Birch's law

Birch's law is an empirical relation in which seismic-wave velocity in a solid varies approximately linearly with density at fixed pressure and composition. It helps connect laboratory measurements of minerals to seismic observations of Earth's interior.

Seismic velocity: The speed at which seismic waves travel through a material. Birch's law describes how this speed changes with density.
Seismology: The study of earthquakes and the propagation of seismic waves through Earth. Birch's law provides a bridge between measured wave speeds and material properties.
Francis Birch: An American geophysicist who helped establish experimental mineral physics and studied Earth's interior. Birch formulated the empirical relation that bears his name.
Birch–Murnaghan equation of state: A finite-strain equation relating pressure and volume in compressed solids. Unlike Birch's law, it models pressure–volume behavior rather than velocity–density trends.
Temperature dependence of seismic velocity: The change in seismic-wave speed caused by changing temperature. Temperature variations can shift velocity at a given density and complicate Birch-law inference.
Density: Mass per unit volume of a material. Density is the quantity paired with seismic velocity in the empirical relation.
Earth's mantle: The thick silicate-rock layer between Earth's crust and core. Mantle density and seismic speeds are compared using Birch-like relations.
Birch's 1952 paper: Francis Birch's paper relating elastic properties and composition to Earth's interior. This work presented the relation linking seismic velocity and density.
Debye model: A model of a solid's vibrational modes used to estimate thermodynamic properties. It predicts material behavior from lattice vibrations rather than an empirical seismic relation.
Seismic velocity–density trade-off: The difficulty of separating density and velocity effects in observations of Earth's interior. Birch's law helps constrain this trade-off but does not uniquely determine composition.

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Core–mantle boundaryRelated: It helped scientists interpret the density and composition contrasts across the interface.