Displacements and stresses due to a single force in a half-space in welded contact with another half-space

Closed-form analytical expressions for the displacements and stresses induced by a single force of arbitrary orientation located in an elastic half-space in welded contact with another elastic half-space are obtained. These expressions are valid for arbitrary values of the Poisson's ratio and for arbitrary source and observer locations. The final results are given in a form that makes numerical computation straightforward and accurate.     

Coseismic well-level changes due to the 1992 Roermond earthquake compared to static deformation of half-space solutions

The M _w 5.4 Roermond earthquake of 1992 April 13 was one of the strongest events during the last 500 years in Central Europe. For the period March–May 1992, we collected records of 194 continuously operating well-level sensors, mostly located within 120  km of the epicentre. Nearly all wells penetrate unconfined or poorly confined Quaternary deposits with high hydraulic conductivities. 81 out of 194 raw data sets show a significant dynamic or step-like response of centimetre amplitude to the passage of seismic waves. Precursory anomalies are not obvious in these records. Coseismic well-level fluctuations could reflect a redistribution of stress and pore pressure in the brittle crust. Systematic analyses of such fluctuations may improve our knowledge of the role of pore fluids in crustal rheology and earthquake mechanics. The rather high number of individual observational records for a single event allows a regional correlation of the signs and amplitudes of the coseismic steps to changes in volume strain caused by the earthquake. The coseismic strain field at the surface was calculated for a homogeneous and a layered half-space. The results show reasonable agreement in the sign of the well-level steps but the amplitudes predicted from the wells' volumetric strain responses are much smaller than those that were recorded. Clearly, the coseismic well-level steps cannot be explained by volume strain changes, as derived from linear elastic models.     

Quasi-static deformation of a poroelastic half-space with anisotropic permeability by two-dimensional surface loads

An analytical solution is obtained of the fully coupled diffusion–deformation system of equations governing the quasi-static plane strain deformation of a poroelastic half-space with anisotropic permeability and compressible constituents. The stresses and the pore pressure are taken as the basic state variables. Displacements are obtained by integrating the coupled constitutive relations. The problem of surface loads is discussed in detail. Explicit analytical solutions are derived for normal line loading, shear line loading and normal strip loading. The permeability anisotropy is found to have a significant effect on the quasi-static deformation of the half-space. However, in the drained and undrained limits, the anisotropy has no effect. The stresses in the drained and undrained states are independent of the poroelastic parameters. Numerical computation of the pore pressure indicates that ignoring permeability anisotropy may lead to an overestimation of the pore pressure at points vertically below the point of normal loading. Further, anisotropy in permeability may lead to a dilution in the theoretical prediction of the Mandel–Cryer Effect.     

Simulation of seismicity due to fluid migration in a fault zone

Spatio-temporal variation of rupture activity is modelled assuming fluid migration in a narrow, porous fault zone formed along a vertical strike-slip fault in a semi-infinite elastic medium. The principle of the effective stress coupled to the Coulomb failure criterion introduces mechanical coupling between fault slip and the pore fluid. The fluid is assumed to flow out of a localized high-pressure fluid compartment in the fault at the onset of earthquake rupture. The duration of the earthquake sequence is assumed to be much shorter than the recurrence period of characteristic events on the fault. Both an earthquake swarm and a foreshock–main-shock sequence can be simulated by changing the relative magnitudes of the initial tectonic stress, pore fluid pressure, fracture strength and so on. When an inhomogeneity is introduced into the spatial distribution of fracture strength, high complexity is observed in the spatio-temporal variation of rupture activity. For example, the time interval between two successive events is highly irregular, and a relatively long quiescence of activity is sometimes observed in a foreshock–main-shock sequence. The quiescence is caused by the temporary arresting of rupture extension, due to an encounter with fault segments having locally high strengths. The frequency–magnitude statistics of intermediate-size events obey the Gutenberg–Richter relation. The calculations show the temporal variation of the b value during some foreshock sequences, and the degree of the change seems to depend on the statistical distribution of the fracture strength.     

