Seeman and Horowicz devised an elegant procedure for the separation of upgoing and downgoing waves in VSP data. Their method is based upon a least-squares solution of the frequency-domain equations which relate the upgoing and downgoing signals at a reference level to the observed signals at other levels in the Earth. The coefficients of these equations are time-shift operations. Unfortunately, for frequencies
where δt is the vertical time sampling interval, the denominator of the solution equations is zero. For this reason the authors only applied the method over a passband:
where the cutoff frequencies δf0 and δf1 are chosen to reflect the useful frequency band of the signal.
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