Persistence and Quiescence of Seismicity on Fault Systems

We study the statistics of simulated earthquakes in a quasistatic model of two parallel heterogeneous faults within a slowly driven elastic tectonic plate. The probability that one fault remains dormant while the other is active for a time Dt following the previous activity shift is proportional to the inverse of Dt to the power 1+x, a result that is robust in the presence of annealed noise and strength weakening. A mean field theory accounts for the observed dependence of the persistence exponent x as a function of heterogeneity and distance between faults. These results continue to hold if the number of competing faults is increased. This is related to the persistence phenomenon discovered in a large variety of systems, which specifies how long a relaxing dynamical system remains in a neighborhood of its initial configuration. Our persistence exponent is found to vary as a function of heterogeneity and distance between faults, thus defining a novel universality class.Comment: 4 pages, 3 figures, Revte

Localized Amplification of Seismic Waves and Correlation with Damage Due to the Northridge Earthquake: Evidence for Focusing in Santa Monica

The analysis of seismograms from 32 aftershocks recorded by 98 seismic stations installed after the Northridge earthquake in the San Fernando Valley, the Santa Monica Mountains, and Santa Monica, California, indicates that the enhanced damage in Santa Monica is explained in the main by focusing due to a lens structure at a depth of several kilometers beneath the surface and having a finite lateral extent. The diagnosis was made from the observation of late-arriving S phases with large amplitudes, localized in the zones of large damage. The azimuths and angles of incidence of the seismic rays that give rise to the greatest focusing effects correspond to radiation that would have emerged from the lower part of the rupture surface of the mainshock. Thus the focusing and, hence, the large damage in Santa Monica were highly dependent on the location of the Northridge event, and an earthquake of similar size, located as little as one source dimension away, would not be likely to repeat this pattern. We show from coda wave analysis that the influence of surface geology as well as site effects on damage in Santa Monica is significantly smaller than are the focusing effects

Seasonally Forced SIR Systems Applied to Respiratory Infectious Diseases, Bifurcations, and Chaos

We investigate models to describe respiratory diseases with fast mutating virus pathogens such that after some years the aquired resistance is lost and hosts can be infected with new variants of the pathogen. Such models were initially suggested for respiartory diseases like influenza, showing complex dynamics in reasonable parameter regions when comparing to historic empirical influenza like illness data, e.g., from Ille de France. The seasonal forcing typical for respiratory diseases gives rise to the different rich dynamical scenarios with even small parameter changes. Especially the seasonality of the infection leads for small values already to period doubling bifurcations into chaos, besides additional coexisting attractors. Such models could in the future also play a role in understanding the presently experienced COVID-19 pandemic, under emerging new variants and with only limited vaccine efficacies against newly upcoming variants. From first period doubling bifurcations, we can eventually infer at which close by parameter regions complex dynamics including deterministic chaos can arise.Marie Skłodowska-Curie grant agreement No. 79249

Precession of a Freely Rotating Rigid Body. Inelastic Relaxation in the Vicinity of Poles

When a solid body is freely rotating at an angular velocity ${\bf \Omega}$, the ellipsoid of constant angular momentum, in the space $\Omega_1, \Omega_2, \Omega_3$, has poles corresponding to spinning about the minimal-inertia and maximal-inertia axes. The first pole may be considered stable if we neglect the inner dissipation, but becomes unstable if the dissipation is taken into account. This happens because the bodies dissipate energy when they rotate about any axis different from principal. In the case of an oblate symmetrical body, the angular velocity describes a circular cone about the vector of (conserved) angular momentum. In the course of relaxation, the angle of this cone decreases, so that both the angular velocity and the maximal-inertia axis of the body align along the angular momentum. The generic case of an asymmetric body is far more involved. Even the symmetrical prolate body exhibits a sophisticated behaviour, because an infinitesimally small deviation of the body's shape from a rotational symmetry (i.e., a small difference between the largest and second largest moments of inertia) yields libration: the precession trajectory is not a circle but an ellipse. In this article we show that often the most effective internal dissipation takes place at twice the frequency of the body's precession. Applications to precessing asteroids, cosmic-dust alignment, and rotating satellites are discussed.Comment: 47 pages, 1 figur

