Introduction

One approach to producing a good subsurface image by a migration technique is to find an operator that resembles the continuous wave equation as close as possible. Even if the operator very closely resembles to the wave equation, the data obtained in a survey is discrete in form and is limited both in the apertures and in the sampling intervals. In order to overcome these problems, the extending common-midpoint gather (Claerbout, 1990) and trace interpolation techniques ( Claerbout, 1992a: Ji, 1992) have been applied.

Another approach to obtaining a good image without artifacts might be an optimization technique that finds the image that best fits the data for a given modeling operator. If the problem is datuming, the operator can be an extrapolation operator from one surface to another. This paper presents an approach to obtaining the optimized images and datumed wavefield for several extrapolation operators in the least-squares sense. It then introduces the application of an interpolation technique.