Velocity sensitivity of seismic body waves to the anisotropic parameters of a TTI-medium
We formulate the derivatives of the phase and group velocities for each of the anisotropic parameters in a tilted transversely isotropic medium (TTI-medium). This is a common geological model in seismic exploration and has five elastic moduli or related Thomsen parameters and two orientation angles defining the axis of symmetry of the rock. We present two independent methods to compute the derivatives and examine the formulae with real anisotropic rocks. The formulations and numerical computations do not encounter any singularity problem when applied to the two quasi shear waves, which is a problem with other approaches. The two methods yield the same results, which show in a quantitative way the sensitivity behaviour of the phase and the group velocities to all of the elastic moduli or Thomsen's anisotropic parameters as well as the orientation angles in the 2D and 3D cases...
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