Residual Surface Displacements Research Articles

Impact of power-law rheology on the viscoelastic relaxation pattern and afterslip distribution following the 2010 Mw 8.8 Maule earthquake

After large earthquakes at subduction zones, the plate interface continues moving due to mostly frictional afterslip or simply afterslip processes. Below approximately 60 km depth, the seismic moment release at the plate interface is quite small indicating that the shear strength is low and stable sliding is the prevailing process. This agrees with the lack of significant interseismic locking at deeper segments (>60 km) resulting from the inversion of geodetic data and thus low afterslip can be expected. However, inversion models that employ linear viscoelastic mantle rheology and an elastic crust result in significant afterslip at depths >60 km. In this paper, we present a combination of a 3D forward geomechanical model with power-law rheology that simulates postseismic relaxation with dislocation creep processes in the crust and upper mantle and an afterslip inversion. We estimate the cumulative viscoelastic relaxation and the afterslip distribution for the first six years following the 2010 Mw 8.8 Maule earthquake in Chile. The cumulative afterslip distribution is obtained from the inversion of the residual surface displacements between the observed displacements from the continuous GPS (cGPS) and the ones from the forward modelling. We investigate five simulations, four with different dislocation creep parameters for the crust, slab, and upper mantle and one with elastic properties for the crust and slab, and a linear viscoelastic upper mantle for comparison. Our preferred simulation considers a weak crust since it shows the best fit to the cumulative cGPS postseismic displacements, a good fit to the time-series, and, in particular, a good spatial correlation between afterslip and aftershock activity. In this simulation, most of the viscoelastic relaxation occurs in the continental lower crust beneath the volcanic arc due to dislocation creep processes. The resulting afterslip pattern from the inversion is reduced at depths >60 km, which correlates to the low cumulative seismic moment that is released from aftershocks at these depths. Furthermore, the cumulative afterslip moment release from this simulation corresponds to 10% of the main shock in six years, which is approximately half of the moment release that results from models with an elastic crust and linear viscosity in the upper mantle. We conclude that an integrated analysis by considering power-rheology with dislocation creep processes in the continental crust and upper mantle along with aftershock activity may be used to constrain location and magnitude postseismic relaxation processes better.

Resolving depth-dependent subduction zone viscosity and afterslip from postseismic displacements following the 2011 Tohoku-oki, Japan earthquake

We developed a 3-D, viscoelastic finite element model of the M9 2011 Tohoku-oki, Japan earthquake capable of predicting postseismic displacements due to viscoelastic relaxation and afterslip. We consider seismically inferred slab geometries associated with the Pacific and Philippine Sea Plate and a wide range of candidate viscoelastic rheologies. For each case, we invert for afterslip based on residual surface displacements (observed GPS minus that predicted due to viscoelastic relaxation) to develop combined viscoelastic relaxation and afterslip models. We are able to find a mechanical model that fully explains all observed geodetic on-land and seafloor horizontal and vertical postseismic displacements. We find that postseismic displacements are in about equal parts due to viscoelastic relaxation and afterslip, but their patterns are spatially distinct. Accurately predicting both horizontal and vertical on-land postseismic displacements requires a mantle wedge viscosity structure that is depth dependent, reflecting the manner in which temperature, pressure, and water content influence viscosity. No lateral heterogeneities within the mantle wedge viscosity structure beneath northern Honshu are required. Westward-directed postseismic seafloor displacements may be due flow via low-temperature, plastic creep within the lower half of a Pacific lithosphere weakened by plate bending. The distribution of afterslip is controlled by the location of coseismic slip from the Tohoku-oki and other regional historic earthquakes. The paradigm by which afterslip is thought of as the dominant postseismic mechanism immediately following earthquakes, with viscoelastic relaxation to follow in later years, is shown to no longer be valid.

Nonelastic strains in solids—an inverse characterization from measured boundary data

Nonelastic strains include the strains caused by thermal expansion, phase transformation, plastic deformation and misfit interface, etc. The nonelastic strains, if given, can be replaced by fictitious body forces and surface tractions. The problem is then treated as an elasticity problem. Such a problem is called a forward problem. There is a body of well-developed knowledge dealing with the forward problems. In this paper, we consider the so-called inverse problems. Overspecified boundary values (both tractions and displacements) are used to calculate the nonelastic strains. Although these surface data are not sufficient to determine the exact distribution of the nonelastic strains, some important characteristic quantities associated with the nonelastic strains are obtained. These quantities include lower bounds of the magnitude of the nonelastic strains (in terms of L 2 norm) and elastic energy, etc. The method is applied to a dislocation problem where we compute the Burger's vector from measured residual surface displacements. Another application is found in determining the material properties of a solid with microscopic defects.

On the Inversion of Residual Stresses From Surface Displacements

When plastic damage regions are accumulated in a material, there exist residual displacements on the surface of the material after all the loadings are removed. The residual displacements are defined as the difference between before and after loading, and can be measured experimentally without destruction of the material. This paper addresses the problem of evaluating the residual stress field caused by the accumulation of the plastic damage regions in a subdomain of the material. The problem is formulated as a system of integral equations relating the surface displacements to the unknown plastic strains. The damage domain, which appears as the domain of integration of the integral equations, is also unknown. Determination of the shape of the damage domain, together with the plastic strains, is a very complicated nonlinear problem. In addition to the residual surface displacement data, it requires more information about the loading history or other restrictive assumptions. However, the residual stress field in the vicinity of the damage domain is obtained after the equivalent damage domain and the equivalent plastic strains are introduced. The problem is an inverse problem, which is substantially different from the conventional forward analysis of structural mechanics. Special attention is given to the uniqueness and stability of the solution.

Nondestructive evaluation of interfacial damages in composite materials

The high stress concentration near the interface of fiber-matrix in composite materials causes the accumulation of the interfacial damages and the degradation of mechanical properties of the materials. In this paper, by using the residual surface displacement data, we evaluate the microscopic damages in terms of Somigliano's dislocations in composites near the interface caused by a series of unknown loadings. The goal of this research is to monitor the processes of the damage evolution near the interface and to relate this microscopic damage to the degradation of the macroscopic mechanical properties of the materials.The problem is an inverse problem, which is substantially different from the conventional forward analysis of structural mechanics. Therefore, the uniqueness and stability must be considered. It is proved that the residual fields and all the characteristic quantities along the interface, such as displacement jumps (Somigliano's dislocations), are uniquely determined by the residual surface displacements. It follows that the traction free parts of the interface correspond to cracks, the normal displacement jumps indicate debonding and the tangential displacement jumps measure the interfacial sliding. A special technique is utilized to stabilize the numerical calculations.

The elastic residual field of a very long strike-slip fault in the presence of a discontinuity

abstract On the basis of dislocation theory, formulas for the elastic residual field of a long strike-slip fault in a half-space with a vertical and horizontal discontinuity are given. The obtained results are applied to the 1966 Parkfield-Cholame earthquake. There is good agreement between the calculated residual stress field and the distribution of aftershocks. The influence of an underlying layer on the residual-surface displacements and strains of a long, vertical strike-slip fault located in the surface layer was found. Both displacements and strains diminish faster as a function of distance from a fault in the presence of a more rigid underlying layer. The computed results show that the dislocation model of a fault in a homogeneous half-space can be inadequate in many cases.