Up-Down Wavefields Reconstruction in Boreholes Using Single-Component Data

Abstract

A standard procedure in processing vertical seismic profile (VSP) data is the separation of up-and downgoing wavefields. We show that the up-down wavefields in boreholes can be reconstructed using only singlecomponent borehole data, given that a full set of surface reflection data is also available. No medium parameters are required. The method is wave-equation based for a general inhomogeneous lossless medium with moderately curved interfaces. It relies on a focusing wavefield from the Marchenko method, which gives the recipe for finding this wavefield that satisfies certain focusing conditions in a reference medium. The up-down wavefields are then reconstructed at borehole positions using this focusing wavefields and the surface reflection response. We show that the method is applicable to boreholes with any general orientation. The requirement is that the source positions in the surface data are regularized to be the same as those in the borehole data, and that source deconvolution and surface multiple removal are applied for the surface data. Numerical results from a field in the North Sea are shown, and three different borehole geometries (horizontal, deviated and vertical) are tested. The result shows that the reconstructed up-down wavefields agree well with those by conventional separation methods.