Spectral Matrix Filtering Applied to Vsp Processing

Abstract

The spectral matrix computed from VSP-traces transfer functions contains information about each wave making up the VSP data set. Using a filter based on the eigenvectors of the spectral matrix leads to a decomposition of input traces in eigensections. The eigensections associated with the largest eigenvalues contain the contribution of the correlated seismic events. Signal space is denoted as the sum of these eigensections. Other eigensections represent noise. When the different waves making up the VSP have very different amplitudes, decomposition of input traces into eigensections leads to wave separation without any required knowledge about the apparent velocities of the waves. Limitations of wave separation by the multichannel filtering are a function of the scalar product values of the waves (in frequency domain) and of the relative wave amplitudes. The spectral matrix filtering can always be used to enhance signal-to-noise ratio on VSP data. The eigenvalues of the spectral matrix can be used to estimate the signal-to-noise ratio as a function of frequency. It is possible to qualify the behavior of a VSP tool in a well and to detect some resonant frequencies probably generated by poor coupling. Field data examples are shown. The first example shows data recorded in a vertical well whose converted shear waves are separated from upgoing and downgoing compressional waves using a spectral matrix filter. This field case shows the efficiency of the spectral matrix filter in extracting weak events. The second example shows data recorded in a highly deviated well, where very close apparent velocity events are successfully separated by use of spectral matrix filtering.