Controls on Rayleigh wave amplitudes: attenuation and focusing

Abstract

A large data set of amplitude measurements of minor and major arc Rayleigh waves in the period range 73–171 s is collected. By comparing these amplitudes with the amplitudes of synthetic waveforms calculated by mode summation, maps of lateral variations in the apparent attenuation structure of the Earth are constructed. An existing formalism for predicting the effects of focusing is employed to calculate amplitude perturbations for the same data set. These perturbations are used to construct ‘pseudo‐attenuation’ maps and these results are compared with the apparent attenuation maps calculated from the data. It is shown that variations in Rayleigh wave amplitude perturbations in the Earth are dominated by attenuation at long wavelengths (below about degree 8) and by elastic structure at shorter wavelengths. It is also shown that the linear approximation for focusing is successful at predicting Rayleigh wave amplitudes using existing phase velocity maps. These results indicate that future attempts to model the velocity structure of the Earth would be assisted by incorporating amplitude data and by jointly inverting for Q structure.

Deep Earth Structure: Q of the Earth from Crust to Core

“…Although Gung and Romanowicz (2004) did not include focusing effects in deriving their model QRLW8, subsequent tests indicated that the model was robust with respect to these effects, in agreement with the predictions of Selby and Woodhouse (2000). In particular, Gung and Romanowicz (2004) compared the degree-8 Q m (r) model obtained with and without focusing terms, the latter computed using expression [8] in the 3D elastic model obtained in the first step, and found no significant changes.…”

“…The applicability of the linear asymptotic approximation to the computation of focusing (eqns [7]-[9]) has been tested by Selby and Woodhouse (2000) on a large data set of Rayleighwave amplitudes on minor and major arcs, in the period range 73-171 s. These authors derived maps of lateral variations of…”

Theory and Observations: Normal Mode and Surface Wave Observations

“…As mentioned in the preceding text, amplitude data are also very useful to constrain lateral heterogeneity. Selby and Woodhouse (2000) found that amplitude variations are dominated by anelastic structure for long wavelengths and by elastic structure at short wavelengths. Amplitude information has been used as additional constraints to investigate elastic structure.…”

Global Imaging of the Earth's Deep Interior: Seismic Constraints on (An)isotropy, Density and Attenuation

“…This strategy led to maps of both even-and odd-degree structure, that were used to construct the first global model of shear attenuation (Romanowicz, 1995). Billien et al (2000) and Selby & Woodhouse (2000; explicitly treated elastic focusing using a linear approximation derived from ray theory (Woodhouse & Wong, 1986). The contribution from focusing to the amplitudes of Rayleigh waves was found to be considerable, even for long periods between 70 s and 170 s. This motivated Billien et al (2000) to jointly invert phase and amplitude measurements of Rayleigh waves for degree-20 maps of phase velocities and attenuation.…”