Berechnung des seismischen Streufeldes für anisotrope Störungen

Abstract

Vorliegende Arbeit beschäftigt sich mit der Streuung der seismischen Wellen infolge unterschiedlicher, unter Anderen anisotroper, Störungen der sphärischen Symmetrie des Modells. Die Streuwellen übelagern das Referenzsignal und ermöglichen Rückschlüsse auf die verursachende Störung. Die Grundlagen für die störtheoretische Berechnung der synthetischen Seismogramme entstanden noch in den siebziger Jahren des zwanzigsten Jahrhunderts durch Arbeiten von Woodhouse, Dahlen und anderer. Eine effiziente Umsetzung dieser Theorie benötigt aber eine Reihe weiterer Annahmen und Vereinfachungen. Friederich entwickelte eine Methode zum Berechnen der synthetischen Seismogrammen für Erdmodelle mit isotropen elastischen Inhomogenitäten. Seine Methode berücksichtigt mehrfache Streuung in die Richtung der Wellenausbreitung. Die vorliegende Arbeit beinhaltet eine Verallgemeinerung der Methode von Friederich auf eine breitere Gruppe der Symmetriestörungen wie anisotrope Inhomogenitäten, Perturbationen der Dichte und Initialspannung sowie Erdrotation. Eine besondere Aufmerksamkeit wird den Auswirkungen beliebiger Asymmetrien in Verteilung der elastischen Materialeigenschaften gewidmet. Insbesondere werden die Effekte der anisotropen Störungen untersucht um die Inversion der anisotropen Erdmodelle zu ermöglichen.

Most minerals in the earth are crystalline substances of low symmetry and thus anisotropic. The effects of this microscopic anisotropy can be mostly neglected due to random orientation of the individual crystals. Processes resulting in some ordering of crystals can produce areas of macroscopic anisotropy on the scale which affects the propogation of seismic waves. Observation of these effects in turn allows conclusions about the processes responsible for the ordering. The geodynamic processes like mantel convection and continental drift with resulting mechanical stress and deformations are probably the most interesting possible sources of macroscopic anisotropy. Calculation of seismic wave fields for a generic anisotropic and thus aspherical earth requires an accurate balance of assumptions and simplifications. Most methods are based on perturbation theory. Woodhouse and Dahlen formulated a degenerative perturbation method which can deal with mode coupling restricted to the singlets inside one multiplet of originally degenerated modes. The generalisation of this method by Woodhouse takes the coupling between multiplets into account. The perturbated wave field can be considered as the sum of the scattered waves for all modes of the unperturbated field. In the simplest case the field before scattering is assumed to be unperturbated. In more advanced methods the multiple scattering is taken into account. In this work we consider a generic perturbation of the radial symmetric earth model and develop a method to calculate the scattering of seismic waves for epicentric distances less than 45 grad. This represents a generalization of Friederichs method originally restricted to isotropic lateral heterogenities. Based on summation of scattered waves associated with different mode branches, it is effective enough to be used for frequecies up to 200 mHz and therefore sensitive for model details on the scale of 10 km. The generalized method introduced here preserves these advantages but is suitable for a wider class of aspherical asymmetries including anisotropy, earth rotation, asphericity of boundary surfaces and deviatoric initial stress perturbations. To illustrate the theory we apply it to anisotropic perturbations and calculate the coupling of spheroidal and toroidal modes. In particular we consider pseudo-Love and pseudo-Rayleigh waves in a transversely isotropic earth and discuss their dependency on model parameters. In Appnedix we calculate a complete catalog of sensitivity kernels for each component of the elastic tensor in both spherical and canonical coordinates.