Phase and group velocity of the fundamental mode surface waves are sensitive to the S-wave velocity at depths up to about 200-300 km. So, the measured dispersion curves can be inverted for the distribution of the shear waves velocity in the crust and upper mantle.
As a rule, the surface wave tomography has been based on the ray theory. The ray theory models adequately represents the wave propagation only when the scale of the heterogeneity is larger than the size of the Fresnel zones.
The inversion is divided into two steps. The first step is the surface-wave tomography in which the measured dispersion curves are inverted to produce 2-D maps of the lateral distribution of phase and group velocities for individual periods and wave-types. The result is the estimation for each geographical location four dispersion curves:
- The phase velocity of Rayleigh waves at periods between 40 and 150 s;
- The phase velocity of Love waves at periods between 40 and 150 s;
- The group velocities of Rayleigh waves between 16 s and 200 s period;
- The group velocities of Love waves between 16 s and 200 s period.
In the second step, at each geographical location, these four dispersion curves are inverted to obtain a local radially anisotropic 1-D shear-velocity model using, for example, a Monte-Carlo method.