Analytical models of volcanic ellipsoidal expansion sources

Modeling non-double-couple earthquakes and surficial deformation in volcanic and geothermal areas usually involves expansion sources. Given an ensemble of ellipsoidal or tensile expansion sources and double-couple ones, it is straightforward to obtain the equivalent single moment tensor under the far-field approximation. On the contrary, the moment tensor interpretation is by no means unique or unambiguous. If the far-field approximation is unsatisfied, the single moment tensor representation is inappropriate. Here we focus on the volume change estimate in the case of single sources, in particular finite pressurized ellipsoidal sources, presenting the expressions for the computation of the volume change and surficial displacement in a closed analytical form. We discuss the implications of different domains of the moment-tensor eigenvalue ratios in terms of volume change computation. We also discuss how the volume change of each source can be obtained from the isotropic component of the total moment tensor, in few cases of coupled sources where the total volume change is null. The new expressions for the computation of the volume change and surficial displacement in case of finite pressurized ellipsoidal sources should make their use easier with respect to the already published formulations.