Until now, we have considered the Earth to be isotropic, even though minerals are anisotropic at the scale of a single crystal. For a planet to behave like an anisotropic solid these crystals must ‘line up’ and be oriented in the same direction over length scales comparable to that of the Fresnel zone of a seismic wave, i.e. over tens or hundreds of kilometres. Surprisingly, there is now ample evidence that such lattice-preferred orientation (LPO) occurs in nature and that the Earth is at least weakly anisotropic near the surface and in its inner core. Since the magnetic field influences the acoustic wave speed in the Sun's convection zone, and the magnetic field has a distinct direction, anisotropy must affect helioseismic observations as well. However, the strong magnetic field associated with sunspots couples acoustic and magneto-acoustic waves and still poses significant problems of interpretation. Away from such anomalies, the averaging of Doppler measurements over annuli (see Chapter 6) destroys any azimuthal anisotropy, however, and magnetic anisotropy plays no role in the interpretation of solar travel times.

The first indication that anisotropy measurably affects terrestrial seismic waves came in 1964, when Hess discovered that the horizontally travelling Pn-waves in the oceans travel with a velocity that depends on direction, indicating that the fast direction of olivine crystals is aligned in the direction of spreading.