Fresnel zones and spatial resolution for P- and SH-waves in transversely isotropic media

Abstract

In an elastically anisotropic medium where the seismic wave velocity is a function of direction, the wavefront shape is nonspherical and, in most cases, assumes a nonelliptical shape. Numerical modelling techniques have been used to calculate the Fresnel‐zone diameter for compressional (P) and shear (SH) waves in transversely isotropic and isotropic media, respectively. The size of the Fresnel zone is found to be predominantly dependent on the curvatures and wavelength of the wavefront as well as the dip angle of the reflector. In addition, the anisotropic elastic parameters δ* (critical near‐vertical anisotropy), ε (the P-wave anisotropy), and γ (the SH-wave anisotropy) are found to significantly affect the size of the Fresnel zone. Numerical modeling results show considerable differences between the Fresnel zones for anisotropic and isotropic velocity functions at various reflector dips. In addition, the Fresnel‐zone dimensions for anisotropic media exhibit asymmetry and considerable change with dip. By way of contrast, those of the corresponding isotropic velocity field exhibit symmetry and negligible variation with dip. The spatial resolution of unmigrated seismic data in an anisotropic medium would consequently be significantly different from that determined for the same medium if it is assumed to be isotropic. Physical modeling results demonstrate that anisotropy can significantly affect the spatial resolving power of seismic waves. The degree of these effects depends on the wavefront curvature, which changes with dip and orientation of the symmetry axis. This observation indicates that the spatial imaging of unmigrated reflection events from the base of thick shale sediments will be affected by anisotropy.