Gutenberg-Richter statistics in topologically realistic system-level earthquake stress-evolution simulations

We discuss the problem of earthquake forecasting in the context of new models for the dynamics based on statistical physics. Here we focus on new, topologically realistic system-level approaches to the modeling of earthquake faults. We show that the frictional failure physics of earthquakes in these complex, topologically realistic models leads to self-organization of the statistical dynamics, and produces statistical distributions characterizing the activity, notably the Gutenberg-Richter magnitude frequency distribution, that are similar to those observed in nature. In particular, we show that a parameterization of friction that includes a simple representation of a dynamic stress intensity factor is needed to organize the dynamics. We also show that the slip distributions for synthetic events obtained in the model are also similar to those observed in nature

Application of an inhomogeneous stress (patch) model to complex subduction zone earthquakes: A discrete interaction matrix approach

In recent years it has been recognized that the level of shear and normal stress along a fault can vary; thus the stress is spatially and temporally inhomogeneous. Moreover, it has also been suspected that faults might interact in some way, with the result that a variety of earthquake magnitudes might be produced along a given length of fault at varying times. In order to explore these ideas we have developed a quantitative formalism, which we call the interaction matrix method, to express the influence of one fault upon another. This matrix is calculated by use of the energy change for a system of interacting cracks or faults and therefore gives energy-consistent results. Specifically, the interaction matrix relates the area-averaged stress on the fault segment to the area-averaged slip state on all the other fault segments in the system. Since any fault can be subdivided into an arbitrary number of fault segments, the interaction matrix can have arbitrary dimension; in fact, the continuum limit is recovered as the dimension of the matrix approaches infinity. We combine this matrix method with a segmentation, or “patch,” model for earthquakes, in which each discrete segment of a fault has the same coseismic stress change (defined as the difference between the driving stress at which healing occurs minus the driving stress at which sliding starts) each time it slips. We show that slip on a patch during an earthquake can vary substantially, depending on how it interacts with other nearby patches. In this model it is quite possible for the spatial distribution of stress on the fault following an event to be again in a spatially inhomogeneous state, rather than in a uniform state, as is often assumed. Hence the seismic moment produced by an earthquake on a given set of patches can vary substantially, depending on the sequence of sliding and healing on the different patches. To apply these ideas, we devised a means to calculate the interaction matrix elements and used them to quantitatively examine earthquake sequences off the Colombia-Ecuador coast and in the Nankai Trough near Japan

Natural Time, Nowcasting and the Physics of Earthquakes: Estimation of Seismic Risk to Global Megacities

This paper describes the use of the idea of natural time to propose a new method for characterizing the seismic risk to the world's major cities at risk of earthquakes. Rather than focus on forecasting, which is the computation of probabilities of future events, we define the term seismic nowcasting, which is the computation of the current state of seismic hazard in a defined geographic region.Comment: 9 Figures, 4 Table

Avalanche-Burst Invasion Percolation: Emergent Scale Invariance on Pseudo-Critical System

As the variety of systems displaying scale invariant characteristics are matched only by their number, it is becoming increasingly important to understand their fundamental and universal elements. Much work has attempted to apply 2nd order phase transition mechanics due to the emergent scale invariance at the critical point. However for many systems, notions of phases and critical points are both artifical and cumbersome. We characterize the critical features of the avalanche burst invasion percolation(AIP) model since it exists as hybrid critical system(of which many self-organized critical systems may fall under). We find behavior strongly representative of critical systems, namely, from the presence of a critical Fisher type distribution, $n_s(\tau, \sigma)$, but other essential features absent like an order parameter and to a lesser degree hyperscaling. This suggests that we do not need a full phase transition description in order to observe scale invariant behavior, and provides a pathway for more suitable descriptionsComment: To be Published in Phys. Rev. E (2023