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).