On the lateral resolution achieved by Kirchhoff migration

Abstract

I show that the implementation of the Kirchhoff summation migration technique is equivalent to the generation of a synthetic focused array. The focused array theory, which is well developed in underwater acoustics, is used to deal with the factors limiting lateral resolution achieved when carrying out point diffractor imaging by Kirchhoff summation. Lateral resolution of a focused array, defined as the horizontal distance between two identical point diffractors which are just resolvable, is obtained from the width of the array response at the 0.35 amplitude points. The focused array theory approach should help in obtaining more insights into the practical aspects of Kirchhoff summation imaging technique, namely, choice of aperture and spatial sampling interval and the influence of velocity errors and seismic frequency. Examples given show how the lateral resolution can be improved by either increasing the array aperture or by using higher seismic frequency. I use the concept of the depth of focus to demonstrate the deterioration in the lateral resolution caused by migration velocity errors. Finally, I illustrate how imaging noise is generated when using a large spatial sampling interval.