local activity (such as trucks or construction). Earthquake early warning systems can be automated to allow for immediate safety actions, such as issuing alerts, stopping elevators at the nearest floors, and switching off utilities. Propagation Velocity In isotropic and homogeneous solids, a P wave travels in a straight line longitudinally; thus, the particles in the solid vibrate along the axis of propagation (the direction of motion) of the wave energy. The velocity of P waves in that kind of medium is given by where is the bulk modulus (the modulus of incompressibility), is the shear modulus (modulus of rigidity, sometimes denoted as and also called the second Lamé parameter), is the density of the material through which the wave propagates, and is the first Lamé parameter. In typical situations in the interior of the Earth, the density usually varies much less than or , so the velocity is mostly "controlled" by these two parameters. The elastic moduli P-wave modulus, , is defined so that and thereby Typical values for P wave velocity in earthquakes are in the range 5 to 8 km/s. The precise speed varies according to the region of the Earth's interior, from less than 6 km/s in the Earth's crust to 13.5 km/s in the lower mantle, and 11 km/s through the inner core. Geologist Francis Birch discovered a relationship between the velocity of P waves and the density of the material the waves are traveling in: which later became known as Birch's law. (The symbol is an empirically tabulated function, and is a constant.) See also Earthquake warning system Lamb waves Love wave S wave Surface wave References External links Animation of a P wave P-wave velocity calculator Purdue's catalog of animated illustrations of seismic waves Animations illustrating simple wave propagation concepts by Jeffrey S. Barker Bayesian Networks for Earthquake Magnitude Classification in a Early Warning System Waves Fluid dynamics Seismology measurement Seismology da:P-bølger