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Abstract

To be able to simulate P-wave propagation in a heterogeneous spherical earth, we solve the acoustic wave equation in spherical coordinates numerically for axisymmetric media. We employ a high-order finite difference scheme that allows us to simulate arbitrary heterogeneous structures with wavelengths as small as 10 km. A standard regular gridding in spherical coordinates leads to a continuously decreasing effective grid increment towards the earth´s centre. To avoid the resulting stability problems, we regrid the lateral domain several times, thereby drastically improving the stability criterion for whole earth models. Treatment of the earth´s centre in a Cartesian system allows us to model wave propagation through the centre of the earth. We present the algorithm in the acoustic approximation and show its applicability to simulate whole-earth P-wave propagation. In the present implementation, wavefields with a dominant period of about 10 s can be simulated. As an application, we investigate, in a parameter study, the influence of scatterers in the earth´s lower mantle on core phases (PKP). Scatterers with various velocity contrasts (up to +_ 30 per cent) have been placed at different locations in the lower mantle to study their effects on the PKP wavefield. The location and the velocity contrast of a scatterer affect the amplitude, the slowness of the scattered phase and its traveltime. In addition to individual scatterers, we also study models with two and more scatterers with different orientations. It is shown that - for the frequency range considered - the difference between a scatterer at the CMB and a scatterer 500 km above the CMB is small. In addition, a global ultra-high-velocity layer and an ultra-low-velocity layer have been placed at the bottom of the mantle, but it turns out that they are not able to produce arrivals in the time window where precursors are usually expected. We demonstrate the advantages of vespagram analysis to distinguish between different scatterer mechanisms, locations of scatterers and diffracted waves from the caustic at 144°.