S U M M A R YThe primary indicators of lateral heterogeneity in the Earth are the slowness and azimuth of incoming seismic signals. On a regional scale, surface waves in the upper mantle and crust are often scattered and/or refracted, which results in deviations from the great-circle azimuth. The slowness and direction of propagation of an arriving wave packet provides information about the lateral heterogeneity, and can be measured by performing beam-forming on the recordings across an array of stations. The azimuthal deviation gives a constraint on the transverse velocity gradient along the path. In addition, its frequency dependence gives information on the depth dependence of the heterogeneity.We have performed beam-forming of fundamental-mode Rayleigh waves in the period range of 20 to 100 s travelling from the south-east of Europe to the NARS-NL array in the Netherlands. The purpose of this study is to obtain new information about the velocity structure beneath the Tornquist-Teisseyre Zone (TTZ). The TTZ is known to be a transition between the higher seismic velocities in the thicker and older Precambrian crust of the East European Platform (EEP), and the lower velocities in the thinner and younger Palaeozioc crust of central and western Europe (tectonic Europe, TE). However, the lateral velocity gradient and the depth extent of this transition are not very well constrained. We have used events located at both sides of the TTZ, and both the direct Rayleigh wave and its coda have been analysed. On the one hand, the deviation of the wave-propagation paths relative to the great circle observed in the direct wave for the events on the eastern side of the TTZ confirms earlier results, i.e. it gives independent evidence for a thicker crust and up to 10 per cent higher velocities in the first 150 km of the upper mantle beneath the EEP than beneath the TE. Such a contrast also explains observed surface head waves refracted along the TTZ. On the other hand, no energy reflected at the TTZ is detected in the coda for the events on the western side. From synthetic experiments based on a linearized theory, we conclude that, from this absence of reflections, no lower bound can be imposed on the width of the transition zone across the TTZ at different depths. Source mechanisms other than the ones for the events used are needed to observe these reflections at different depths, for both a sharp and a smooth transition.
S U M M A R YDelay-time tomography can be either linearized or non-linear. In the case of linearized tomography, an error due to the linearization is introduced. If the tomography is performed in a non-linear fashion, the theory used is more accurate from the physical point of view, but if the data have a statistical error, a noise bias in the model is introduced due to the non-linear propagation of errors. We investigate the error propagation of a weakly non-linear delay-time tomography example using second-order perturbation theory. This enables us to compare the linearization error with the noise bias. We show explicitly that the question of whether a non-linear inversion methods leads to a better estimation of the model parameters than a linearized method is dependent on the signal-to-noise ratio. We also show that, in cases of poor data quality, a linearized inversion method leads to a better estimation of the model parameters than a non-linear method.
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