The Barycentric Fixed Mass Method for Multifractal Analysis

We present a novel method to estimate the multifractal spectrum of point distributions. The method incorporates two motivated criteria (barycentric pivot point selection and non-overlapping coverage) in order to reduce edge effects, improve precision and reduce computation time. Implementation of the method on synthetic benchmarks demonstrates the superior performance of the proposed method compared with existing alternatives routinely used in the literature. Finally, we use the method to estimate the multifractal properties of the widely studied growth process of Diffusion Limited Aggregation and compare our results with recent and earlier studies. Our tests support the conclusion of a genuine but weak multifractality of the central core of DLA clusters, with Dq decreasing from 1.75+/-0.01 for q=-10 to 1.65+/-0.01 for q=+10

Forecasting the rates of future aftershocks of all generations is essential to develop better earthquake forecast models

Currently, one of the best performing and most popular earthquake forecasting models rely on the working hypothesis that: "locations of past background earthquakes reveal the probable location of future seismicity". As an alternative, we present a class of smoothed seismicity models (SSMs) based on the principles of the Epidemic Type Aftershock Sequence (ETAS) model, which forecast the location, time and magnitude of all future earthquakes using the estimates of the background seismicity rate and the rates of future aftershocks of all generations. Using the Californian earthquake catalog, we formulate six controlled pseudo-prospective experiments with different combination of three target magnitude thresholds: 2.95, 3.95 or 4.95 and two forecasting time horizons: 1 or 5 year. In these experiments, we compare the performance of:(1) ETAS model with spatially homogenous parameters or GETAS (2) ETAS model with spatially variable parameters or SVETAS (3) three declustering based SSMs (4) a simple SSM based on undeclustered data and (5) a model based on strain rate data, in forecasting the location and magnitude of all (undeclustered) target earthquakes during many testing periods. In all conducted experiments, the SVETAS model comes out with consistent superiority compared to all the competing models. Consistently better performance of SVETAS model with respect to declustering based SSMs highlights the importance of forecasting the future aftershocks of all generations for developing better earthquake forecasting models. Among the two ETAS models themselves, accounting for the optimal spatial variation of the parameters leads to strong and statistically significant improvements in forecasting performance

Forecasting the full distribution of earthquake numbers is fair, robust and better

Forecasting the full distribution of the number of earthquakes is revealed to be inherently superior to forecasting their mean. Forecasting the full distribution of earthquake numbers is also shown to yield robust projections in the presence of "surprise" large earthquakes, which in the past have strongly deteriorated the scores of existing models. We show this with pseudo-prospective experiments on synthetic as well as real data from the Advanced National Seismic System (ANSS) database for California, with earthquakes with magnitude larger than 2.95 that occurred between the period 1971-2016. Our results call in question the testing methodology of the Collaboratory for the study of earthquake predictability (CSEP), which amounts to assuming a Poisson distribution of earthquake numbers, which is known to be a poor representation of the heavy-tailed distribution of earthquake numbers. Using a spatially varying ETAS model, we demonstrate a remarkable stability of the forecasting performance, when using the full distribution of earthquake numbers for the forecasts, even in the presence of large earthquakes such as Mw 7.1 Hector Mine, Mw 7.2 El Mayor-Cucapah, Mw 6.6 Sam Simeon earthquakes, or in the presence of intense swarm activity in Northwest Nevada in 2014. While our results have been derived for ETAS type models, we propose that all earthquake forecasting models of any type should embrace the full distribution of earthquake numbers, such that their true forecasting potential is revealed

Objective Estimation of Spatially Variable Parameters of Epidemic Type Aftershock Sequence Model: Application to California

The ETAS model is widely employed to model the spatio-temporal distribution of earthquakes, generally using spatially invariant parameters. We propose an efficient method for the estimation of spatially varying parameters, using the Expectation-Maximization (EM) algorithm and spatial Voronoi tessellation ensembles. We use the Bayesian Information Criterion (BIC) to rank inverted models given their likelihood and complexity and select the best models to finally compute an ensemble model at any location. Using a synthetic catalog, we also check that the proposed method correctly inverts the known parameters. We apply the proposed method to earthquakes included in the ANSS catalog that occurred within the time period 1981-2015 in a spatial polygon around California. The results indicate a significant spatial variation of the ETAS parameters. We find that the efficiency of earthquakes to trigger future ones (quantified by the branching ratio) positively correlates with surface heat flow. In contrast, the rate of earthquakes triggered by far-field tectonic loading or background seismicity rate shows no such correlation, suggesting the relevance of triggering possibly through fluid-induced activation. Furthermore, the branching ratio and background seismicity rate are found to be uncorrelated with hypocentral depths, indicating that the seismic coupling remains invariant of hypocentral depths in the study region. Additionally, triggering seems to be mostly dominated by small earthquakes. Consequently, the static stress change studies should not only focus on the Coulomb stress changes caused by specific moderate to large earthquakes but also account for the secondary static stress changes caused by smaller earthquakes

Systematic Assessment of the Static Stress-Triggering Hypothesis using Inter-earthquake Time Statistics

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, Skempton's 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

