Predictability in the ETAS Model of Interacting Triggered Seismicity

As part of an effort to develop a systematic methodology for earthquake forecasting, we use a simple model of seismicity based on interacting events which may trigger a cascade of earthquakes, known as the Epidemic-Type Aftershock Sequence model (ETAS). The ETAS model is constructed on a bare (unrenormalized) Omori law, the Gutenberg-Richter law and the idea that large events trigger more numerous aftershocks. For simplicity, we do not use the information on the spatial location of earthquakes and work only in the time domain. We offer an analytical approach to account for the yet unobserved triggered seismicity adapted to the problem of forecasting future seismic rates at varying horizons from the present. Tests presented on synthetic catalogs validate strongly the importance of taking into account all the cascades of still unobserved triggered events in order to predict correctly the future level of seismicity beyond a few minutes. We find a strong predictability if one accepts to predict only a small fraction of the large-magnitude targets. However, the probability gains degrade fast when one attempts to predict a larger fraction of the targets. This is because a significant fraction of events remain uncorrelated from past seismicity. This delineates the fundamental limits underlying forecasting skills, stemming from an intrinsic stochastic component in these interacting triggered seismicity models.Comment: Latex file of 20 pages + 15 eps figures + 2 tables, in press in J. Geophys. Re

Mainshocks are aftershocks of conditional foreshocks: How do foreshock statistical properties emerge from aftershock laws

The inverse Omori law for foreshocks discovered in the 1970s states that the rate of earthquakes prior to a mainshock increases on average as a power law ~ 1/(t_c-t)^p' of the time to the mainshock occurring at t_c. Here, we show that this law results from the direct Omori law for aftershocks describing the power law decay ~ 1/(t-t_c)^p of seismicity after an earthquake, provided that any earthquake can trigger its suit of aftershocks. In this picture, the seismic activity at any time is the sum of the spontaneous tectonic loading and of the activity triggered by all preceding events weighted by their corresponding Omori law. The inverse Omori law then emerges as the expected (in a statistical sense) trajectory of seismicity, conditioned on the fact that it leads to the burst of seismic activity accompanying the mainshock. The often documented apparent decrease of the b-value of the GR law at the approach to the main shock results straightforwardly from the conditioning of the path of seismic activity culminating at the mainshock. In the space domain, we predict that the phenomenon of aftershock diffusion must have its mirror process reflected into an inward migration of foreshocks towards the mainshock. In this model, foreshock sequences are special aftershock sequences which are modified by the condition to end up in a burst of seismicity associated with the mainshock.Comment: Latex document of 35 pages, 10 figure

Electro-Magnetic Earthquake Bursts and Critical Rupture of Peroxy Bond Networks in Rocks

We propose a mechanism for the low frequency electromagnetic emissions and other electromagnetic phenomena which have been associated with earthquakes. The mechanism combines the critical earthquake concept and the concept of crust acting as a charging electric battery under increasing stress. The electric charges are released by activation of dormant charge carriers in the oxygen anion sublattice, called peroxy bonds or positive hole pairs (PHP), where a PHP represents an $O_3X/^{OO}\backslash YO_3$ with $X,Y = Si^{4+}, Al^{3+}...$, i.e. an $O^-$ in a matrix of $O^{2-}$ of silicates. We propose that PHP are activated by plastic deformations during the slow cooperative build-up of stress and the increasingly correlated damage culminating in a large ``critical'' earthquake. Recent laboratory experiments indeed show that stressed rocks form electric batteries which can release their charge when a conducting path closes the equivalent electric circuit. We conjecture that the intermittent and erratic occurrences of EM signals are a consequence of the progressive build-up of the battery charges in the Earth crust and their erratic release when crack networks are percolating throughout the stressed rock volumes, providing a conductive pathway for the battery currents to discharge. EM signals are thus expected close to the rupture, either slightly before or after, that is, when percolation is most favored.Comment: 17 pages with 3 figures, extended discussion with 1 added figure and 162 references. The new version provides both a synthesis of two theories and a review of the fiel

Tertiary sequence of deformation in a thin-skinned/thick-skinned collision belt: The Zagros Folded Belt (Fars, Iran)

