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Abstract We review properties and processes of earthquake rupture zones based on field studies, laboratory observations, theoretical models and simulations, with the goal of assessing the possible dominance of different processes in different parts of the rupture and validity of commonly used models. Rupture zones may be divided into front , intermediate , and tail regions that interact to different extents. The rupture front is dominated by fracturing and granulation processes and strong dilatation, producing faulting products that are reworked by subsequent sliding behind. The intermediate region sustains primarily frictional sliding with relatively high slip rates that produce appreciable stress transfer to the propagating front. The tail region further behind is characterized by low slip rates that effectively do not influence the propagating front, although it (and the intermediate region) can spawn small offspring rupture fronts. Wave-mediated stress transfer can also trigger failures ahead of the rupture front. Earthquake ruptures are often spatially discontinuous and intermittent with a hierarchy of asperity and segment sizes that radiate waves with different tensorial compositions and frequency bands. While different deformation processes dominating parts of the rupture zones can be treated effectively with existing constitutive relations, a more appropriate analysis of earthquake processes would require a model that combines aspects of fracture, damage-breakage, and frictional frameworks. 

Abstract The development of new earthquake forecasting models is often motivated by one of the following complementary goals: to gain new insights into the governing physics and to produce improved forecasts quantified by objective metrics. Often, one comes at the cost of the other. Here, we propose a question-driven ensemble (QDE) modeling approach to address both goals. We first describe flexible epidemic-type aftershock sequence (ETAS) models in which we relax the assumptions of parametrically defined aftershock productivity and background earthquake rates during model calibration. Instead, both productivity and background rates are calibrated with data such that their variability is optimally represented by the model. Then we consider 64 QDE models in pseudoprospective forecasting experiments for southern California and Italy. QDE models are constructed by combining model parameters of different ingredient models, in which the rules for how to combine parameters are defined by questions about the future seismicity. The QDE models can be interpreted as models that address different questions with different ingredient models. We find that certain models best address the same issues in both regions, and that QDE models can substantially outperform the standard ETAS and all ingredient models. The best performing QDE model is obtained through the combination of models allowing flexible background seismicity and flexible aftershock productivity, respectively, in which the former parameterizes the spatial distribution of background earthquakes and the partitioning of seismicity into background events and aftershocks, and the latter is used to parameterize the spatiotemporal occurrence of aftershocks. 

We image the shallow seismic structure across the Southern San Andreas Fault (SSAF) using signals from freight trains and trucks recorded by a dense nodal array, with a linear component perpendicular to SSAF and two 2D subarrays centered on the Banning Fault and Mission Creek Fault (MCF). Particle motion analysis in the frequency band 2–5 Hz shows that the examined traffic sources can be approximated as moving single‐ or multi‐point sources that primarily induce Rayleigh waves. Using several techniques, we resolve strong lateral variations of Rayleigh wave velocities andQ‐values across the SSAF, including 35% velocity reduction across MCF toward the northeast and strong attenuation around the two fault strands. We further resolve 10% mass density reduction and 45% shear modulus decrease across the MCF. These findings suggest that the MCF is currently the main strand of the SSAF in the area with important implications for seismic hazard assessments.

 

We present results on radiated seismic energy during simulations of dynamic ruptures in a continuum damage-breakage rheological model incorporating evolution of damage within the seismic source region. The simulations vary in their initial damage zone width and rate of damage diffusion with parameter values constrained by observational data. The radiated energy recorded at various positions around the source is used to calculate seismic potency and moment. We also calculate the normalized radiated energy from the source, in a way that allows comparing between results of different simulations and highlighting aspects related to the dilatational motion during rupture. The results show that at high-frequencies, beyond the dominant frequency of the source ($( {f > 3{f}_d} )$, the damage process produces an additional burst of energy mainly in the Pwaves. This eccess of high-frequency energy is observed by comparing the radiated energy to a standard Brune's model with a decay slope of the radiated energy of n = 2. While the Swaves show good agreement with the n = 2 slope, the Pwaves have a milder slope of n = 1.75 or less depending on the damage evolution at the source. In the used damage-breakage rheology, the rate of damage diffusivity governs the damage evolution perpendicular to the rupture direction and dynamic changes of the damage zone width. For increasing values of damage diffusivity, dilatational energy becomes more prominent during rupture, producing a high-frequency dilatational signature within the radiation pattern. The high-frequency radiation pattern of the Pwaves includes two main lobes perpendicular to the rupture direction, reflecting high-rate local tensile cracking during the overall shear rupture process. Analysing the possible existence and properties of such high-frequency radiation pattern in observed Pwaves could provide important information on earthquake source processes.

