Mathematica as a powerful and practical tool for displaying animated three-dimensional structures of the Earth's interior

Seismic tomographic studies have determined three-dimensional (3-D) velocity structures, in detail, of the crust and the upper mantle of the Earth. Yet, simple two-dimensional (2-D) sections have generally been used to present 3-D tomographic results. Here we show 3-D views and animations of the Earth's structure that are made as easy as 2-D sections, by using Mathematica. As an example, low-velocity zones in the upper mantle are shown in three dimensions, together with major volcanoes, mid-crustal reflectors, earthquake hypocenters, the Moho discontinuity and the upper plane of the subducted slab, that are observed in northeastern Japan. Low velocities in volcanic areas generally correspond to high temperatures, and indicate possible presence of magma. The 3-D animations enable us to investigate the spatial relation between low-velocity zones, volcanoes, reflectors, earthquakes and the slab, and thus enable us to study magma ascent pathways in detail.