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Much of our understanding of the basic structure and composition of Earth and the other planets in our solar system is not strenuously debated. We can infer a surprising amount of information from the size, mass and moment of inertia of the planets, all of which can be determined from routine astronomical observations. Measurements of surface chemical composition, either by direct sampling (as has been done on Earth, the moon, and Mars) or through spectroscopic observations, can be used to estimate elemental abundances and the degree of chemical differentiation that occurred as the planets condensed from the solar nebula. Remote observations of the gravitational field can be used to understand how a planet's mass is distributed, whereas the strength and shape of the magnetic field provides some constraint on the structure of a metallic core. The specifics of structure and composition, however, are much more debatable. And it is these details that tell us a much more extensive and ultimately more interesting story about the internal dynamics of the planets and their evolution. As a result, trying to determine them is frontier research in almost all fields of earth and planetary science.
Even on Earth, many of these details have to be inferred from remote observations. Because we cannot sample the deep Earth, we must deduce its composition either by looking at the clues hidden in igneous and metamorphic rocks, or by examining proxies for composition and structure such as the three-dimensional variation of the velocity of seismic waves produced by earthquakes and sampled by networks of seismometers on the surface. The late Francis Birch, the eminent Harvard geophysicist, and his colleagues and students worked out the basic methodology that brings these distinct observations together. Birch showed how the stiffness of rocks changes under the extreme conditions of pressure and temperature deep within planets, as well as with chemical composition. Because the speed of seismic waves depends on the stiffness of the medium through which they propagate, it is possible to calculate temperature and composition from maps of seismic velocity. Most current research is based on Birch's work and it has even been extended to the most extreme temperature and pressure conditions of Earth's core. For example, much of our understanding of the large- and small-scale convection patterns driving plate tectonics has come about by using Birch-type proxies for temperature and composition.
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