 

We propose a theoretical modelling framework for earthquake occurrence and clustering based on a family of invariant Galton–Watson (IGW) stochastic branching processes. The IGW process is a rigorously defined approximation to imprecisely observed or incorrectly estimated earthquake clusters modelled by Galton–Watson branching processes, including the Epidemic Type Aftershock Sequence (ETAS) model. The theory of IGW processes yields explicit distributions for multiple cluster attributes, including magnitude-dependent and magnitude-independent offspring number, cluster size and cluster combinatorial depth. Analysis of the observed seismicity in southern California demonstrates that the IGW model provides a close fit to the observed earthquake clusters. The estimated IGW parameters and derived statistics are robust with respect to the catalogue lower cut-off magnitude. The proposed model facilitates analyses of multiple quantities of seismicity based on self-similar tree attributes, and may be used to assess the proximity of seismicity to criticality.

 

The spatial geometry of seismicity encodes information about loading and failure processes, as well as properties of the underlying fault structure. Traditional approaches to characterizing geometrical attributes of seismicity rely on assumed locations and geometry of fault surfaces, particularly at depth, where resolution is overall quite poor. In this study, we develop an alternative approach to quantifying geometrical properties of seismicity using techniques from anisotropic point process theory. Our approach does not require prior knowledge about the underlying fault properties. We characterize the geometrical attributes of 32 distinct seismicity regions in California and introduce a simple four class classification scheme that covers the range of geometrical properties observed. Most of the regions classified as having localized seismicity are within northern California, while nearly all of the regions classified as having distributed seismicity are within southern California. In addition, we find that roughly 1 out of 4 regions exhibit orthogonal seismicity structures. The results of this study provide a foundation for future analyses of geometrical properties of seismicity and new observables to compare with numerical modelling studies.

 

The spatial organization of deformation may provide key information about the timing of catastrophic failure in the brittle regime. In an ideal homogenous system, deformation may continually localize toward macroscopic failure, and so increasing localization unambiguously signals approaching failure. However, recent analyses demonstrate that deformation, including low‐magnitude seismicity, and fractures and strain in triaxial compression experiments, experience temporary phases of delocalization superposed on an overall trend of localization toward large failure events. To constrain the conditions that promote delocalization, we perform a series of X‐ray tomography experiments at varying confining pressures (5–20 MPa) and fluid pressures (0–10 MPa) on Westerly granite cores with varying amounts of preexisting damage. We track the spatial distribution of the strain events with the highest magnitudes of the population within a given time step. The results show that larger confining pressure promotes more dilation, and promotes greater localization of the high strain events approaching macroscopic failure. In contrast, greater amounts of preexisting damage promote delocalization. Importantly, the dilative strain experiences more systematic localization than the shear strain, and so may provide more reliable information about the timing of catastrophic failure than the shear strain.

 

Abstract Clustering is a fundamental feature of earthquakes that impacts basic and applied analyses of seismicity. Events included in the existing short-duration instrumental catalogs are concentrated strongly within a very small fraction of the space–time volume, which is highly amplified by activity associated with the largest recorded events. The earthquakes that are included in instrumental catalogs are unlikely to be fully representative of the long-term behavior of regional seismicity. We illustrate this and other aspects of space–time earthquake clustering, and propose a quantitative clustering measure based on the receiver operating characteristic diagram. The proposed approach allows eliminating effects of marginal space and time inhomogeneities related to the geometry of the fault network and regionwide changes in earthquake rates, and quantifying coupled space–time variations that include aftershocks, swarms, and other forms of clusters. The proposed measure is used to quantify and compare earthquake clustering in southern California, western United States, central and eastern United States, Alaska, Japan, and epidemic-type aftershock sequence model results. All examined cases show a high degree of coupled space–time clustering, with the marginal space clustering dominating the marginal time clustering. Declustering earthquake catalogs can help clarify long-term aspects of regional seismicity and increase the signal-to-noise ratio of effects that are subtler than the strong clustering signatures. We illustrate how the high coupled space–time clustering can be decreased or removed using a data-adaptive parsimonious nearest-neighbor declustering approach, and emphasize basic unresolved issues on the proper outcome and quality metrics of declustering. At present, declustering remains an exploratory tool, rather than a rigorous optimization problem, and selecting an appropriate declustering method should depend on the data and problem at hand. 

Significant imbalances in terrestrial water storage (TWS) and severe drought have been observed around the world as a consequence of climate changes. Improving our ability to monitor TWS and drought is critical for water‐resource management and water‐deficit estimation. We use continuous seismic ambient noise to monitor temporal evolution of near‐surface seismic velocity,dv/v, in central Oklahoma from 2013 to 2022. The deriveddv/vis found to be negatively correlated with gravitational measurements and groundwater depths, showing the impact of groundwater storage on seismic velocities. The hydrological effects involving droughts and recharge of groundwater occur on a multi‐year time scale and dominate the overall derived velocity changes. The thermoelastic response to atmospheric temperature variations occurs primarily on a yearly timescale and dominates the superposed seasonal velocity changes in this study. The occurrences of droughts appear simultaneously with local peaks ofdv/v, demonstrating the sensitivity of near‐surface seismic velocities to droughts.