Acoustic simulation of P-wave propagation in a heterogeneous spherical earth: numerical method and application to precursor waves to PKPdf

To be able to simulate P-wave propagation in a heterogeneous spherical eart h, we solve the acoustic wave equation in spherical coordinates numerically for axisymmetric media. We employ a high-order finite difference scheme th at allows us to simulate arbitrary heterogeneous structures with wavelength s as small as 10 km. A standard regular gridding in spherical coordinates l eads to a continuously decreasing effective grid increment towards the eart h's centre. To avoid the resulting stability problems, we regrid the latera l domain several times, thereby drastically improving the stability criteri on for whole earth models. Treatment of the earth's centre in a Cartesian s ystem allows us to model wave propagation through the centre of the earth. We present the algorithm in the acoustic approximation and show its applica bility to simulate whole-earth P-wave propagation. In the present implement ation, wavefields with a dominant period of about 10 s can be simulated. As an application, we investigate, in a parameter study, the influence of sca tterers in the earth's lower mantle on core phases (PKP). Scatterers with v arious velocity contrasts (up to +/- 30 per cent) have been placed at diffe rent locations in the lower mantle to study their effects on the PKP wavefi eld. The location and the velocity contrast of a scatterer affect the ampli tude, the slowness of the scattered phase and its traveltime. In addition t o individual scatterers, we also study models with two and more scatterers with different orientations. It is shown that-for the frequency range consi dered-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 win dow 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 degree s.