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384                                                       Claudia Troise et al.



               3. Displacement Shapes and Maximum Vertical to
                  Horizontal Ratios

               As noted in several papers (e.g. De Natale and Pingue, 1993; De Natale et al.,
          1997) the shape of vertical ground deformation pattern at Campi Flegrei is
          remarkably constant, independent from the total amount of displacement (during
          both uplift and subsidence episodes) which share the same shape apart from the
          sign. This feature has been interpreted as the strong effect of ring faults, which
          represent displacement discontinuities at the caldera borders, and act to stabilize the
          location of the pressure source axis (De Natale et al., 1997). Recently, Battaglia
          et al. (2006) noted a marked difference in the ratio between horizontal and vertical
          displacements associated with the first phase of large uplift (1982–1983) and the
          subsequent subsidence episode (1985–1995) respectively, thus demonstrating that
          different source depth and geometry are involved and reflect different mechanisms.
          In order to understand the nature of the present uplift episode, it is then crucial to
          compare it to previous episodes.
             It is well known that surface deformations cannot uniquely constrain the source
          (De Natale and Pingue, 1996). However, inferences on source properties can be
          extracted from geodetic data, provided simple geometries and mechanisms are
          preassigned to the source. In volcanic areas, ellipsoidal sources of homogeneous
          pressure changes are most often hypothesized, sometimes degenerating into penny-
          shaped cracks (Gudmundsson, 2006). It is also well known that using only vertical
          displacement data and simple homogeneous pressure sources cannot be uniquely
          constrained, whereas the joint use of vertical and horizontal displacements is
          generally able to uniquely constrain the depth and mechanism of such predefined
          sources. The most powerful way to monitor both vertical and horizontal
          displacements at the same time is to make use of GPS data. Although the precise
          modeling of displacement sources generally requires a dense geodetic data sampling,
          it is possible to use continuous GPS measurements to extract (from the ratio between
          horizontal and vertical data) basic information about source geometry and depth,
          and to detect possible changes of the ratio which would indicate modifications in the
          depth and/or shape of the intrusion, for example, during intrusions.
             We have computed, using an FEM program (DIANA), the ratios of maximum
          horizontal to maximum vertical surface displacement for different ellipsoidal
          sources in a homogeneous elastic medium with ring faults defined as conical
          surfaces on which shear stress is null and opening is via normal strain (see Troise
          et al., 2003). An axial-symmetric scheme has been used. The dip of the ring faults is
          751, and an average size of 50 m for the smallest elements in the central part of the
          model has been used. The scheme has a total size of 20 km   20 km to avoid border
          effects (Troise et al., 2003). Resulting curves of displacement ratios versus depth for
          three kinds of ellipsoidal sources are shown in Figure 8a. Maximum displacement
          ratios are strongly constrained on source geometry, and particularly in the case of
          shallow depth sources. Monitoring displacement ratios by continuous GPS should
          be then be a very effective method to constrain source geometry and detect
          intrusive episodes that cause a significant increase in the ratio of maximum
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