Application of singular value decomposition to vertical seismic profiling

Abstract An essential part of the interpretation of vertical seismic profiles (VSP) is the separation of the upgoing and downgoing waves. This paper presents a new approach which is based on the decomposition of time-shifted VSP sections into eigenimages, using singular value decomposition (SVD). The first few eigenimages of the time-shifted VSP section contain the contributions of the horizontally aligned downgoing waves. The last few eigenimages contain the contribution of uncorrelated noise components. The separated upgoing waves are recovered as a partial sum of the eigenimages.Important aspects of this approach are that regular sampling of the recording levels is not required, that the first-break times need not be measured with extreme accuracy, that noise rejection may be automatically included in the processing, and that eigenimages or sums of eigenimages which may be computed as part of the approach can provide important additional information.