Helioseismic measurements are simulated using a new 3D acoustic algorithm (GALE – Global Acoustic Linearized Euler) that solves the conservation form of the linearized compressible Euler equations over background velocity flows. We explore the possibility of measuring helioseismic signatures of various profiles of meridional circulation against the effect of realization noise - modeled with a randomized frequency distribution of sources. We employ hydrodynamic and dynamo mean-field models in order to test the smallest parameter changes that result in the transition from one- to two-cell meridional circulation. The resulting helioseismic measurements provide a baseline for the minimal differences that can exist between the two regimes and show that a complete disambiguation of the regimes may not currently be possible. We also test meridional circulation profiles with more measurable differences, calculated using physics-based parameter changes in mean-field models.