Use of the Wigner-Ville distribution to separate seismic events and to analyse reflected vibroseis signals in the time-frequency plane

Abstract

As a seismic signal travels from its source through the earth to a measuring device, its character is alte-red due to earth absorption and frequency dispersion. The selection of an appropriate time-frequency distribution along with a practical implementatIon enables earth absorption parameters and frequency dispersion to be determined with all information from the recorded signal being preserved. The methods outlined in this paper apply only to seismic surveys where a chirp signal is emitted as a source, thus allowing information to be spread across the time-frequency plane. Such surveys are referred to as Vibroseis surveys. To achieve a practical geophysical interpretation from a time-frequency (t-f) analysis of a reflected Vibroseis signal, event separation must be achieved. The Wigner-Ville Distribution (WVD) has been shown to concentrate signal energy along the instantaneous frequency law of the emitted Vibroseis SOl.lrCe signal [5]. Thus the WVD provides the basis of achieving event separation in the t-f plane. Bouachache, (1982) [4J, [5J was successful in using the WVD to determine earth absorption parameters from a single component down going Vibroseis signal from a Vertical Seismic Profile (VSP). In principle, this method can be extended to the multicomponent case, but only if, a successful t-f plane event separation can be achieved. This paper outlines the basic seismic problem to be solved along with the a time-frequency interpretation. Several possible so1\ltions are reviewed. The WVD is shown not to be the best solution. The overheads of parametric modelling are discussed, with the presentation of test results. The use of the Cross WVD (XWVD) is finally presented as the most promising solution.