We consider the question of deblending for seismic shot records generated from simultaneous random sources at different locations, i.e., how to decompose them into isolated records involving one source at a time. As an example, seismic-while-drilling experiments use active drill-string sources and receivers to look around and ahead of the borehole, but these receivers also record noise from the operation of the drill bit. A conventional method for deblending is independent component analysis (ICA), which assumes a “cocktail-party” mixing model where each receiver records a linear combination of source signals assumed to be statistically independent, and where only one source can have a Gaussian distribution. In this note, we extend the applicability of ICA to seismic shot records with markedly more complex mixing models with unknown wave kinematics, provided the following assumptions are met. 1. The active source is fully controllable, which means that it can be used to input a wide range of non-Gaussian random signals into the subsurface. 2. The waves are a linear function of the source, have a finite speed of propagation, and follow finite-length paths. The last assumption implies a scale separation, in frequency, between the mixing matrix elements (Green’s functions) and the random input signals. In this regime, we show that the key to the success of ICA is careful windowing to frequency bands over which the Green’s functions are approximately constant.