PHYSICS OFTHE EARTH AND P LAN ETA RY _________ INTERIORS ELSEVIER Physics of the Earth and Planetary Interiors 84 (1994) 139—160 A new technique in demodulation of normal modes Ramin Nawab Philippe Lognonné Laboratoire de Sismologie, Institut de Physique du Globe de Paris, 4 place Jussieu, 75252 Paris Cedex 05, France (Received 6 May 1993; revision accepted 8 December 1993) Abstract Lateral heterogeneities of the Earth produce amplitude modulations of the so-called unresolved multiplets. A spectral fitting technique based on the polynomial interpolation of Hermite allows the retrieval of these slowly varying modulation functions. No restrictive hypothesis on coupling among multiplets is necessary. Modulation functions are constrained in time within a Q-cycle for data with typical signal-to-noise ratios. Sensitivity to noise is reduced by the introduction of cosine tapers and by a priori information on the modulation functions. The method then damps rapid oscillations caused by noise and becomes stable. These amplitude modulations can be used in a first stage for inversions where both phase and amplitude are necessary, and generalize basic mode observables such as the local frequency. 1. Introduction signals and then invert these observables to re- trieve the aspherical structure. The simplest ob- Lateral variations of the deep structure of the servable is the frequency of the maximum of an Earth can be retrieved by non-linear and simulta- unresolvably split normal mode resonance peak neous inversions of a large set of spectra of and its deviation from the spherical frequency of normal modes (see, e.g. Ritzwoller et al., 1986, the multiplet. As shown by Jordan (1978), this 1988; Giardini et al., 1987, 1988). Such methods deviation, known as the location parameter (A), imply, however, theoretical approximations on the is, up to the first order of the perturbation theory normal modes, for instance by neglecting cou- of the Earth’s normal modes (see, e.g. Dahien, pling effects. This is also the case for stripping or 1979) and for times shorter than the inverse of stacking methods (see, e.g. Dziewonski and the frequency shift (short time approximation), Gilbert, 1973a, b; Gilbert and Dziewonski, 1975; related to the depth-averaged structure between Buland et al., 1979), which extract from a global the source and the receiver. Inversions of these set of normal modes the eigenfrequencies under observables have been performed by Silver and the isolated multiplet hypothesis. Jordan (1981), Masters et a!. (1982), Roult and Other inversion methods, in contrast, extract Romanowicz (1984), and others. More exact ex- in a first step some observables from the seismic pressions have been developed by Dahlen (1974), Woodhouse and Girnius (1982), Davis and Hen- _______ son (1986) and Romanowicz and Roult (1986), * Corresponding author, including either coupling effects or higher-order 0031-9201/94/$07JJ0 © 1994 Elsevier Science B.V. All rights reserved SSDI 0031-9201(94)05030-2