The recently introduced method of ‘signal apparition’ offers a fundamentally different approach to separation of multiple interfering sources, by using a periodic sequence of source signatures along one source line. This leads to exact separation of signals in diamond-shaped regions of the frequency-wavenumber domain which are twice as large compared to those recovered by other methods. In this paper we investigate the method’s sensitivity to the appearance of white noise in the periodic sequence, and show that signal apparition is stable by using a probabilistic model. We also demonstrate the stability by numerical simulations on a finite-difference synthetic data set generated over a complex salt model.