A simple seismic record synthesis for common-depth-point data was examined for analytic representation in terms of its harmonic spectrum. This frequency-domain investigation revealed that the primary-reflection signal can be completely recovered in the absence of random noise, or it can be better recovered in the presence of random noise than normal stacking affords, especially, if the coherent-noise-to-random-noise ratio is high. The success of this technique is founded upon the principle that difference equations in the time domain become algebraic equations in the frequency domain. The technique is partially 'probabilistic' because analytic solutions for the primary-reflection signal are stacked for further attenuation of noise.The constituents of the seismic records, after static and normal-moveout corrections, are: identical, coincident, primary-reflection signal; identical, time-shifted coherent noise; and random noise. The coherent-noise time shifts must be determined for application of the semideterministic technique; methods are discussed in the Data Processing section.