Abstract

The problem of emphasizing signals on multiple trace seismograms is approached by considering a relationship between the input and output records. It is proposed that the transformation to output record be one which causes the output traces to be most "similar" or "in phase" according to a certain definition of this property. If the noise and signal are "properly behaved," it may be demonstrated that a linear transformation chosen by this criterion must have a response emphasizing frequency ranges of high input signal-to-noise ratio. The determination of such a transformation from the input data alone is carried out for discrete linear operators. The numerical work involved in computing such operators is formidable. As an example the computations were carried out for a mixture of an artificial signal introduced into a noise record. The results are about as good as those obtained with conventional filtering techniques depending on prior knowledge of input signal-to-noise ratios.

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