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Earthquakes generate seismic waves of compressional and shear modes (P and S waves, respectively). Much of the knowledge about the internal structure of the Earth comes from earthquake observations, as seismic waves propagate throughout the globe. Many seismic stations on the surface of the Earth together yield a large amount of seismic data, which enable observers to determine accurate locations of earthquake hypocenters and accurate travel time of seismic waves. Seismologists thus determine velocities of seismic waves propagating through the Earth. Generally, waves travel faster through cold material than they do through hot. Temperature heterogeneity exists in the Earth because cold lithosphere (plate) subducts at the trench and high-temperature lava erupts at volcanoes. Therefore, high- or low-seismic velocity regions are present within the Earth, and differences from the average velocity (called velocity perturbations) are determined from seismic studies. An image of velocity perturbations of the inner Earth is called seismic tomography. Analogous to X-rays in medical tomography (CT: computerized tomography), seismic rays are used to probe the Earth in seismic tomography. Differences in velocity allow scientists to calculate the size, density, and elastic properties of the Earth's interior and use that information to make predictions about the shape, materials, and thermal conditions of the Earth. The knowledge of the internal structure is essential to understand geologic processes like plate tectonics and continental drift.

Recently, major advances in the study of seismic tomography have been made with the advent of computer software and hardware. One of them is the development of three-dimensional (3D) seismic tomography, which unveils many important aspects of the Earth. In general, however, many 3D tomographic results have been shown in two-dimensional (2D) sections. 3D presentations are only rarely made. In 2D sections, it is not easy to investigate, for example, the spatial correlation between low- (or high-) velocity regions and important geophysical processes (for example, earthquake hypocenter, volcano location, and plate movement). Such correlation, however, is clearly seen and studied in detail in a 3D view.

In this paper, we present a simple, practical, and effective way to show a 3D view and animation of the Earth's structure by using Mathematica. We select the region of northeastern (NE) Japan where interesting features typical to a volcanic area are observed. They are the presence of mid-crustal S wave reflectors and the occurrence of low-frequency microearthquakes [1, 2]. The reflectors are thin magma bodies located at about 8 to 15 km beneath the surface. Due to the acoustic impedance difference between magma and surrounding crustal rocks like granite, S waves are distinctly reflected on the magma-rock interface. Microearthquakes of magnitude less than 2.5 are frequently observed in and around the low-velocity zones, and have relatively low-characteristic frequencies (around 2 Hz), compared with the ordinary seismic frequency band (up to ~20 Hz). These observations indicate the close relationship between magnetism, slow-velocity anomalies, low-frequency microearthquakes and S wave reflectors [2, 3]. Here, the low-velocity zones are shown in three dimensions, and are discussed in relation to the occurrence of low-frequency microearthquakes and the presence of mid-crustal S wave reflectors. The 3D views suggest magma ascent pathways in the Japan island arc.

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