Reflection, refraction and mode conversion of long-period surface waves and the measurement of Q−1 for free oscillations

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Abstract
Filtered time series of Rayleigh waves from 4 events recorded on the quartz accelerometer at the IGPP, Camp Elliott Station, were analyzed. Attenuation (Q−1) was computed for spheroidal fundamental modes (oS19 to oS24) from several sequences of time-lapsed records for each event. A five-fold variation in measured Q−1 (and some variations in peak frequency) was assumed to be the result of lateral inhomogeneities in earth structure. Utilizing the duality between Rayleigh waves and fundamental-mode spheroidal oscillations, model power spectra were computed by summing the simulated Fourier transforms of dispersed wave trains. The effect of lateral variations in earth structure resulting in reflection, refraction and mode conversion of fundamental-mode surface waves was simulated by changes in amplitude, phase angle, and group and component travel times. Assuming an anelastic 10,000/Q of 33.3 (Q = 300), the observed range of measured Q−1 (and peak frequency) variations was duplicated by models with up to 5 per cent of the fundamental-mode Rayleigh-wave energy being “scattered”, i.e., reflected, refracted or converted to higher modes. In the real Earth, this would call for lateral variations in velocity structure well below the upper few hundred kilometers of the mantle. Recent seismological investigations have suggested lateral variations at these depths.

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