The principal assertion of Schoenberger's discussion appears to be that (3), which is correctly derived from equations in Section IV and corresponds to a space shift, should instead be written as (4), corresponding to a space sample. However, the space-convolution operator corresponding to a seismometer is indeed meant to be a space-shift operator. An array of seismometers is used as a weighted sum of space-shift operators, just as a time-domain, sample-point operator is made up of a weighted sum of time-shift operators. Equation (5.2), which Schoenberger indicates as being related to his (4), actually comes from (3) with x and y set to zero.

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