Task 2: Space-time evolution of the stress field following earthquakes and episodes of magma upwelling

Mechanical effects left by an earthquake on its fault plane, in the post-seismic phase, were investigated employing the "displacement discontinuity method" and imposing the release of a constant, uni-directional shear traction. Due to unsymmetric interaction between the fault plane and the free surface, significant normal stress components are left over the shallow portion of the fault surface after the earthquake (Figure 46): these are compressive for normal faults, tensile for thrust faults, and are typically comparable to the stress drop. In Figure 46 the s-axis is along the strike of the fault, the d-axis is along the dip (positive upwards). Several observations can be explained from the present model: low-dip thrust faults and high-dip normal faults are found to be favoured, according to the Coulomb failure criterion, in repetitive earthquake cycles; the shape of dip-slip faults near the surface is predicted to be upward-concave; the shallow aftershock activity commonly observed in the hanging block of a thrust event is easily explained. The detailed results of this research are reported in Bonafede and Neri (2000).

  

Figure 46: Normal stress induced by uniform stress drop over a high-dip normal fault and a low-dip thrust fault. The near-surface part of a normal fault is affected by compressive stress, while tensile stresses act there for a thrust fault.

  

Figure 47: According to the stress-drop-discontinuity condition, en-echelon fault segments, rotated in the direction of the tensile principal stress axis, must accompany brittle faulting at depth (left). On the contrary, anelastic deformation at depth is preferably accompanied by antithetic faulting in brittle surface layers (right).

The study of the effects induced by structural inhomogeneities on the stress and displacement fields around strike-slip faults has been recently completed. An elastic medium is considered, made up of an upper layer bounded by a free surface and welded to a lower half-space characterized by different elastic parameters. Shear cracks with assigned stress drop are employed as mathematical models of strike-slip faults which are considered as vertical and planar. If the crack is entirely embedded within the lower medium (case A), a Cauchy-kernel integral equation is obtained, which is solved by employing an expansion of the dislocation density in Chebyshev polynomials. If the crack is within the lower medium but it terminates at the interface (case B), a generalized Cauchy singularity appears in the integral kernel. This singularity affects the singular behaviour of the dislocation density at the crack tip touching the interface. Finally, the case of a crack crossing the interface is considered (case C). The crack is split into two interacting sections, each placed in a homogeneous medium and both open at the interface. Two coupled generalized Cauchy equations are obtained and solved for the dislocation density distribution of each crack section. An asymptotic study near the intersection between the crack and the interface shows that the dislocation densities for each crack section are bounded at the interface, where a jump discontinuity appears. As a corollary, the stress drop must be discontinuous at the interface, with a jump proportional to the rigidity contrast between the adjoining media. This finding is shown to have important implications for the development of geometrical complexities within transform fault zones: planar strike-slip faults cutting across layer discontinuities with arbitrary stress drop values are shown to be admissible only if the interface between different layers becomes unwelded during the earthquake. Planar strike-slip faulting may also take place in mature transform zones, where a repetitive earthquake cycle has already developed. Otherwise, the fault cannot be planar: we infer that strike-slip faulting at depth is plausibly accompanied by en-echelon surface breaks (Figure 47) in a shallow sedimentary layer (where the stress drop is lower than prescribed by the discontinuity condition), while ductile deformation (or steady sliding) at depth is preferably accommodated by antithetic faulting in the upper brittle layer (endowed with lower rigidity but higher stress), giving rise to bookshelf faulting (Figure 47). Results of this research were presented at several international conferences. A paper has been submitted for publication (Bonafede et al. 2000). The South Iceland seismic zone provides several instances of application of both types of complexities.

  

Figure 48: Stress concentration induced by strike-slip faulting across layer interfaces. The panel on the right shows the incremental stress present in the layered model compared to the homogeneous half-space model (on the right). Accurate re-location of aftershocks in several areas of the world actually show a sharp concentration of events along bedding planes.