Magnitude Of Earthquakes Controls The Size Distribution Of Their Triggered Events

The driving concept behind one of the most successful statistical forecasting models, the ETAS model, has been that the seismicity is driven by spontaneously occurring background earthquakes that cascade into multitudes of triggered earthquakes. In nearly all generalizations of the ETAS model, the magnitudes of the background and the triggered earthquakes are assumed to follow Gutenberg-Richter law with the same exponent (\b{eta}-value). Furthermore, the magnitudes of the triggered earthquakes are always assumed to be independent of the magnitude of the triggering earthquake. Using an EM algorithm applied to the Californian earthquake catalogue, we show that the distribution of earthquake magnitudes exhibits three distinct \b{eta}-values: \b{eta}_b for background events; \b{eta}_a-{\delta} and \b{eta}_a+{\delta}, respectively, for triggered events below and above the magnitude of the triggering earthquake; the two last values express a correlation between the magnitudes of triggered events with that of the triggering earthquake, a feature so far absent in all proposed operational generalizations of the ETAS model. The ETAS model incorporating this kinked magnitude distribution provides by far the best description of seismic catalogs and could thus have the best forecasting potential. We speculate that the kinked magnitude distribution may result from the system tending to restore the symmetry of the regional displacement gradient tensor that has been broken by the initiating event. The general emerging concept could be that while the background events occur primarily to accommodate the symmetric stress tensor at the boundaries of the system, the triggered earthquakes are quasi-Goldstone fluctuations of a self-organized critical deformation state.Comment: Accepted for publication in JGR: Solid Eart

Earthquake precursors in the light of peroxy defects theory: critical review of systematic observations

The starting point of the present review is to acknowledge that there are innumerable reports of non-seismic types of earthquake precursory phenomena that are intermittent and seem not to occur systematically, while associated reports are not widely accepted by the geoscience community at large because no one could explain their origins. We review a unifying theory for a solid-state mechanism, based on decades of research bridging semi-conductor physics, chemistry and rock physics. A synthesis has emerged that all pre-earthquake phenomena could trace back to one fundamental physical process: the activation of electronic charges (electrons and positive holes) in rocks subjected to ever-increasing tectonic stresses prior to any major seismic activity, via the rupture of peroxy bonds. In the second part of the review, we critically examine satellite and ground station data, recorded before past large earthquakes, as they have been claimed to provide evidence that precursory signals tend to become measurable days, sometimes weeks before the disasters. We review some of the various phenomena that can be directly predicted by the peroxy defect theory , namely, radon gas emanations, corona discharges, thermal infrared emissions, air ionization, ion and electron content in the ionosphere, and electro-magnetic anomalies. Our analysis demonstrates the need for further systematic investigations, in particular with strong continuous statistical testing of the relevance and confidence of the precursors. Only then, the scientific community will be able to assess and improve the performance of earthquake forecasts

Is seismicity operating at a critical point?

Seismicity and faulting within the Earth crust are characterized by many scaling laws that are usually interpreted as qualifying the existence of underlying physical mechanisms associated with some kind of criticality in the sense of phase transitions. Using an augmented Epidemic-Type Aftershock Sequence (ETAS) model that accounts for the spatial variability of the background rates $\mu(x,y)$, we present a direct quantitative test of criticality. We calibrate the model to the ANSS catalog of the entire globe, the region around California, and the Geonet catalog for the region around New Zealand using an extended Expectation-Maximization (EM) algorithm including the determination of $\mu(x,y)$. We demonstrate that the criticality reported in previous studies is spurious and can be attributed to a systematic upward bias in the calibration of the branching ratio of the ETAS model, when not accounting correctly for spatial variability. We validate the version of the ETAS model which possesses a space varying background rate $\mu(x,y)$ by performing pseudo prospective forecasting tests. The non-criticality of seismicity has major implications for the prediction of large events

A paradigm for developing earthquake probability forecasts based on geoelectric data

We examine the precursory behavior of geoelectric signals before large earthquakes by means of an algorithm including an alarm-based model and binary classification. This algorithm, introduced originally by Chen and Chen [Nat. Hazards., 84, 2016], is improved by removing a time parameter for coarse-graining of earthquake occurrences, as well as by extending the single station method into a joint stations method. We also determine the optimal frequency bands of earthquake-related geoelectric signals with the highest signal-to-noise ratio. Using significance tests, we also provide evidence of an underlying seismoelectric relationship. It is appropriate for machine learning to extract this underlying relationship, which could be used to quantify probabilistic forecasts of impending earthquakes, and to get closer to operational earthquake prediction

Coupled mechano-electrokinetic Burridge-Knopoff model of fault sliding events and transient geoelectric signals

We introduce the first fully self-consistent model combining the seismic micro-ruptures occurring within a generalized Burridge-Knopoff spring-block model with the nucleation and propagation of electric charge pulses within a coupled mechano-electrokinetic system. This model provides a general theoretical framework for modeling and analyzing geoelectric precursors to earthquakes. In particular, it can reproduce the unipolar pulses that have often been reported before large seismic events, as well as various observed anomalies in the statistical moments of the ambient electric fields and the power-law exponent transition of the power spectra of electric fields