## 2 Method
### Definition of the Spectra of Geophysical Phenomena and the Error Curves of MOCAST+ and GRACE  
Having calculated the space-time variations of the gravity signals of our geophysical database, we then proceed to the calculation of the localized spectra. Depending on the spatial extent of the phenomenon, the radius of the spherical cap was chosen accordingly to entirely contain the gravity signal. The detectability is then defined by requesting the signal spectrum or at least part of it to be larger than the mission error spectral curves. We consider the error degree variances of GRACE [7; 29] (GRACE Sci. team meeting), which is defined as the average of 150 monthly error curves for the interval 2002-2017. For MOCAST+, different configurations have been calculated, including Bender configurations with couples or triplets of satellites [10], and with payload of a gradiometer (Tzz or Tyy components; x,y,z Cartesian right-handed system centered on the satellite; x along orbit, z towards center of earth, and y orthogonal to orbit plane) and a supplemental clock, assuming \"nominal\" and \"improved\" scenarios for the clock's performance [3]. In particular, the \"nominal\" and \"improved\" clocks differ in terms of sampling frequency, which in the \"improved\" clock's case rises to 1 Hz from the 0.1 Hz of the nominal frequency. For both the clocks, the sensitivity is at the level of 0.2 m\({}^{2}\)/s\({}^{2}\)/\(\sqrt{\rm Hz}\) for a broad frequency band. The clocks are used to measure the potential difference between the satellites and this is performed by employing three clocks in combination with an optical link [3]. This strategy has been demonstrated to better mitigate both the noises arising from baseline fluctuations as well as the phase noise of the local oscillator. Apart from this, no other laser or optical links are required. The gradiometers have similar performance to those already simulated in the frame of the MOCASS study, with a sensitivity better than 10 mE /\(\sqrt{\rm Hz}\) in the frequency range of \(10^{-6}\)-\(10^{-2}\) Hz. In the testing phase, different distances between couples or triplets of satellites were also considered (100 km or 1000 km). A further factor affecting the instrumental noise is the attitude control error, which affects the Tzz component, while the out of orbit plane component (Tyy) is insensitive to rotations around the \(y\)-axis, where the largest control error occurs. The attitude control in the simulations, with respect to the optimal noise scenario for the gradiometers, is set at the 0.1 nrad/s level, which is below that of the present gyroscope technology. For this reason, the error curve for the Tyy recovery was included, which due to its lower criticality to attitude control enables the full exploitation of the instrumental noise level. The following table, Table 2, summarizes the different configurations simulated, while the corresponding error curves are shown in Figure 8.  
As is evident, the best configuration, which corresponds to the lowest error curve in Figure 8, is obtained with 2 triplets carrying improved clocks, the gradiometer, and an inter-satellite distance (D in Table 2) of 1000 km. For a more complete discussion of the mission scenarios and simulations we refer to [2; 3].