Avalanches in the Weakly Driven Frenkel-Kontorova Model

A damped chain of particles with harmonic nearest-neighbor interactions in a spatially periodic, piecewise harmonic potential (Frenkel-Kontorova model) is studied numerically. One end of the chain is pulled slowly which acts as a weak driving mechanism. The numerical study was performed in the limit of infinitely weak driving. The model exhibits avalanches starting at the pulled end of the chain. The dynamics of the avalanches and their size and strength distributions are studied in detail. The behavior depends on the value of the damping constant. For moderate values a erratic sequence of avalanches of all sizes occurs. The avalanche distributions are power-laws which is a key feature of self-organized criticality (SOC). It will be shown that the system selects a state where perturbations are just able to propagate through the whole system. For strong damping a regular behavior occurs where a sequence of states reappears periodically but shifted by an integer multiple of the period of the external potential. There is a broad transition regime between regular and irregular behavior, which is characterized by multistability between regular and irregular behavior. The avalanches are build up by sound waves and shock waves. Shock waves can turn their direction of propagation, or they can split into two pulses propagating in opposite directions leading to transient spatio-temporal chaos. PACS numbers: 05.70.Ln,05.50.+q,46.10.+zComment: 33 pages (RevTex), 15 Figures (available on request), appears in Phys. Rev.

Aperiodicity in one-way Markov cycles and repeat times of large earthquakes in faults

A common use of Markov Chains is the simulation of the seismic cycle in a fault, i.e. as a renewal model for the repetition of its characteristic earthquakes. This representation is consistent with Reid's elastic rebound theory. Here it is proved that in {\it any} one-way Markov cycle, the aperiodicity of the corresponding distribution of cycle lengths is always lower than one. This fact concurs with observations of large earthquakes in faults all over the world

Use of specific Green's functions for solving direct problems involving a heterogeneous rigid frame porous medium slab solicited by acoustic waves

A domain integral method employing a specific Green's function (i.e., incorporating some features of the global problem of wave propagation in an inhomogeneous medium) is developed for solving direct and inverse scattering problems relative to slab-like macroscopically inhomogeneous porous obstacles. It is shown how to numerically solve such problems, involving both spatially-varying density and compressibility, by means of an iterative scheme initialized with a Born approximation. A numerical solution is obtained for a canonical problem involving a two-layer slab.Comment: submitted to Math.Meth.Appl.Sc

On the Occurrence of Finite-Time-Singularities in Epidemic Models of Rupture, Earthquakes and Starquakes

We present a new kind of critical stochastic finite-time-singularity, relying on the interplay between long-memory and extreme fluctuations. We illustrate it on the well-established epidemic-type aftershock (ETAS) model for aftershocks, based solely on the most solidly documented stylized facts of seismicity (clustering in space and in time and power law Gutenberg-Richter distribution of earthquake energies). This theory accounts for the main observations (power law acceleration and discrete scale invariant structure) of critical rupture of heterogeneous materials, of the largest sequence of starquakes ever attributed to a neutron star as well as of earthquake sequences.Comment: Revtex document of 4 pages including 1 eps figur

The Slab Puzzle of the Alpine‐Mediterranean Region: Insights from a new, High‐Resolution, Shear‐Wave Velocity Model of the Upper Mantle

Mediterranean tectonics since the Lower Cretaceous has been characterized by a multi‐phase subduction and collision history with temporally and spatially‐variable, small‐scale plate configurations. A new shear‐wave velocity model of the Mediterranean upper mantle (MeRE2020), constrained by a very large set of over 200,000 broadband (8‐350 s), inter‐station, Rayleigh‐wave, phase‐velocity curves, illuminates the complex structure and fragmentation of the subducting slabs. Phase‐velocity maps computed using these measurements were inverted for depth‐dependent, shear‐wave velocities using a stochastic particle‐swarm‐optimization algorithm (PSO). The resulting three‐dimensional (3‐D) model makes possible an inventory of slab segments across the Mediterranean. Fourteen slab segments of 200‐800 km length along‐strike are identified. We distinguish three categories of subducted slabs: attached slabs reaching down to the bottom of the model; shallow slabs of shorter length in down‐dip direction, terminating shallower than 300 km depth; and detached slab segments. The location of slab segments are consistent with and validated by the intermediate‐depth seismicity, where it is present. The new high‐resolution tomography demonstrates the intricate relationships between slab fragmentation and the evolution of the relatively small and highly curved subduction zones and collisional orogens characteristic of the Mediterranean realm