Determination of Fresnel zones from traveltime measurements

Abstract

Abstract For a horizontally stratified (isotropic) earth, the rms-velocity of a primary reflection is a key parameter for common-midpoint (CMP) stacking, interval-velocity computation (by the Dix formula) and true-amplitude processing (geometrical-spreading compensation). As shown here, it is also a very desirable parameter to determine the Fresnel zone on the reflector from which the primary zero-offset reflection results. Hence, the rms-velocity can contribute to evaluating the resolution of the primary reflection. The situation that applies to a horizontally stratified earth model can be generalized to three-dimensional (3-D) layered laterally inhomogeneous media. The theory by which Fresnel zones for zero-offset primary reflections can then be determined purely from a traveltime analysis--without knowing the overburden above the considered reflector--is presented. The concept of a projected Fresnel zone is introduced and a simple method of its construction for zero-offset primary reflections is described. The projected Fresnel zone provides the image on the earth's surface (or on the traveltime surface of primary zero-offset reflections) of that part of the subsurface reflector (i.e., the actual Fresnel zone) that influences the considered reflection. This image is often required for a seismic stratigraphic analysis. Our main aim is therefore to show the seismic interpreter how easy it is to find the projected Fresnel zone of a zero-offset reflection using nothing more than a standard 3-D CMP traveltime analysis.