Effects of heterogeneity on frictional-viscous deformation and the depth-extent of the seismogenic zone

<p>Current conceptual fault models define a seismogenic zone, where earthquakes nucleate, characterised by velocity-weakening fault rocks in a dominantly frictional regime. The base of the seismogenic zone is commonly inferred to coincide with a thermally controlled onset of velocity-strengthening slip or distributed viscous deformation. The top of the seismogenic zone may be determined by low-temperature diagenetic processes and the state of consolidation and alteration. Overall, the seismogenic zone is therefore described as bounded by transitions in frictional and rheological properties. These properties are relatively well-determined for monomineralic systems and simple, planar geometries; but, many exceptions, including deep earthquakes, slow slip, and shallow creep, imply processes involving compositional, structural, or environmental heterogeneities. We explore how such heterogeneities may alter the extent of the seismogenic zone.</p><p> </p><p>We consider mixed viscous-frictional deformation and suggest a simple rule of thumb to estimate the role of heterogeneities by a combination of the viscosity contrast within the fault, and the ratio between the bulk shear stress and the yield strength of the strongest fault zone component. In this model, slip behaviour can change dynamically in response to stress and strength variations with depth and time. We quantify the model numerically, and illustrate the idea with a few field-based examples: 1) earthquakes within the viscous regime, deeper than the thermally-controlled seismogenic zone, can be triggered by an increase in the ratio of shear stress to yield strength, either by increased fluid pressure or increased local stress; 2) there is commonly a depth range of transitional behaviour at the base of the seismogenic zone – the thickness of this zone increases markedly with increased viscosity contrast within the fault zone; and 3) fault zone weakening by phyllosilicate growth and foliation development increases viscosity ratio and decreases bulk shear stress, leading to efficient, stable, fault zone creep. These examples are not new interpretations or observations, but given the substantial complexity of heterogeneous fault zones, we suggest that a simplified, conceptual model based on basic strength and stress parameters is useful in describing and assessing the effect of heterogeneities on fault slip behaviour.         </p>

Numerical modelling of strain localization by anisotropy generation during viscous deformation

<p>Localization and softening mechanisms in a deforming lithosphere are important for subduction initiation or the generation of tectonic nappes during orogeny. Many localization mechanisms have been proposed as being important during the viscous, creeping, deformation of the lithosphere, such as thermal softening, grain size reduction, reaction-induced softening or anisotropy development. However, which localization mechanism is the controlling one and under which deformation conditions is still contentious. In this contribution, we focus on strain localization in viscous material due to the generation of anisotropy, for example due to the development of a foliation. We numerically model the generation and evolution of anisotropy during two-dimensional viscous deformation in order to quantify the impact of anisotropy development on strain localization and on the effective softening. We use a pseudo-transient finite difference (PTFD) method for the numerical solution. We calculate the finite strain ellipse during viscous deformation. The aspect ratio of the finite strain ellipse serves as proxy for the magnitude of anisotropy, which determines the ratio of normal to tangential viscosity. To track the orientation of the anisotropy during deformation, we apply the so-called director method. We will present first results of our numerical simulations and discuss their application to natural shear zones.</p>

Seismic attenuation and rheology of crustal rocks: results from numerical tests

<p>Seismic attenuation of the rocks mainly depends on their intrinsic anelasticity, which is the dissipation of seismic energy as it propagates through the medium. Several studies have already demonstrated that seismic attenuation, described by the Q-factor, is intrinsically related to the rocks’ viscosity, considering their common dependency on composition, grain size, fluid content, and T-P conditions. However, viscous deformation of the rocks occurs through different mechanisms: diffusion creep, numerous mechanisms of the dislocation creep, pressure solution, which are expressed by several Arrhenius-type constitutive laws. This makes more complex the investigation of quantitative relationships between seismic attenuation and viscous rocks' rheology.</p><p>The main purpose of this study is to investigate the mutual dependence of the seismic attenuation and viscous deformation of the crustal rocks. To this aim, we performed several numerical tests to check the variability of some physical properties (e.g., elastic modulus, Poisson’s ratio) and improve the existing relationships between seismic attenuation and viscous deformation of several natural rock samples. The Burgers mechanical model and Arrhenius relation are included in these test series to achieve a closer approximation of the rocks’ viscous deformation.</p><p>In this way, it will be possible to predict the viscous rheology of rocks from the laws describing the seismic attenuation and viceversa. The obtained results will be used to (1) constrain the Q-factor and rheological (creep) parameters, which are still subjected to high uncertainties, (2) validate/modify the existing seismic attenuation and rheological laws, (3) increase the robustness of the geodynamic and rocks’ mechanics numerical codes and our understanding of the role that rocks’ rheology exerts on the tectonic processes.</p>

Experimental evidence that viscous shear zones generate periodic pore sheets

In experiments designed to understand deep shear zones, we show that periodic porous sheets emerge spontaneously during viscous creep and that they facilitate mass transfer. These findings challenge conventional expectations of how viscosity in solid rocks operates and provide quantitative data in favour of an alternative paradigm, that of the dynamic granular fluid pump model. On this basis, we argue that our results warrant a reappraisal of the community's perception of how viscous deformation in rocks proceeds with time and suggest that the general model for deep shear zones should be updated to include creep cavitation. Through our discussion we highlight how the integration of creep cavitation, and its Generalised Thermodynamic paradigm, would be consequential for a range of important solid Earth topics that involve viscosity in Earth materials like, for example, slow earthquakes.

