Seismic acquisition systems are disclosed that allow contemporaneous seismic sources to be separated from a composite signal comprising two or more constituent seismic sources. In some embodiments, a representation of the composite signal may be developed that includes a noise contribution of undesired signals present in the composite signal. Additionally, an operator, referred to herein as an “annihilator”, may be developed such that it may be conditioned and inverted to minimize undesired noise contributions in the composite signal. This inversion may assist in recovering the constituent seismic sources from the composite signal. Furthermore, in some embodiments, the accuracy with which the constituent source measurements are approximated may be increased by implementing them as random sweeps having a conventional length.