Seismic P-wave diffraction modeling to determine anisotropy parameters in VTI medium

Anisotropic properties of medium will give a velocity variation of different direction. Generally, anisotropic properties of VTI medium (weak anisotropy) are studied through reflected P-wave function but now we introduce an approach using a diffraction function instead of reflection function. The equations which related a phase and group velocity will be used in this study, these equations use the asumption that the difference between tangent of phase and group velocity angles of the P-wave were approximately zero, and the validity of this assumption should be tested before numerical and physical modeling. As a result, a polynomial equation has been derived for a weak anisotropic medium which relates travel time of a transverse P-wave from diffraction source point to receiver in surface to anisotropy parameter, where | and | < 1. A mathematical test of the polynomial of diffraction equation has been done for different models. The result of physical modeling shows there are inaccuracies caused by an offset between the original sources to the projected diffraction point on the surface. Thus, it is necessary a correction prior applying the equation to real data. The application of anisotropy parameters in pre-stack depth migration processing give a better results in the case of dipping layers compared to the reflection method.