Introduction

Many land data are recorded irregularly or in a pseudo-regular fashion in source and receiver coordinates. On the other hand, many data processing algorithms need regularly sampled data. A source equalization algorithm, which is based on reciprocity, requires that at each source location there is a geophone location. In reality this poses a problem: it is very common for an acquisition geometry to have interlaced source and receiver stations. Certain kinds of interpolation algorithms will handle that problem very efficiently. However, usually the geometry has additional twists to it, like unequal near offset distances. An algorithm which is to be applied to real data has to be able to handle such irregular spacings.

For my application, I chose to use slant stacks of shot gathers for two reasons. Source equalization operates under the assumption of varying source behaviour and quasi regular receiver properties. Under that assumption it is more convenient to reposition receivers. Slant stacks have the property that the data decomposition can be carried out in a least squares sense incorporating irregular geometry; Clement Kostov (1990) describes the linear properties of that operator in detail. The least squares approach greatly reduces artifacts introduced by data boundaries. It can be shown that the least-squares slant stack operator easily handles irregular spacing in x-t.