Ambiguity of the Moment Tensor

An earthquake on a fault separating two dissimilar materials does not have a well-defined moment density tensor. We present a complete characterization of this bimaterial ambiguity in the general case of slip on a fault in an anisotropic medium. The ambiguity can be eliminated by utilizing a potency density rather than a moment density representation of a bimaterial source

Self-similar slip pulses during rate-and-state earthquake nucleation

For a wide range of conditions, earthquake nucleation zones on rate- and state-dependent faults that obey either of the popular state evolution laws expand as they accelerate. Under the “slip” evolution law, which experiments show to be the more relevant law for nucleation, this expansion takes the form of a unidirectional slip pulse. In numerical simulations these pulses often tend to approach, with varying degrees of robustness, one of a few styles of self-similar behavior. Here we obtain an approximate self-similar solution that accurately describes slip pulses growing into regions initially sliding at steady state. In this solution the length scale over which slip speeds are significant continually decreases, being inversely proportional to the logarithm of the maximum slip speed V_(max), while the total slip remains constant. This slip is close to D_c(1−a/b)^(−1), where D_c is the characteristic slip scale for state evolution and a and b are the parameters that determine the sensitivity of the frictional strength to changes in slip rate and state. The pulse has a “distance to instability” as well as a “time to instability,” with the remaining propagation distance being proportional to (1−a/b)^(−2) [ln(V_(max)Θ_(bg)/D_c)]^(−1), where Θ_(bg) is the background state into which the pulse propagates. This solution provides a reasonable estimate of the total slip for pulses growing into regions that depart modestly from steady state

A window into the complexity of the dynamic rupture of the 2011 Mw 9 Tohoku-Oki earthquake

The 2011 Mw 9 Tohoku-Oki earthquake, recorded by over 1000 near-field stations and multiple large-aperture arrays, is by far the best recorded earthquake in the history of seismology and provides unique opportunities to address fundamental issues in earthquake source dynamics. Here we conduct a high resolution array analysis based on recordings from the USarray and the European network. The mutually consistent results from both arrays reveal rupture complexity with unprecedented resolution, involving phases of diverse rupture speed and intermittent high frequency bursts within slow speed phases, which suggests spatially heterogeneous material properties. The earthquake initially propagates down-dip, with a slow initiation phase followed by sustained propagation at speeds of 3 km/s. The rupture then slows down to 1.5 km/s for 60 seconds. A rich sequence of bursts is generated along the down-dip rim of this slow and roughly circular rupture front. Before the end of the slow phase an extremely fast rupture front detaches at about 5 km/s towards the North. Finally a rupture front propagates towards the south running at about 2.5 km/s for over 100 km. Key features of the rupture process are confirmed by the strong motion data recorded by K-net and KIK-net. The energetic high frequency radiation episodes within a slow rupture phase suggests a patchy image of the brittle-ductile transition zone, composed of discrete brittle asperities within a ductile matrix. The high frequency is generated mainly at the down-dip edge of the principal slip regions constrained by geodesy, suggesting a variation along dip of the mechanical properties of the mega thrust fault or their spatial heterogeneity that affects rise time

Deep ductile shear localization facilitates near-orthogonal strike-slip faulting in a thin brittle lithosphere

Some active fault systems comprise near-orthogonal conjugate strike-slip faults, as highlighted by the 2019 Ridgecrest and the 2012 Indian Ocean earthquake sequences. In conventional failure theory, orthogonal faulting requires a pressure-insensitive rock strength, which is unlikely in the brittle lithosphere. Here, we conduct 3D numerical simulations to test the hypothesis that near-orthogonal faults can form by inheriting the geometry of deep ductile shear bands. Shear bands nucleated in the deep ductile layer, a pressure-insensitive material, form at 45 degree from the maximum principal stress. As they grow upwards into the brittle layer, they progressively rotate towards the preferred brittle faulting angle, ~30 degree, forming helical shaped faults. If the brittle layer is sufficiently thin, the rotation is incomplete and the near-orthogonal geometry is preserved at the surface. The preservation is further facilitated by a lower confining pressure in the shallow portion of the brittle layer. For this inheritance to be effective, a thick ductile fault root beneath the brittle layer is necessary. The model offers a possible explanation for orthogonal faulting in Ridgecrest, Salton Trough, and Wharton basin. Conversely, faults nucleated within the brittle layer form at the optimal angle for brittle faulting and can cut deep into the ductile layer before rotating to 45 degree. Our results thus reveal the significant interactions between the structure of faults in the brittle upper lithosphere and their deep ductile roots

Linear elastic fracture mechanics predicts the propagation distance of frictional slip

When a frictional interface is subject to a localized shear load, it is often (experimentally) observed that local slip events initiate at the stress concentration and propagate over parts of the interface by arresting naturally before reaching the edge. We develop a theoretical model based on linear elastic fracture mechanics to describe the propagation of such precursory slip. The model's prediction of precursor lengths as a function of external load is in good quantitative agreement with laboratory experiments as well as with dynamic simulations, and provides thereby evidence to recognize frictional slip as a fracture phenomenon. We show that predicted precursor lengths depend, within given uncertainty ranges, mainly on the kinetic friction coefficient, and only weakly on other interface and material parameters. By simplifying the fracture mechanics model we also reveal sources for the observed non-linearity in the growth of precursor lengths as a function of the applied force. The discrete nature of precursors as well as the shear tractions caused by frustrated Poisson's expansion are found to be the dominant factors. Finally, we apply our model to a different, symmetric set-up and provide a prediction of the propagation distance of frictional slip for future experiments

