Model of Viscoelastic Relaxation of Shallow Crustal Material for Seismically Induced Tension Cracks in the Chile-Peru Forearc

Many tension cracks were induced by past subduction zone earthquakes in the forearc of northern Chile and southern Peru (e.g., Baker et al., 2013, Nature Geosci., 6(6), 492.), and some have been newly created or reopened by recent earthquakes. Some cracks cut 8 to 10 meters into basement rocks. These cracks occur where the largest coseismic tension occurs, regardless of whether the surface is flat or with a topographic slope. This implies that the cracks, representing permanent tensile deformation, are induced by coseismic static stress. In an elastic system without a topographic gradient, it is generally not possible to create permanent tensile deformation in the upper plate during an earthquake, because the energy released by an earthquake cannot exceed the maximum strain energy that is available to cause the earthquake. Thus, the cracks seem to contradict the elastic rebound theory for earthquakes. Here we propose that the forearc cracks form because of the viscoelastic behaviour of near surface material. Laboratory experiments in previous industrial studies show that shallow rocks and sands feature intrinsic viscoelastic behavior so that accumulated stress inside them can be relaxed relatively quickly. For shale gas reservoir rocks and dry unconsolidated reservoir sands, the relaxation time is seen to range from days to decades. Although no laboratory experiments have been conducted on Chile-Peru forearc near-surface materials, typically unconsolidated sands, we assume that they exhibit similar behavior. The actual relaxation time and the presence of nonlinearity are unimportant, as long as significant relaxation takes place within a fraction of the recurrence interval of megathrust earthquakes. If so, stress accumulated during the interseismic period is relaxed near the surface resulting in permanent shortening, but the deeper crustal material is able to build up elastic strain. During the earthquake, elastic rebound of the deeper material induces tensile stress in the shallow material, readily reaching its tensile strength to generate cracks. We construct finite element models including near-surface viscoelasticity to further illustrate the mechanism. Based on the concepts presented in this work, the observed coseismic tensile cracks can be reconciled with the elastic rebound theory.