Magma reservoir failure on the terrestrial planets: Assessing the importance of gravitational loading in simple elastic models

Results from a finite element model characterizing tensile rupture of an internally pressurized ellipsoidal magma reservoir within an axisymmetric elastic half space illustrate that gravity plays a critical role in this process. Failure to incorporate gravitational loading correctly, which is the case for most published models, affects for example: (a) application of corrections designed to account for the presence of the free surface in analytical models; (b) inferences about the internal pressure that a reservoir can sustain prior to rupture; (c) conclusions about the importance of neutral buoyancy, i.e. the relative host rock and magma density structures; and, (d) predictions about the location at which rupture of the reservoir wall will occur and the style of intrusion which will be favored. Analyses that reduce magma reservoirs to a cavity within an unloaded elastic medium, inflated by only an excess pressure component, sacrifice important information and should not be used to interpret reservoir activity or to calibrate more advanced models of volcanic regions and phenomena; an exception to this rule occurs, however, when constraining the pressure that can be inferred from surface displacements for a reservoir of known geometry. In a gravitationally loaded model, the characteristics of the failure process are insensitive to geologically plausible variations in the tensile strength, shear modulus, density structure and gravitational acceleration. As a result the half-space analysis presented here, which will benefit from future expansion to include topography and other factors, can yield insight into not only magma reservoirs on Earth but those thought to have formed within the crusts of Mars, Venus and other solar system bodies as well.