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

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

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Title: Use of the Wigner-Ville distribution to separate seismic events and to analyse reflected vibroseis signals in the time-frequency plane
Author: Boles, P; Boashash, B
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.
Description: The results presented in this paper demonstrate that an appropriate time-frequency analysis of a Linear FM vibroseis signal can be performed by use of the Cross Wigner-Ville Distribution. It provides the desired matched filter approach to the seismic problem and appears to provide the required event separation in the time-frequency plane. It is a simple matter to modify existing interpretation techniques for use with the Cross Wigner-Ville Distribution. (Additional details can be found in the comprehensive book on Time-Frequency Signal Analysis and Processing (see http://www.elsevier.com/locate/isbn/0080443354). In addition, the most recent upgrade of the original software package that calculates Time-Frequency Distributions and Instantaneous Frequency estimators can be downloaded from the web site: www.time-frequency.net. This was the first software developed in the field, and it was first released publicly in 1987 at the 1st ISSPA conference held in Brisbane, Australia, and then continuously updated).
URI: http://hdl.handle.net/10576/10819
Date: 1987-08

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