S U M M A R Y As a model for the 2-D horizontal propagation of seismic surface waves, we study the propagation of non-plane acoustic waves in homogeneous and inhomogeneous media. W e find that their phase velocity depends not only on the medium but also on the local geometry of the wavefield, especially on the distribution of amplitudes around the point of observation. The phase velocity of a wave is therefore conceptually and in most cases numerically different from the phase velocity parameter in the wave equation, which is determined by the elastic properties of the medium. The same distinction must be made for seismic surface waves. Although it is a common observation that waves of the same period can propagate with different phase velocities over the same path, the fundamental character of this observation has apparently not been recognized, and the two phase velocities are frequently confused in the seismological literature. We derive a local relationship between the two phase velocities that permits a correct structural interpretation of acoustic waves in inhomogeneous media, and also of non-plane seismic surface waves in laterally homogeneous parts of the medium.

[1] Regional seismic tomography provides valuable information on the structure of shields, thereby gaining insight to the formation and stabilization of old continents. Fennoscandia (known as the Baltic Shield for its exposed part) is a composite shield for which the last recorded tectonic event is the intrusion of the Rapakivi granitoids around 1.6 Ga. A seismic experiment carried out as part of the European project Svecofennian-Karelia-Lapland-Kola (SVEKALAPKO) was designed to study the upper mantle of the Finnish part of the Baltic Shield, especially the boundary between Archean and Proterozoic domains. We invert the fundamental mode Rayleigh waves to obtain a three-dimensional shear wave velocity model using a ray-based method accounting for the curvature of wave fronts. The experiment geometry allows an evaluation of lateral variations in velocities down to 150 km depth. The obtained model exhibits variations of up to ±3% in S wave velocities. As the thermal variations beneath Finland are very small, these lateral variations must be caused by different rock compositions. The lithospheres beneath the Archean and Proterozoic domains are not noticeably different in the S wave velocity maps. A classification of the velocity profiles with depth yields four main families and five intermediate regions that can be correlated with surface features. The comparison of these profiles with composition-based shear wave velocities implies both lateral and vertical variations of the mineralogy.

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SUMMARY Acceleration power spectral densities of vertical seismic noise at the best seismic stations show a minimum near 3 mHz. We suggest that this minimum is caused by a cancellation near this frequency of Newtonian attraction vs. free air and inertial effects exerted by atmospheric phenomena on the sensor mass. Simplistic models of atmospheric phenomena are used to quantify this effect and examples are shown for special atmospheric events.

S U M M A R YWe present a 2-D reformulation of surface wave scattering theory in terms of potentials, which allows an extension of the Born single-scattering approach to include multiple forward scattering. No additional numerical effort compared to single scattering is required for a computation of the wavefield over the whole heterogeneous region. Born single scattering for elastic surface waves and both multiple and single scattering for acoustic waves are also covered by the formulation. It is valid for fully anisotropic perturbations of the reference medium. We use the flexibility of our formulation to compare the different approximations with each other and, additionally, test all of them against an exact solution for the particular case of a cylindrical inclusion in a layered waveguide.Our numerical results, obtained for shear velocity contrasts of about 6 per cent, show that the method which includes multiple scattering is superior to the single-scattering methods if the scattering region extends over more than one wavelength. If coupling to higher modes is suppressed, the multiple-scattering method still yields nearly exact results for the vertical displacement. The influence of mode coupling and type conversion leads to only small errors in vertical displacement. Moreover, as we show for a cylinder with a diameter of two wavelengths, even an acoustic treatment of surface waves including multiple forward scattering may be more accurate than single scattering within an elastic treatment. For scatterer sizes below one wavelength the single-scattering approaches are accurate enough, while elastic and acoustic treatments of surface waves may differ considerably.The proposed multiple-scattering method is numerically very efficient, because the numerical effort mainly depends on the degrees of smoothness of the wavefield and the heterogeneity, and is not directly coupled to the wavelength.