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Register a new userMultifractal Omori Law for Earthquake Triggering: New Tests on the California, Japan and Worldwide Catalogs
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The Multifractal Stress-Activated (MSA) model is a statistical model of triggered seismicity based on mechanical and thermodynamic principles. It predicts that, above a triggering magnitude cut-off $M_0$, the exponent $p$ of the Omori law for the seismic decay of aftershocks is a linear increasing function $p(M) =a M+b$ of the main shock magnitude $M$. We previously reported empirical support for this prediction, using the Southern California SCEC catalog. Here, we confirm this law using an updated, longer version of the same catalog, as well as new methods to estimate $p$. One of this methods is the newly defined Scaling Function Analysis, adapted from the wavelet transform. This method is able to measure a singularity ($p$-value), erasing the possible regular part of a time series. The Scaling Function Analysis also proves particularly efficient to reveal the coexistence of several types of relaxation laws (typical Omori sequences and short-lived swarms sequences) which can be mixed within the same catalog. The same methods are used on data from the worlwide Harvard CMT and show results compatible with those of Southern California. For the Japanese JMA catalog, we still observe a linear dependence of $p$ on $M$, yet with a smaller slope. The scaling function analysis shows however that results for this catalog may be biased by numerous swarm sequences, despite our efforts to remove them before the analysis.
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Plate motions are governed by equilibrium between basal and edge forces. Great earthquakes may induce differential static stress changes across tectonic plates, enabling a new equilibrium state. Here we consider the torque balance for idealized circular plates and find a simple scalar relationship for changes in relative plate speed as a function of its size, upper mantle viscosity, and coseismic stress changes. Applied to Japan, the 2011 $mathrm{M}_{mathrm{W}}=9.0$ Tohoku earthquake generated coseismic stresses of $10^2-10^5$~Pa that could have induced changes in motion of small (radius $sim100$~km) crustal blocks within Honshu. Analysis of time-dependent GPS velocities, with corrections for earthquake cycle effects, reveals that plate speeds may have changed by up to $sim3$ mm/yr between $sim3.75$-year epochs bracketing this earthquake, consistent with an upper mantle viscosity of $sim 5times10^{18}$Pa$cdot$s, suggesting that great earthquakes may modulate motions of proximal crustal blocks at frequencies as high as $10^-8$~Hz.
A likely source of earthquake clustering is static stress transfer between individual events. Previous attempts to quantify the role of static stress for earthquake triggering generally considered only the stress changes caused by large events, and often discarded data uncertainties. We conducted a robust two-fold empirical test of the static stress change hypothesis by accounting for all events of magnitude M>=2.5 and their location and focal mechanism uncertainties provided by catalogs for Southern California between 1981 and 2010, first after resolving the focal plane ambiguity and second after randomly choosing one of the two nodal planes. For both cases, we find compelling evidence supporting the static triggering with stronger evidence after resolving the focal plane ambiguity above significantly small (about 10 Pa) but consistently observed stress thresholds. The evidence for the static triggering hypothesis is robust with respect to the choice of the friction coefficient, Skemptons coefficient and magnitude threshold. Weak correlations between the Coulomb Index (fraction of earthquakes that received positive Coulomb stress change) and the coefficient of friction indicate that the role of normal stress in triggering is rather limited. Last but not the least, we determined that the characteristic time for the loss of the stress change memory of a single event is nearly independent of the amplitude of the Coulomb stress change and varies between ~95 and ~180 days implying that forecasts based on static stress changes will have poor predictive skills beyond times that are larger than a few hundred days on average.
We present the condensation method that exploits the heterogeneity of the probability distribution functions (PDF) of event locations to improve the spatial information content of seismic catalogs. The method reduces the size of seismic catalogs while improving the access to the spatial information content of seismic catalogs. The PDFs of events are first ranked by decreasing location errors and then successively condensed onto better located and lower variance event PDFs. The obtained condensed catalog attributes different weights to each event, providing an optimal spatial representation with respect to the spatially varying location capability of the seismic network. Synthetic tests on fractal distributions perturbed with realistic location errors show that condensation improves spatial information content of the original catalog. Applied to Southern California seismicity, the new condensed catalog highlights major mapped fault traces and reveals possible additional structures while reducing the catalog length by ~25%. The condensation method allows us to account for location error information within a point based spatial analysis. We demonstrate this by comparing the multifractal properties of the condensed catalog locations with those of the original catalog. We evidence different spatial scaling regimes characterized by distinct multifractal spectra and separated by transition scales. We interpret the upper scale as to agree with the thickness of the brittle crust, while the lower scale (2.5km) might depend on the relocation procedure. Accounting for these new results, the Epidemic Type Aftershock Model formulation suggests that, contrary to previous studies, large earthquakes dominate the earthquake triggering process. This implies that the limited capability of detecting small magnitude events cannot be used to argue that earthquakes are unpredictable in general.
We consider a general stochastic branching process, which is relevant to earthquakes as well as to many other systems, and we study the distributions of the total number of offsprings (direct and indirect aftershocks in seismicity) and of the total number of generations before extinction. We apply our results to a branching model of triggered seismicity, the ETAS (epidemic-type aftershock sequence) model. The ETAS model assumes that each earthquake can trigger other earthquakes (``aftershocks). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. Due to the large fluctuations of the number of aftershocks triggered directly by any earthquake (``fertility), there is a large variability of the total number of aftershocks from one sequence to another, for the same mainshock magnitude. We study the regime where the distribution of fertilities mu is characterized by a power law ~1/mu^(1+gamma). For earthquakes, we expect such a power-law distribution of fertilities with gamma = b/alpha based on the Gutenberg-Richter magnitude distribution ~10^(-bm) and on the increase ~10^(alpha m) of the number of aftershocks with the mainshock magnitude m. We derive the asymptotic distributions p_r(r) and p_g(g) of the total number r of offsprings and of the total number g of generations until extinction following a mainshock. In the regime gamma<2 relevant for earhquakes, for which the distribution of fertilities has an infinite variance, we find p_r(r)~1/r^(1+1/gamma) and p_g(g)~1/g^(1+1/(gamma -1)). These predictions are checked by numerical simulations.
We propose a new physically-based ``multifractal stress activation model of earthquake interaction and triggering based on two simple ingredients: (i) a seismic rupture results from activated processes giving an exponential dependence on the local stress; (ii) the stress relaxation has a long memory. The combination of these two effects predicts in a rather general way that seismic decay rates after mainshocks follow the Omori law 1/t^p with exponents p linearly increasing with the magnitude M of the mainshock and the inverse temperature. We carefully test the prediction on the magnitude dependence of p by a detailed analysis of earthquake sequences in the Southern California Earthquake catalog. We find power law relaxations of seismic sequences triggered by mainshocks with exponents p increasing with the mainshock magnitude by approximately 0.1-0.15 for each magnitude unit increase, from p(M=3) approx 0.6 to p(M=7) approx 1.1, in good agreement with the prediction of the multifractal model. The results are robust with respect to different time intervals, magnitude ranges and declustering methods. When applied to synthetic catalogs generated by the ETAS (Epidemic-Type Aftershock Sequence) model constituting a strong null hypothesis with built-in magnitude-independent $p$-values, our procedure recovers the correct magnitude-independent p-values. Our analysis thus suggests that a new important fact of seismicity has been unearthed. We discuss alternative interpretations of the data and describe other predictions of the model.
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