Freznel zone in VTI and orthorhombic media

Abstract

The reflecting zone in the subsurface insonified by the first quarter of a wavelength and the portion of the reflecting surface involved in these reflections is called the Fresnel zone or first Fresnel zone. The horizontal resolution is controlled by acquisition factors and the size of the Fresnel zone. We derive an analytic expression for the radius of the Fresnel zone in time domain in transversely isotropic medium with a vertical symmetry axis (VTI) using the perturbation method from the parametric offset-traveltime equation. The acoustic assumption is used for simplification. The Shanks transform is applied to stabilize the convergence of approximation and to improve the accuracy. The similar strategy is applied for the azimuth-dependent radius of the Fresnel zone in orthorhombic (ORT) model for a horizontal layer. Different with the VTI case, the Fresnel zone in ORT model has a quasi-elliptic shape. We show that the size of the Fresnel zone is proportional to the corresponding traveltime, depth and the frequency. From the numerical examples, we can see that the Shanks transform approximations for Fresnel zone are very accurate for both VTI and ORT media.