correcting for source and receiver effects on amplitude, the remaining signal is compared to predictions of elastic focusing effects using the great-circle ray approximation, exact ray theory (ERT) and finite-frequency theory (FFT). We find that, for the earth models we have tested, ERT provides the best fit at 50 s, and FFT is most successful at 75 and 125 s, indicating that the broad zone of surface wave sensitivity cannot be neglected for the longer periods in our experiment. The bias introduced into attenuation models by focusing effects, which is assessed by inverting the measured amplitudes for 2-D attenuation maps, is most important at high spherical-harmonic degrees. Unaccounted-for scattering of seismic energy may slightly (<5 per cent) raise average global attenuation values at short periods but has no detectable effect at longer periods. The findings of this study also provide a set of guidelines for handling source, receiver and focusing effects that can be applied to surface wave amplitudes measured for the real Earth.