CHARACTERIZING LONG-PERIOD SEISMIC EFFECTS OF LONG-WAVELENGTH ELASTICAND ANELASTIC MODELS

We present the results of a synthetic investigation designed to charac terize the effects of long-wavelength elastic and anelastic models on the amplitudes and phases of long-period normal mode multiplets and Ra yleigh wavepackets. Normal mode synthetics are created for recently co nstructed long-wavelength elastic and anelastic aspherical models of t he Earth's upper mantle, using both the multiplet self-coupling approx imation 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 wav epackets for 331 source-receiver pairs are compiled for each type of s ynthetic. The effects of anelastic and elastic structures are compared quantitatively with one another and with the predictions of zeroth or der (in 1/l) asymptotic normal mode theory and linearized ray theory ( LRT), and difficulties and advantages of applying these theoretical si mplifications are identified and discussed. Although anelastic structu res have only a minor effect on phases, long-wavelength models of anel astic and elastic structure each perturb amplitude measurements, with anelasticity accounting for up to approximately 1/3 of the normal mode perturbations and up to approximately 1/2 of the surface wave amplitu de 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 di splay qualitative agreement with the predictions of the approximations , for both normal mode spectra and surface wave measurements significa nt quantitative departures from zeroth-order asymptotic theory and LRT are observed. The part of tbe synthetic elastic amplitude signal not forecast by the approximate theories obscures the effects of aspherica l anelasticity, particularly for normal modes, and can severely bias e stimates of anelastic structure based solely on the approximations. In contrast, if an a priori model of aspherical elastic structure is ass umed, the transfer functions that map amplitude anomalies from the ela stic model to those for a model which includes anelastic asphericity a re 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 c ent of the variance of surface wave transfer functions. Therefore, wit h the assumption of a priori elastic models, or in joint inversions of amplitude and phase data for elastic and anelastic structure, the app roximations considered should prove useful for estimating models of as pherical attenuation.