Spatial resolution in anisotropic media

Abstract

Fresnel-zone considerations are the essence of horizontal resolution on seismic sections. The first Fresnel-zone is described as the subsurface area over which reflected energy adds constructively to cause a seismic reflection event. Contributions from higher order Fresnel-zones are assumed to cancel each other out. Therefore only the first Fresnel-zone defines the actual reflector response. The size or extent of this zone determines the lateral resolving power of the seismic method. This establishes the spatial resolution with which important lithological changes along with seismic profile direction may be observed. Seismic wave velocity is a function of direction in an elastically anisotropic medium and hence the wavefront shape is non-spherical. It can assume an elliptical or non-elliptical shape. The Fresnel-zone dimensions for P and SH waves are calculated using numerical modelling techniques. Results obtained at varying reflector dips using transversely anisotropic velocity functions are compared with the corresponding values for the isotropic case. This comparison is carried out for both P and SH waves. The size of the Fresnel-zone is found to be predominantly dependent on the shapes or curvatures and wavelength of the wavefront as well as the elastic constants d* and ?. The dip or attitude of the reflector is also found to have a remarkable influence on the dimensions of the Fresnzel-zone. Results from numerical studies show considerable variations between the Fresnel-zones for anisotropic and isotropic velocity functions at various reflector dips. Consequently the spatial resolution in an anisotropic medium would be significantly different from that determined for the same medium if it is assumed to be isotropic. This observation indicates that the lateral resolution of reflection events from the base of thick shale sequences is most likely to be affected.