Reciprocity theorem to compute the static deformation due to a point dislocation buried in a spherically symmetric earth

Intriguing reciprocity relations exist between the static deformation excited by a point dislocation in a SNREI earth and those generated by external forces, such as tidal force, surface loading and surface shear forces. Coseismic deformations can be rewritten as follows: (1) potential change in terms of the tide deformation field, (2) radial displacement in terms of the load and tidal deformation fields, and (3) tangential displacement in terms of shear and torsional deformation fields. The relations greatly reduce the effort to compute the coseismic crustal deformation in a spherically symmetric earth.     

数字高程模型在活动断层位置及地表变形变位特征提取研究中的应用

活动断层的位置分布及其地表变形变位特征的准确识别是研究和评价活动断层的基础,国内外学者利用数字高程模型(DEM)对断层提取进行了大量研究。本文基于DEM的活动断层位置的提取方法进行综述,总结了DEM提取断层位置的地貌形态特征分析、图像处理以及综合处理提取方法,突出介绍了高分辨率DEM在详细的断层位置分布提取中的优势,DEM在断层地表变形变位及其特征参数提取研究中的最新应用进展。随着高分辨率DEM的快速发展,DEM及其空间分析技术已成为一种常见的地学研究方法,将其与野外调查、遥感、测年等技术结合进行综合分析,能够促进对活动断层的深入研究,并成为断层定量化研究强有力的技术手段。     

Mechanics of normal fault networks subject to slip-weakening friction

We seek to understand how the stress interactions and the slip-weakening process combine within a non-coplanar, normal fault network to allow a slip instability to develop, and shape the final slip distribution on the system. In a first part, we perform a non-linear spectral analysis to investigate the conditions of stability and the process of slip initiation in an antiplane non-coplanar fault system subject to a slip-dependent friction law. That numerical model allows determining the zones that are able to slip within a fault network, as well as the location of the stress singularities. The resulting slip profiles on the faults show only a few different shapes, some of them with long, linear sections. This leads to formulate a general classification of slip profiles that can be used to infer the degree of fault interaction within any non-coplanar system. In a second part of work, we use our modelling to try reproducing the cumulative slip profiles measured on three real normal interacting faults forming a large-scale en echelon system. For that, we assume that cumulative slip profiles can be compared to the first static modal solution of our conceptual model. We succeed reproducing the profiles quite well using a variable weakening along the faults. Overall, the weakening rate decreases in the direction of propagation of the fault system. Yet, modelling the slip along the propagating, isolated termination segment of the system requires an unlikely distribution of weakening. This suggests that factors not considered in our analysis may contribute to slip profile shaping on isolated, propagating faults.     

Scaling relations of earthquakes and aseismic deformation in a damage rheology model

We perform analytical and numerical studies of scaling relations of earthquakes and partition of elastic strain energy between seismic and aseismic components using a thermodynamically based continuum damage model. Brittle instabilities occur in the model at critical damage level associated with loss of convexity of the strain energy function. A new procedure is developed for calculating stress drop and plastic strain in regions sustaining brittle instabilities. The formulation connects the damage rheology parameters with dynamic friction of simpler frameworks, and the plastic strain accumulation is governed by a procedure that is equivalent to Drucker–Prager plasticity. The numerical simulations use variable boundary forces proportional to the slip-deficit between the assumed far field plate motion and displacement of the boundary nodes. These boundary conditions account for the evolution of elastic properties and plastic strain in the model region. 3-D simulations of earthquakes in a model with a large strike-slip fault produce scaling relations between the scalar seismic potency, rupture area, and stress drop values that are in good agreement with observations and other theoretical studies. The area and potency of the simulated earthquakes generally follow a linear log–log relation with a slope of 2/3, and are associated with stress drop values between 1 and 10 MPa. A parameter-space study shows that the area-potency scaling is shifted to higher stress drops in simulations with parameters corresponding to lower dynamic friction, more efficient healing, and higher degree of seismic coupling.