In passive seismic interferometry, new reflection data can be retrieved by crosscorrelating recorded noise data. The quality of the retrieved reflection data is, among others, dependent on the duration and number of passive sources present during the recording time, the source distribution, and the source strength. To investigate these relations we set up several numerical modeling studies. To carry out the modeling in a feasible time, we design a finite-difference algorithm for the simulation of long-duration passive seismic measurements of band-limited noise signatures in the subsurface. Novel features of the algorithm include the modeling of thousands of randomly placed sources during one modeling run. The modeling experiments explore the dependency relation between the retrieved reflections and source-signature length, source positions, number of sources, and source amplitude variations. From these experiments we observed that the positions of the passive sources and the length of the source signals are of direct influence on the quality of the retrieved reflections. Random amplitude variations among source signals do not seem to have a big impact on the retrieved reflections.