Volumetric and shear processes in crystalline rock approaching faulting.

Understanding the approach to faulting in continental rocks is critical for identifying processes leading to fracturing in geomaterials and the preparation process of large earthquakes. In situ dynamic X-ray imaging and digital volume correlation analysis of a crystalline rock core, under a constant confining pressure of 25 MPa, are used to elucidate the initiation, growth, and coalescence of microfractures leading to macroscopic failure as the axial compressive stress is increased. Following an initial elastic deformation, microfractures develop in the solid, and with increasing differential stress, the damage pervades the rock volume. The creation of new microfractures is accompanied by propagation, opening, and closing of existing microfractures, leading to the emergence of damage indices that increase as powers of the differential stress when approaching failure. A strong spatial correlation is observed between microscale zones with large positive and negative volumetric strains, microscale zones with shears of opposite senses, and microscale zones with high volumetric and shear strains. These correlations are attributed to microfracture interactions mediated by the heterogeneous stress field. The rock fails macroscopically as the microfractures coalesce and form a geometrically complex 3D volume that spans the rock sample. At the onset of failure, more than 70% of the damage volume is connected in a large fracture cluster that evolves into a fault zone. In the context of crustal faulting dynamics, these results suggest that evolving rock damage around existing locked or future main faults influences the localization process that culminates in large brittle rupture events.

Dynamic earthquake rupture in the lower crust.

Earthquakes in the continental crust commonly occur in the upper 15 to 20 km. Recent studies demonstrate that earthquakes also occur in the lower crust of collision zones and play a key role in metamorphic processes that modify its physical properties. However, details of the failure process and sequence of events that lead to seismic slip in the lower crust remain uncertain. Here, we present observations of a fault zone from the Bergen Arcs, western Norway, which constrain the deformation processes of lower crustal earthquakes. We show that seismic slip and associated melting are preceded by fracturing, asymmetric fragmentation, and comminution of the wall rock caused by a dynamically propagating rupture. The succession of deformation processes reported here emphasize brittle failure mechanisms in a portion of the crust that until recently was assumed to be characterized by ductile deformation.

Earthquake-induced transformation of the lower crust.

The structural and metamorphic evolution of the lower crust has direct effects on the lithospheric response to plate tectonic processes involved in orogeny, including subsidence of sedimentary basins, stability of deep mountain roots and extension of high-topography regions. Recent research shows that before orogeny most of the lower crust is dry, impermeable and mechanically strong 1 . During an orogenic event, the evolution of the lower crust is controlled by infiltration of fluids along localized shear or fracture zones. In the Bergen Arcs of Western Norway, shear zones initiate as faults generated by lower-crustal earthquakes. Seismic slip in the dry lower crust requires stresses at a level that can only be sustained over short timescales or local weakening mechanisms. However, normal earthquake activity in the seismogenic zone produces stress pulses that drive aftershocks in the lower crust 2 . Here we show that the volume of lower crust affected by such aftershocks is substantial and that fluid-driven associated metamorphic and structural transformations of the lower crust follow these earthquakes. This provides a 'top-down' effect on crustal geodynamics and connects processes operating at very different timescales.

Abundant off-fault seismicity and orthogonal structures in the San Jacinto fault zone.

The trifurcation area of the San Jacinto fault zone has produced more than 10% of all earthquakes in southern California since 2000, including the June 2016 Mw (moment magnitude) 5.2 Borrego Springs earthquake. In this area, the fault splits into three subparallel strands and is associated with broad VP /VS anomalies. We synthesize spatiotemporal properties of historical background seismicity and aftershocks of the June 2016 event. A template matching technique is used to detect and locate more than 23,000 aftershocks, which illuminate highly complex active fault structures in conjunction with a high-resolution regional catalog. The hypocenters form dipping seismicity lineations both along strike and nearly orthogonal to the main fault, and are composed of interlaced strike-slip and normal faults. The primary faults change dip with depth and become listric by transitioning to a dip of ~70° near a depth of 10 km. The Mw 5.2 Borrego Springs earthquake and past events with M > 4.0 occurred on the main faults, whereas most of the low-magnitude events are located in a damage zone (several kilometers wide) at seismogenic depths. The lack of significant low-magnitude seismicity on the main fault traces suggests that they do not creep. The very high rate of aftershocks likely reflects the large geometrical fault complexity and perhaps a relatively high stress due to a significant length of time elapsed since the last major event. The results provide important insights into the physics of faulting near the brittle-ductile transition.

