Ground Deformation Modeling in Volcanic Areas

Abstract

This chapter summarizes the main methods and problems in the modeling of ground deformations in volcanic areas. The basic model is assumed as a strain source embedded within an elastic medium. In particular, the success in explaining ground deformations in several volcanic areas by the simplest model, a nucleus of isotropic strain (generally known as the Mogi’s model) is emphasized, as well as the main limitations of this model, which are often misleading. The effect of varying the shape of the source is reviewed, showing why only the joint use of both vertical and horizontal deformations are effective in constraining source shape and depth. Formulas are also reported for computing ground deformations due to point sources of various shapes in homogenous elastic media. More complex sources, resulting from heterogeneous distributions of source intensity can be built by a superposition of elementary sources. Such complex sources can arise, for instance, from heterogeneous pressure distributions in porous rocks saturated by fluids (magma or water), or from heterogeneous crack opening along volcanic rifts. A general inversion scheme is given in order to allow computation of heterogeneous strain-source distributions from ground deformation data. Furthermore, the effect of the rheology of the medium is examined, considering the main deviations, from the most commonly used homogeneous elastic media, expected in volcanic areas. These include heterogeneities of the elastic parameters and the visco-elastic behavior of rocks. Both of these effects can be thought of, in volcanic areas, as being due to the presence of high temperatures nonuniformly distributed within the medium, and to the presence of different products of the eruptions. Such effects, in principle, can modify the shape of the deformation field for a given source, and/or introduce a complex time dependence of the deformation from the source-time function. Finally, the effect of the presence of stress-strain discontinuities in the elastic medium is thoroughly examined. Such discontinuities are represented, for instance, by faults. In addition, surfaces of contact between different lithologies can be caused, in volcanic areas, by eruptive activity involving different products. In particular, in collapse calderas, where younger and lighter pyroclastic products fill the depressions formed in the more competent rock, the borders of collapsed basins can represent a discontinuity in the medium. In this case, it is shown that the shapes of the ground deformations are strongly affected by the geometry of the caldera structure, and are much less sensitive to the depth of the pressure source. As a consequence, the modeling of ground deformations in calderas should take into account the presence of caldera borders, in order to obtain meaningful results about the shape and depth of the pressure source.