A spectacular example of wave propagation occurs during an earthquake. The initial formidable release of energy at the epicentre propagates through the Earth’s layers as seismic waves. In a three‐dimensional body, vibrations can travel in different ways, each with a different velocity. The so‐called P‐waves or primary waves are pressure waves. Like sound waves, the displacement of the medium is in the same direction as the wave itself. These are the fastest seismic waves, travelling through water and rocks at velocities of up to several kilometres per second.

The S‐waves or secondary waves are transverse. The displacement is in a direction perpendicular to the motion. For instance, a wave on a string moves along the string in the horizontal direction but the displacement takes place in the vertical direction. Typically, these waves are about 60 per cent slower than the P‐waves but they are very destructive because they induce shear (shear arises when forces acting on a body are unaligned, pushing one part of a body in one direction, and another part of the body in the opposite direction). These waves can be understood through the proper analysis of differential equations forming the basis of modern seismology. Their study is particularly useful for early warning systems, identifying the epicentre, and studying the composition of the Earth’s mantle

As seismic P‐waves travel through the Earth’s mantle, they are refracted at the interface between different materials. In the absence of an inner core, a simple tracing of rays predicts the existence of a shadow region where no waves are observed. The observation of P‐waves by Inge Lehmann in 1936 in that shadow region (dashed line) indicated the existence of a solid inner core with different material property (her predictions were eventually confirmed in the 1970s). Note that actual P‐waves are not straight, as drawn here, but bent due to the inhomogeneity of material properties within the Earth.