Earth structure from fundamental and higher-mode waveform analysis

Abstract

We present a technique for the inversion of fundamental and higher-mode waveform data for regional Earth structure. Seismograms are represented as a sum of travelling modes, and an adaptive quadrature scheme based on Filon's method is developed to evaluate the wavenumber integrals efficiently. The difference between an observed and synthetic seismogram is approximated as a linear functional of the residual dispersion which, in turn, is parameterized by perturbations to the Earth structure. The data functionals used by the inversion are branch cross-correlation functions (bccfs) between a particular single-mode synthetic and the observed seismogram. To reduce the effects of ambient noise and the interference by spurious signals and other modes, the bccfs are windowed and tapered about zero lag. The sensitivity of the bccfs to amplitude differences between the synthetic and observed seismograms is reduced by an orthogonalization procedure which strips from the linearized system of equations any information that can otherwise be explained by adjusting the scalar amplitudes of the mode branches. The bccfs are inverted for Earth structure using an iterative, generalized least-squares algorithm. Numerical experiments with synthetic data show that, if the starting model is far enough from the true solution and the path lengths are long enough, the bccfs can be sufficiently dephased to lock the inversion into a spurious local minimum. However, this situation can usually be spotted by a direct comparison of the model synthetics with data and corrected by initializing the inversion with a perturbation to the starting model designed to roughly align the fundamental and first-higher mode groups; interactive software has been developed for this purpose. We have applied these methods to vertical-component data from two well-studied paths, one crossing Eurasia from sources in the Kurils-Japan area to a receiver array centred on the Baltic Shield, and the other crossing the Pacific from the New Hebrides to the western United States. Structures derived from dispersion data by Cara and Cara, Nercessian & Nolet were used as starting models, and bccfs up to the fourth-higher mode were inverted. Although the starting models produced synthetics in reasonably good agreement with the data, a 760 variance reduction on the order of 70 per cent was achieved for both paths. The final models show substantial differences in the two shear-velocity profiles below 200 km depth, in agreement with the results of Cara et al. and inferences based on the study of multiple-ScS travel times by Sipkin & Jordan. Synthetics generated from these models are in excellent agreement with the complex higher-mode waveforms observed for the entire range of receiver distances and source depths.where A(Ao, w ) is the amplitude at an array centroid A,, and k ( w ) is the dispersion function. The stack can thus be writtenwhere H ( k ) is known as the 'array response' (Nolet 1975;Nolet & Panza 1976) and is simply the Higher-mode wavefom analysis 761 digital Fourier tr...

Generalized seismological data functionals

“…it is easy to implement differential weighting schemes (e.g. downweighting the high-amplitude surface waves) to improve the resolution and variance of the model parameters (Lerner-Lam & Jordan 1983, 1987Gee, Lerner-Lam & Jordan 1985).…”

“…Recent examples include Cara & LCvCque's (1987) method to invert wave group envelopes, Nolet's (1990) partitioned waveform inversion, and Luo & Schuster's (1991a) inversion of 'skeletalized' data. One strategy, closely related to the approach adopted here, has been developed for travelling modes by Lerner-Lam & Jordan (1983). They have posed the linearized inverse problem in terms of the difference between the observed cross-correlation function, or arnplitudc information gets scramhled tngether with phnqe cross-correlagram, Cms(t) = ii,(t) @ s ( t ) , and the modelpredicted cross-correlagram, C,,(t) = ii,,,(t) @ S ( t ) , where ilm(f) is the synthetic for the rnth mode.…”

Measurements of mantle wave velocities and inversion for lateral heterogeneities and anisotropy: 3. Inversion

“…The vertical resolution will benefit greatly from the analysis of shorter periods and of overtones (Nolet, 1977;Cara, 1979;Lerner-Lam and Jordan, 1983;Nolet et al, 1986). In particular, overtones will be needed to better constrain polarization anisotropy Cara, 1983, 1985).…”

Automatic 1-D waveform inversion of marine seismic refraction data

“…Waveforms have also been used in the inversion of low-frequency seismograms (Woodhouse & Dziewonski 1984;Lerner-Lam & Jordan 1983) and reflection seismograms (Gauthier, Virieux & Tarantola 1986;Mora 1987;Pan, Phinney & Odom 1988). These studies have demonstrated the ability of seismic waveforms to be used in linearized inversion schemes instead of traveltimes.…”