Lawrence Berkeley National Laboratory

I explore a different type of approximation to the exact anisotropic wave velocities as a function of incidence angle in vertically transversely isotropic (VTI) media. This method extends the Thomsen weak anisotropy approach to stronger anisotropy without significantly affecting the simplicity of the formulas. One important improvement is that the peak of the quasi-SV-wave speed vsv(theta) is located at the correct incidence angle theta= theta max, rather than always being at the position theta = 45o, which universally holds for Thomsen's approximation although max theta = 45o is actually never correct for any VTI anisotropic medium. The magnitudes of all the wave speeds are also more closely approximated for all values of the incidence angle. Furthermore, the value of theta max (which is needed in the new formulas) can be deduced from the same data that are typically used in the weak anisotropy data analysis. The two examples presented are based on systems having vertical fractures. The first set of model fractures has their axes of symmetry randomly oriented in the horizontal plane. Such a system is then isotropic in the horizontal plane and, therefore, exhibits vertical transverse isotropic (VTI) symmetry. The second set of fractures also has axes of symmetry in the horizontal plane, but it is assumed these axes are aligned so that the system exhibits horizontal transverse isotropic (HTI) symmetry. Both types of systems are easily treated with the new wave speed formulation.