International audienceWe describe how thin-skinned/thick-skinned deformation in the Zagros Folded Belt interacted in time and space. Homogeneous fold wavelengths (15.8 ± 5.3 km), tectono-sedimentary evidence for simultaneous fold growth in the past 5.5 ± 2.5 Ma, drainage network organization, and homogeneous peak differential stresses (40 ± 15 MPa) together point to buckling as the dominant process responsible for cover folding. Basin analysis reveals that basement inversion occurred ∼20 Ma ago as the Arabia/Eurasian plate convergence reduced and accumulation of Neogene siliciclastics in foreland basin started. By 10 Ma, ongoing contraction occurred by underplating of Arabian crustal units beneath the Iranian plate. This process represents 75% of the total shortening. It is not before 5 Ma that the Zagros foreland was incorporated into the southward propagating basement thrust wedge. Folds rejuvenated by 3–2 Ma because of uplift driven by basement shortening and erosion. Since then, folds grew at 0.3—0.6 mm/yr and forced the rivers to flow axially. A total shortening of 65–78 km (16–19%) is estimated across the Zagros. This corresponds to shortening rates of 6.5–8 km/Ma consistent with current geodetic surveys. We point out that although thin-skinned deformation in the sedimentary cover may be important, basement-involved shortening should not be neglected as it requires far less shortening. Moreover, for such foreland folded belts involving basement shortening, underplating may be an efficient process accommodating a significant part of the plate convergence

Gravity-driven instabilities: interplay between state-and-velocity dependent frictional sliding and stress corrosion damage cracking

We model the progressive maturation of a heterogeneous mass towards a gravity-driven instability, characterized by the competition between frictional sliding and tension cracking, using array of slider blocks on an inclined basal surface, which interact via elastic-brittle springs. A realistic state- and rate-dependent friction law describes the block-surface interaction. The inner material damage occurs via stress corrosion. Three regimes, controlling the mass instability and its precursory behavior, are classified as a function of the ratio $T_c/T_f$ of two characteristic time scales associated with internal damage/creep and with frictional sliding. For $T_c/T_f \gg 1$, the whole mass undergoes a series of internal stick and slip events, associated with an initial slow average downward motion of the whole mass, and progressively accelerates until a global coherent runaway is observed. For $T_c/T_f \ll 1$, creep/damage occurs sufficiently fast compared with nucleation of sliding, causing bonds to break, and the bottom part of the mass undergoes a fragmentation process with the creation of a heterogeneous population of sliding blocks. For the intermediate regime $T_c/T_f \sim 1$, a macroscopic crack nucleates and propagates along the location of the largest curvature associated with the change of slope from the stable frictional state in the upper part to the unstable frictional sliding state in the lower part. The other important parameter is the Young modulus $Y$ which controls the correlation length of displacements in the system.Comment: 40 pages, 13 figure

Stress and earthquakes in southern California, 1850–2004

[1] We compute the stress tensor in the upper crust of southern California as a function of time and compare observed seismicity with the estimated stress at the time of each earthquake. Several recent developments make it possible to do this much more realistically than before: ( 1) a wealth of new geodetic and geologic data for southern California and ( 2) a catalog of moment tensors for all earthquakes with magnitudes larger than 6 since 1850 and larger than 5 since 1910. We model crustal deformation using both updated geodetic data and geologically determined fault slip rates. We subdivide the crust into elastic blocks, delineated by faults which move freely at a constant rate below a locking depth with a rate determined by the relative block motion. We compute normal and shear stresses on nodal planes for each earthquake in the catalog. We consider stress increments from previous earthquakes ("seismic stress'') and aseismic tectonic stress, both separately and in combination. The locations and mechanisms of earthquakes are best correlated with the aseismic shear stress. Including the cumulative coseismic effects from past earthquakes does not significantly improve the correlation. Correlations between normal stress and earthquakes are always very sensitive to the start date of the catalog, whether we exclude earthquakes very close to others and whether we evaluate stress at the hypocenter or throughout the rupture surface of an earthquake. Although the correlation of tectonic stress with earthquake triggering is robust, other results are unstable apparently because the catalog has so few earthquakes

A reassessment of outer-rise seismicity and its implications for the mechanics of oceanic lithosphere

We use body-waveform modelling to constrain the source parameters of earthquakes occurring globally in oceanic lithosphere beneath the subduction zone outer rise and outer trench slope. These data are then used to map the stress state in the lithosphere of the downgoing plate as it bends into the subduction zone. Our results provide new constraints on the faulting of oceanic lithosphere at the outer rise, which is important for understanding the transmission of plate-driving forces through the subduction system. In all cases, shallow normal-faulting earthquakes are observed at the top of the plate, and are separated in depth from any deeper thrust-faulting earthquakes. No temporal variation associated with large thrust-faulting earthquakes on the subduction interface is seen in the depth extent of each type of faulting at the outer rise. The transition depth from trench-normal extension to compression is found to vary in agreement with models in which deformation is driven by the combination of in-plane stresses and bending stresses, resulting principally from slab pull. Combining the seismologically derived constraints on the thickness of the elastic core of the plate with estimates of the plate curvature, we place upper bounds on the strength of the lithosphere at the outer rise, which is required to be ≲300 MPa for a constant yield stress model, or governed by an effective coefficient of friction of ≲0.3