Stability of faults with heterogeneous friction properties and effective normal stress

Abundant geological, seismological and experimental evidence of the heterogeneous structure of natural faults motivates the theoretical and computational study of the mechanical behavior of heterogeneous frictional fault interfaces. Fault zones are composed of a mixture of materials with contrasting strength, which may affect the spatial variability of seismic coupling, the location of high-frequency radiation and the diversity of slip behavior observed in natural faults. To develop a quantitative understanding of the effect of strength heterogeneity on the mechanical behavior of faults, here we investigate a fault model with spatially variable frictional properties and pore pressure. Conceptually, this model may correspond to two rough surfaces in contact along discrete asperities, the space in between being filled by compressed gouge. The asperities have different permeability than the gouge matrix and may be hydraulically sealed, resulting in different pore pressure. We consider faults governed by rate-and-state friction, with mixtures of velocity-weakening and velocity-strengthening materials and contrasts of effective normal stress. We systematically study the diversity of slip behaviors generated by this model through multi-cycle simulations and linear stability analysis. The fault can be either stable without spontaneous slip transients, or unstable with spontaneous rupture. When the fault is unstable, slip can rupture either part or the entire fault. In some cases the fault alternates between these behaviors throughout multiple cycles. We determine how the fault behavior is controlled by the proportion of velocity-weakening and velocity-strengthening materials, their relative strength and other frictional properties. We also develop, through heuristic approximations, closed-form equations to predict the stability of slip on heterogeneous faults. Our study shows that a fault model with heterogeneous materials and pore pressure contrasts is a viable framework to reproduce the full spectrum of fault behaviors observed in natural faults: from fast earthquakes, to slow transients, to stable sliding. In particular, this model constitutes a building block for models of episodic tremor and slow slip events

A physical model for seismic noise generation from sediment transport in rivers

Measuring sediment flux in rivers remains a significant problem in studies of landscape evolution. Recent studies suggest that observations of seismic noise near rivers can help provide such measurements, but the lack of models linking observed seismic quantities to sediment flux has prevented the method from being used. Here, we develop a forward model to describe the seismic noise induced by the transport of sediment in rivers. The model provides an expression for the power spectral density (PSD) of the Rayleigh waves generated by impulsive impacts from saltating particles which scales linearly with the number of particles of a given size and the square of the linear momentum. After incorporating expressions for the impact velocity and rate of impacts for fluvially transported sediment, we observe that the seismic noise PSD is strongly dependent on the sediment size, such that good constraints on grain size distribution are needed for reliable estimates of sediment flux based on seismic noise observations. The model predictions for the PSD are consistent with recent measurements and, based on these data, a first attempt at inverting seismic noise for the sediment flux is provided

Dynamics of a velocity strengthening fault region: Implications for slow earthquakes and postseismic slip

We consider the effect of permanent stress changes on a velocity strengthening rate-and-state fault, through numerical simulations and analytical results on 1-D, 2-D, and 3-D models. We show that slip transients can be triggered by perturbations of size roughly larger than Lb = Gdc/bσ, where G is the shear modulus, dc and b are the characteristic slip distance and the coefficient of the evolution effect of rate-and-state friction, respectively, and σ is the effective normal stress. Perturbations that increase the Coulomb stress lead to the strongest transients, but creep bursts can also be triggered by perturbations that decrease the Coulomb stress. In the latter case, peak slip velocity is attained long after the perturbation, so that it may be difficult in practice to identify their origin. The evolution of slip in a creep transient shares many features with the nucleation process of a rate-and-state weakening fault: slip initially localizes over a region of size not smaller than Lb and then accelerates transiently and finally expands as a quasi-static propagating crack. The characteristic size Lb implies a constraint on the grid resolution of numerical models, even on strengthening faults, that is more stringent than classical criteria. In the transition zone between the velocity weakening and strengthening regions, the peak slip velocity may be arbitrarily large and may approach seismic slip velocities. Postseismic slip may represent the response of the creeping parts of the fault to a stress perturbation of large scale (comparable to the extent of the main shock rupture) and high amplitude, while slow earthquakes may represent the response of the creeping zones to a more localized stress perturbation. Our results indicate that superficial afterslip, observed at usually seismogenic depths, is governed by a rate-strengthening rheology and is not likely to correspond to stable weakening zones. The predictions of the full rate-and-state framework reduce to a pure velocity strengthening law on a timescale longer than the duration of the acceleration transient, only when the triggering perturbation extends over length scales much larger than Lb

Seismic radiation from regions sustaining material damage

We discuss analytical results for seismic radiation during rapid episodes of inelastic brittle deformation that include, in addition to the standard moment term, a damage-related term stemming from changes of elastic moduli in the source region. The radiation from the damage-related term is associated with products of the changes of elastic moduli and the total elastic strain components in the source region. Order of magnitude estimates suggest that the damage-related contribution to the motion in the surrounding elastic solid, which is neglected in standard calculations, can have appreciable amplitude that may in some cases be comparable to or larger than the moment contribution. A decomposition analysis shows that the damage-related source term has an isotropic component that can be larger than its double-couple component