Multi-aperture ultrasound and photoacoustic imaging systems improve the imaging quality in terms of contrast, field of view, and potentially resolution in comparison to single aperture setups. However, the behavior of signal-to-noise ratio (SNR) in these systems has not been well understood. In this study, we propose a low-parameter predictive model for signal analysis based on the Fourier diffraction theorem. Furthermore, an analytical approach for SNR estimation is devised for both coherent and incoherent compounding methods. The theory is evaluated in simulations and experiments. The results show a great agreement with the theoretical expectation of k-space model for both mono-static and bi-static signals. In addition, the evaluated noise power and peak SNR results follow the analytical expectations. As the number of compounded reconstructed datasets increases, the noise power increases linearly and non-linearly for coherent and incoherent methods, respectively. Still, as demonstrated in both theory and results, for correlated sources, the SNR increases linearly with the number of coherently compounded reconstructions, while it can remain unchanged or even reduced if incoherent compounding is employed. Moreover, for uncorrelated sources, it is shown that compounding different views from several spatially diverse apertures may lead to a decrease in SNR.