Text S2. Source depth from the gravity amplitude ratio

Underground mass changes driven by volcanic process may result in gravity changes observable at different sites on the ground surface. Under the assumption of a point mass source, the amplitude ratio between the gravity signals from two different sites can be used to set constraints on the source location. In particular, the value of the amplitude ratio (y ) is defined by the following equation:
\begin{equation} y=\ \frac{Z_{j}{(X_{i}^{2}+Z_{i}^{2})}^{3/2}}{Z_{i}{(X_{j}^{2}+Z_{j}^{2})}^{3/2}\text{.\ }}\nonumber \\ \end{equation}
Where Zij and Xij refer to the relative depth and horizontal distance from a pair of recording stations to the mass source, respectively. If Xijis constrained, for example, through the assumption that the source lies beneath the summit craters, y will depend exclusively on (and can be used to define) the source depth. When working with time series,y can be defined as the gradient between two signals within a defined time window (Fig. 4C and D).