is applied. The coefficients and order of the fit rational function are determined using non-linear least squares fitting [@Markwardt]. Constraints are imposed on $\hat{\alpha}_{MAG}(f)$ to ensure continuity such $\hat{\alpha}_{MAG}(f_0)=1$ and $\hat{\alpha}_{MAG}'(f_0) =0$, where $f_0$=2 Hz. Figure \[merging\_fit\] shows the $n=1, m=3$ (one zero, three pole) fit for $ \hat{\alpha}_{MAG}$.

Fitting $\alpha_{MAG}(f)$ with boundary conditions at $f_0$=2 Hz decreases available degrees of two freedom such that rational functions with three or more fit parameters are required for a reasonable approximation. Figure \[merging\_fit\] shows the best fit rational function (Equation \[eq:ratfit\]) with three poles and one zero (e.g. $m=3$ and $n=1$), to the MAG merging coefficient, $\alpha_{MAG}$ with applied boundary conditions at 2 Hz. Ensuring a piecewise continuous merging coefficient requires constraining the function at 2 Hz to unity gain and a local extremum. For $f< 2$ Hz, the coefficient $\alpha_{MAG}$ is explicitly set to unity, e.g. Figure \[merging\_alpha\], while for $f > 2$ Hz, $\alpha_{MAG}=\hat{\alpha}_{MAG}$. The SCM coefficients are determined from ${{\alpha}}_{SCM} =1-{\alpha}_{MAG}$. The optimal merging coefficients $\alpha_{MAG}$ and $\alpha_{SCM}$ are shown in Figure \[merging\_alpha\](a). The the weighted instrumental noise floors, and the optimal merged SCaM noise floors are shown in Figure \[merging\_alpha\](b).

![Nonlinear least square fit of three pole, one 