RAYLEIGH WAVE REJECTION BY OPTIMUM FILTERING OF VERTICAL ARRAYS
TELEDYNE INDUSTRIES INC ALEXANDRIA VA EARTH SCIENCES DIV
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Optimum array processes such as the maximum likelihood filters are usually derived from the cross correlation matrix of the time series oupputs of the array. With a vertical array, however, the correlations of both the incoming P-wave signals and Rayleigh wave noise are predictable from the structure. This paper presents the theory of maximum likelihood filters in vertical arrays which can provide undistorted estimates of the signal or the various Rayleigh modes with the other modes canceled out. The performance of these optimum processes will be dependent upon the validity of the underlying assumptions such as horizontal bedding, known instrument calibration, and knowledge of both P and S velocities with depth. Examples are shown of the performance of the optimum filters using synthesized data where the underlying assumptions are satisfied. Then these same optimum filters are applied to data from the UBO vertical array.