Abstract

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  
f=k2δt,k=0,1,2,...,
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:  
δf0f12δtδf1,
where the cutoff frequencies δf0 and δf1 are chosen to reflect the useful frequency band of the signal.
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