Aspects of modelling the tectonics of large volcanoes on the terrestrial planets

Analytic solutions for the responses of planetary lithospheres to volcanic loads have been used to model faulting and infer elastic plate thicknesses. Predictions of the distribution of faulting around volcanic loads, based on the application of Anderson's criteria for faulting to the results of the models, do not agree well with observations. Such models do not give the stress state in the load itself, but only suggest a state of horizontal compressive stress there. Further, these models have considered only the effect of an instantaneously emplaced load. They do not address the time evolution of stresses, nor do they consider the effect of a load which grows. A finite element approach allows us to assign elements to the load itself, and thus permits calculation of the stress state and stress history within the edifice. The effects of episodic load growth can also be treated. When these effects are included, models give much better agreement with observations. We use the finite element code TECTON to construct axisymmetric models of volcanoes resting on an elastic lithospheric plate overlying a viscoelastic asthenosphere. We have implemented time-dependent material properties in order to simulate incremental volcano growth. The viscoelastic layer was taken to extend to a sufficient depth so that a rigid lower boundary has no significant influence on the results. The code first calculates elastic deformations and stresses and then determines the time-dependent viscous deformations and stresses. Time in the model scales as the Maxwell time tau(m) in the asthenosphere. We consider a volcano 25 km in height and 200 km in radius on an elastic lithosphere 40 km thick (parameters approximately appropriate to Ascraeus Mons). The volcano consists of three load increments applied at intervals of 1000 tau(m). Contours of maximum deviatoric stress in the fully-grown edifice at the conclusion of flexure (t = 3000 tau(m)) are shown.