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An introduction to anisotropy.

What is anisotropy:

Anisotropy means that seismic velocities vary with the direction of propagation. To consider the Earth isotropic is a too restrictive view to model the propagation of seismic waves in the real Earth. Hidden effects of anisotropy are important when fine details of the Earth's structure are investigated.

Anisotropy can be also understood as a different reaction to stresses in different directions: let's take the example of a sheet structure with horizontal layers - a milfoils-like structure. The rigidity of the system is different when stresses are applied laterally or vertically. Stresses that are applied vertically mostly affect less rigid layers, whereas stresses applied at the ends of the layers, horizontally, compress all the layers. It is obvious that a granite is isotropic, but that schists are anisotropic, due to their sheet structure. When shear stresses are applied, the structure is then completely modified as you can see in the figures below: the type of deformation is different with the direction of the shear (compare the horizontal shear with the vertical one).

Fig. 1: hard materials are less sheared than soft ones.

Fig. 2: all materials are here deformed similarly.

Anisotropy exists at least at three scales:

Anisotropy and seismic waves:

In anisotropic media, the phase velocity varies with azimuth. In the Earth, the variation for P- and S-waves is of a few per cent.

When a S-wave passes through an anisotropic zone, the wave is split in two projected waves (S1 and S2), their vectorial sum equals the original wave. The S1 and S2 waves propagate at slightly different velocities, they get a time shift which is such as when the wave exits this zone, the split remains, as you can see below.

Fig. 3: seismic wave splitted by passing an anisotropic zone (redrawn after Crampin, 1985).

Direct evidence of anisotropy is difficult to observe, and many seismologists were first reluctant to this idea, which, in addiction, lead to computational problems as the number of unknowns increase when you consider anisotropy. What is more, observing the angular dependence of the seismic velocities is difficult because of local heterogeneities in any media.

Seismic anisotropy can be defined as anisotropic properties which show up on the scale of a seismic wavelength.

Anisotropy and surface waves: Love-Rayleigh incompatibility or discrepancy

The upper mantle anisotropy can be observed on surface wave dispersion curves. It has been demonstrated that Love waves for example had a too high velocity to fit a unique isotropic model. There are several observations of Love- and Rayleigh-wave dispersion curves which cannot be accounted for by simple isotropic models presenting smooth depth variations of velocity ; such observations are often referred to as Love-Rayleigh discrepancies.

The locations and the possible sources of anisotropy may be multiple.

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