Characterizing Long-Period Seismic Effects of Long-Wavelength Elastic and Anelastic Models

Abstract

SUMMARY We present the results of a synthetic investigation designed to characterize the effects of long-wavelength elastic and anelastic models on the amplitudes and phases of long-period normal mode multiplets and Rayleigh wavepackets. Normal mode synthetics are created for recently constructed long-wavelength elastic and anelastic aspherical models of the Earth's upper mantle, using both the multiplet self-coupling approximation and the more accurate ±5 multiplet-multiplet coupling of the Galerkin method. Amplitude and phase measurements of the normal mode spectral peaks between 2 and 9 mHz and of the first eight Rayleigh wavepackets for 331 source-receiver pairs are compiled for each type of synthetic. the effects of anelastic and elastic structures are compared quantitatively with one another and with the predictions of zeroth order (in 1/l) asymptotic normal mode theory and linearized ray theory (LRT), and difficulties and advantages of applying these theoretical simplifications are identified and discussed. Although anelastic structures have only a minor effect on phases, long-wavelength models of anelastic and elastic structure each perturb amplitude measurements, with anelasticity accounting for up to ∼1/3 of the normal mode perturbations and up to ∼1/2 of the surface wave amplitude effect. Zeroth-order asymptotic theory and LRT predict that elastic and anelastic amplitude effects should qualitatively differ from one another, and thus should be separable in the data. While synthetics display qualitative agreement with the predictions of the approximations, for both normal mode spectra and surface wave measurements significant quantitative departures from zeroth-order asymptotic theory and LRT are observed. the part of the synthetic elastic amplitude signal not forecast by the approximate theories obscures the effects of aspherical anelasticity, particularly for normal modes, and can severely bias estimates of anelastic structure based solely on the approximations. In contrast, if an a priori model of aspherical elastic structure is assumed, the transfer functions that map amplitude anomalies from the elastic model to those for a model which includes anelastic asphericity are much more accurately forecast by zeroth-order asymptotic theory and LRT. Asymptotic theory accounts for over 85 per cent of the variance of such transfer functions for normal modes, and LRT predicts 67 per cent of the variance of surface wave transfer functions. Therefore, with the assumption of a priori elastic models, or in joint inversions of amplitude and phase data for elastic and anelastic structure, the approximations considered should prove useful for estimating models of aspherical attenuation.