A viscoplastic model of creep in shale

We have developed a viscoplastic model that reproduces creep behavior and inelastic deformation of rock during loading-unloading cycles. We use a Perzyna-type description of viscous deformation that derives from a maximization of dissipated energy during plastic flow, in combination with a modified Cam-clay model of plastic deformation. The plastic flow model is of the associative type, and the viscous deformation is proportional to the ratio of driving stress and a material viscosity. Our model does not rely on any explicit time parameters; therefore, it is well-suited for standard and cyclic loading of materials. We validate the model with recent triaxial experiments of time-dependent deformation in clay-rich (Haynesville Formation) and carbonate-rich (Eagle Ford Formation) shale samples, and we find that the deformation during complex, multiscale loading-unloading paths can be reproduced accurately. We elucidate the role and physical meaning of each model parameter, and we infer their value from a gradient-descent minimization of the error between simulation and experimental data. This inference points to the large, and often unrecognized, uncertainty in the preconsolidation stress, which is key to reproducing the observed hysteresis in material deformation.

Detection of Plastic Strain Using GNSS Data of Pre- and Post-Seismic Deformation of the 2011 Tohoku-oki Earthquake

<p>In general, there are three mechanisms causing crustal deformation: elastic, viscous, and plastic deformation. The separation of observed crustal deformation to each component has been a challenging problem. Meneses-Gutierrez and Sagiya (2016, EPSL) have successfully separated inelastic deformation from observed geodetic data from the comparison of GNSS data before and after the 2011 Tohoku-oki earthquake in the northern Niigata-Kobe tectonic zone (NKTZ), central Japan. In this study, we further succeed in separating plastic deformation as well as viscous deformation in the northern NKTZ using GNSS data before and after the 2011 Tohoku-oki earthquake, under the assumptions that elastic deformation is principally caused by the plate coupling along the Japan trench and that plastic deformation ceased after the Tohoku-oki earthquake due to the stress drop caused by the earthquake. The cease of plastic deformation can be understood with the concept of stress shadow used in the field of seismic activity. The separated strain rates are about 30 nanostrain/yr both for the plastic deformation in the preseismic period and for the viscous deformation in both the pre- and post-seismic periods, which means that the inelastic strain rate in the northern NKTZ is about 60 and 30 nanostrain/yr in the pre- and post-seismic periods, respectively. This result requires the revision of the strain rate paradox in Japan. The strain rate was exceptionally faster before the Tohoku-oki earthquake due to the effect of plastic strain, and the discrepancy between the geodetic and geologic strain rates is much smaller in usual time, when the plastic strain is off. In oder to understand the onset timing of plastic deformation, the information on stress history is essentially important.</p><p> </p>

Stress and deformation mechanisms at a subduction zone: insights from 2-D thermomechanical numerical modelling

SUMMARY Numerous processes such as metamorphic reactions, fluid and melt transfer and earthquakes occur at a subducting zone, but are still incompletely understood. These processes are affected, or even controlled, by the magnitude and distribution of stress and deformation mechanism. To eventually understand subduction zone processes, we quantify here stresses and deformation mechanisms in and around a subducting lithosphere, surrounded by asthenosphere and overlain by an overriding plate. We use 2-D thermomechanical numerical simulations based on the finite difference and marker-in-cell method and consider a 3200 km wide and 660 km deep numerical domain with a resolution of 1 km by 1 km. We apply a combined visco-elasto-plastic deformation behaviour using a linear combination of diffusion creep, dislocation creep and Peierls creep for the viscous deformation. We consider two end-member subduction scenarios: forced and free subduction. In the forced scenario, horizontal velocities are applied to the lateral boundaries of the plates during the entire simulation. In the free scenario, we set the horizontal boundary velocities to zero once the subducted slab is long enough to generate a slab pull force large enough to maintain subduction without horizontal boundary velocities. A slab pull of at least 1.8 TN m–1 is required to continue subduction in the free scenario. We also quantify along-profile variations of gravitational potential energy (GPE). We evaluate the contributions of topography and density variations to GPE variations across a subduction system. The GPE variations indicate large-scale horizontal compressive forces around the trench region and extension forces on both sides of the trench region. Corresponding vertically averaged differential stresses are between 120 and 170 MPa. Furthermore, we calculate the distribution of the dominant deformation mechanisms. Elastoplastic deformation is the dominant mechanism in the upper region of the lithosphere and subducting slab (from ca. 5 to 60 km depth from the top of the slab). Viscous deformation dominates in the lower region of the lithosphere and in the asthenosphere. Considering elasticity in the calculations has an important impact on the magnitude and distribution of deviatoric stress; hence, simulations with increased shear modulus, in order to reduce elasticity, exhibit considerably different stress fields. Limiting absolute stress magnitudes by decreasing the internal friction angle causes slab detachment so that slab pull cannot be transmitted anymore to the horizontal lithosphere. Applying different boundary conditions shows that forced subduction simulations are stronger affected by the applied boundary conditions than free subduction simulations. We also compare our modelled topography and gravity anomaly with natural data of seafloor bathymetry and free-air gravity anomalies across the Mariana trench. Elasticity and deviatoric stress magnitudes of several hundreds of MPa are required to best fit the natural data. This agreement suggests that the modelled flexural behaviour and density field are compatible with natural data. Moreover, we discuss potential applications of our results to the depth of faulting in a subducting plate and to the generation of petit-spot volcanoes.