Wolfgang Friederich

Surface wave dispersion and upper mantle structure beneath southern Germany from joint inversion of network recorded teleseismic events

We have determined the dispersion of fundamental mode Rayleigh waves in Southern Germany in the frequency range 4–50 mHz by simultaneously inverting data from 66 teleseismic events recorded at a network of up to 9 broadband stations. Three different inversion experiments were performed: determination of (1) isotropic phase velocity, of (2) azimuthally anisotropic phase velocity assuming a plane wave traveling across the network, and (3) isotropic phase velocity but now allowing for non-plane properties of the wavefield. In experiments (1) and (2), for each event amplitude, phase and deviation from the great circle azimuth were estimated as well. We have obtained remarkably stable results for phase velocity over the whole frequency range. Between 7 and 25 mHz azimuthal anisotropy is definitely below 0.5 percent. Below 7 and above 25 mHz we found up to 3 percent anisotropy but with negligible variance reduction compared to the isotropic inversion experiment (1). Admitting non-plane wavefields in the inversion still yields nearly identical phase velocities. On inversion of the phase velocity curve in terms of shear-wave velocity we obtained a rather shallow asthenosphere with minimum υS of 4.28 km/s at about 130 km depth covered by a thin lid with υS of 4.63 km/s.

Evidence for upper mantle anisotropy beneath southern Germany from Love and Rayleigh wave dispersion

We advance evidence for the existence of seismic anisotropy in the upper mantle beneath Southern Germany from the dispersion of Love and Rayleigh waves. The evidence is based upon a substantial Love-Rayleigh discrepancy observed between periods of 40 s and 120 s. An isotropic mantle model clearly fails to explain the observed dispersion curves. Systematic inversion experiments with transversely isotropic models show that anisotropy at depths between 70 km and 200 km is sufficient to explain the observed dispersion curves. Our data require neither anisotropy at greater depths nor anisotropy in the crust though we cannot exclude its presence there. A search for azimuthal anisotropy of Rayleigh wave propagation indicates a weak, but possibly insignifant azimuthal anisotropy of about 1% for periods less than 40 s with fast directions between 20 and 50 degrees east of north. At larger periods azimuthal anisotropy is less than 1% and the fast directions scatter considerably as period varies.

Inferring the orientation-distribution function from observed seismic anisotropy : General considerations and an inversion of surface-wave dispersion curves

—A general relation linking the elasticity tensor of an anisotropic medium with that of the constituting single crystals and the function describing the orientation distribution of the crystals is derived. By expanding the orientation distribution function (ODF) into tensor spherical harmonics and using canonical components of the elasticity tensors, it is shown that the elastic tensor of the medium is completely determined by a finite number of expansion coefficients, namely those with harmonic degree l≤ 4. The number of expansion coefficients actually needed to determine the elastic constants of the medium depends on the symmetry of the single crystals. For hexagonal symmetry of the single crystals it is shown that only 8 real numbers are required to fix the 13 elastic constants which are for example needed to determine the azimuthal dependence of surface wave velocities. Thus, inversions of observations of seismic anisotropy are feasible which do not make any a priori assumptions on the orientation of the crystals. As a byproduct of the derivation, a formula is given which allows the easy calculation of the elastic constants of a medium composed of hexagonal crystals obeying an arbitrary ODF. An application of the theoretical results to the inversion of surface wave dispersion curves for an anisotropic 1D-mantle model is presented. For the S-wave velocities the results are similar to those of previous inversions but the new approach also yields P-wave velocities consistent with the assumption of oriented olivine. Moreover it provides a hint of the orientation distribution of the crystals.