Probabilistic model of waiting times between large failures in sheared media.

Using a probabilistic approximation of a mean-field mechanistic model of sheared systems, we analytically calculate the statistical properties of large failures under slow shear loading. For general shear F(t), the distribution of waiting times between large system-spanning failures is a generalized exponential distribution, ρ_{T}(t)=λ(F(t))P(F(t))exp[-∫_{0}^{t}dτλ(F(τ))P(F(τ))], where λ(F(t)) is the rate of small event occurrences at stress F(t) and P(F(t)) is the probability that a small event triggers a large failure. We study the behavior of this distribution as a function of fault properties, such as heterogeneity or shear rate. Because the probabilistic model accommodates any stress loading F(t), it is particularly useful for modeling experiments designed to understand how different forms of shear loading or stress perturbations impact the waiting-time statistics of large failures. As examples, we study how periodic perturbations or fluctuations on top of a linear shear stress increase impact the waiting-time distribution.

Probing failure susceptibilities of earthquake faults using small-quake tidal correlations.

Mitigating the devastating economic and humanitarian impact of large earthquakes requires signals for forecasting seismic events. Daily tide stresses were previously thought to be insufficient for use as such a signal. Recently, however, they have been found to correlate significantly with small earthquakes, just before large earthquakes occur. Here we present a simple earthquake model to investigate whether correlations between daily tidal stresses and small earthquakes provide information about the likelihood of impending large earthquakes. The model predicts that intervals of significant correlations between small earthquakes and ongoing low-amplitude periodic stresses indicate increased fault susceptibility to large earthquake generation. The results agree with the recent observations of large earthquakes preceded by time periods of significant correlations between smaller events and daily tide stresses. We anticipate that incorporating experimentally determined parameters and fault-specific details into the model may provide new tools for extracting improved probabilities of impending large earthquakes.

ExPlanes: exploring planes in triplet data.

Many methods for the analysis of gene expression-, protein- or metabolite-data focus on the investigation of binary relationships, while the underlying biological processes creating this data may generate relations of higher than bivariate complexity. We give a novel method ExPlanes that helps to explore certain types of ternary relationships in a statistically robust, Bayesian framework. To arrive at an characterization of the data structure contained in triplet data we investigate 2-dimensional planes being the only linear structures that cannot be inferred from projections of the data. The key part of our methodology is the definition of a robust, Bayesian plane posterior under the assumption of an invariant prior and a Gaussian error model. A numerical representation of the plane posterior can be explored interactively. Beyond this purely Bayesian approach we can use the plane posterior to construct a family of posterior-based test statistics that allow testing the data for different plane related hypotheses. To demonstrate practicability we queried triplets of metabolic data from a plant crossing experiment for the presence of plane-, line- and point-structures by using posterior-based test statistics and were able to show their distinctiveness.

Micromechanical model for deformation in solids with universal predictions for stress-strain curves and slip avalanches.

A basic micromechanical model for deformation of solids with only one tuning parameter (weakening epsilon) is introduced. The model can reproduce observed stress-strain curves, acoustic emissions and related power spectra, event statistics, and geometrical properties of slip, with a continuous phase transition from brittle to ductile behavior. Exact universal predictions are extracted using mean field theory and renormalization group tools. The results agree with recent experimental observations and simulations of related models for dislocation dynamics, material damage, and earthquake statistics.

Universal mean moment rate profiles of earthquake ruptures.

Earthquake phenomenology exhibits a number of power law distributions including the Gutenberg-Richter frequency-size statistics and the Omori law for aftershock decay rates. In search for a basic model that renders correct predictions on long spatiotemporal scales, we discuss results associated with a heterogeneous fault with long-range stress-transfer interactions. To better understand earthquake dynamics we focus on faults with Gutenberg-Richter-like earthquake statistics and develop two universal scaling functions as a stronger test of the theory against observations than mere scaling exponents that have large error bars. Universal shape profiles contain crucial information on the underlying dynamics in a variety of systems. As in magnetic systems, we find that our analysis for earthquakes provides a good overall agreement between theory and observations, but with a potential discrepancy in one particular universal scaling function for moment rates. We primarily use mean field theory for the theoretical analysis, since it has been shown to be in the same universality class as the full three-dimensional version of the model (up to logarithmic corrections). The results point to the existence of deep connections between the physics of avalanches in different systems.