Artifactual log-periodicity in finite size data: Relevance for earthquake aftershocks

The recently proposed discrete scale invariance and its associated log-periodicity are an elaboration of the concept of scale invariance in which the system is scale invariant only under powers of specific values of the magnification factor. We report on the discovery of a novel mechanism for such log-periodicity relying solely on the manipulation of data. This ``synthetic'' scenario for log-periodicity relies on two steps: (1) the fact that approximately logarithmic sampling in time corresponds to uniform sampling in the logarithm of time; and (2) a low-pass-filtering step, as occurs in constructing cumulative functions, in maximum likelihood estimations, and in de-trending, reddens the noise and, in a finite sample, creates a maximum in the spectrum leading to a most probable frequency in the logarithm of time. We explore in detail this mechanism and present extensive numerical simulations. We use this insight to analyze the 27 best aftershock sequences studied by Kisslinger and Jones [1991] to search for traces of genuine log-periodic corrections to Omori's law, which states that the earthquake rate decays approximately as the inverse of the time since the last main shock. The observed log-periodicity is shown to almost entirely result from the ``synthetic scenario'' owing to the data analysis. From a statistical point of view, resolving the issue of the possible existence of log-periodicity in aftershocks will be very difficult as Omori's law describes a point process with a uniform sampling in the logarithm of the time. By construction, strong log-periodic fluctuations are thus created by this logarithmic sampling.Comment: LaTeX, JGR preprint with AGU++ v16.b and AGUTeX 5.0, use packages graphicx, psfrag and latexsym, 41 eps figures, 26 pages. In press J. Geophys. Re

Multifractal Scaling of Thermally-Activated Rupture Processes

We propose a ``multifractal stress activation'' model combining thermally activated rupture and long memory stress relaxation, which predicts that seismic decay rates after mainshocks follow the Omori law $\sim 1/t^p$ with exponents $p$ linearly increasing with the magnitude $M_L$ of the mainshock and the inverse temperature. We carefully test this prediction on 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 $p(M_L=3) \approx 0.6$ to $p(M_L=7) \approx 1.1$, in good agreement with the prediction of the multifractal model.Comment: four pages and 2 figure

Dragon-kings: mechanisms, statistical methods and empirical evidence

This introductory article presents the special Discussion and Debate volume "From black swans to dragon-kings, is there life beyond power laws?" published in Eur. Phys. J. Special Topics in May 2012. We summarize and put in perspective the contributions into three main themes: (i) mechanisms for dragon-kings, (ii) detection of dragon-kings and statistical tests and (iii) empirical evidence in a large variety of natural and social systems. Overall, we are pleased to witness significant advances both in the introduction and clarification of underlying mechanisms and in the development of novel efficient tests that demonstrate clear evidence for the presence of dragon-kings in many systems. However, this positive view should be balanced by the fact that this remains a very delicate and difficult field, if only due to the scarcity of data as well as the extraordinary important implications with respect to hazard assessment, risk control and predictability.Comment: 20 page

New model for surface fracture induced by dynamical stress

We introduce a model where an isotropic, dynamically-imposed stress induces fracture in a thin film. Using molecular dynamics simulations, we study how the integrated fragment distribution function depends on the rate of change and magnitude of the imposed stress, as well as on temperature. A mean-field argument shows that the system becomes unstable for a critical value of the stress. We find a striking invariance of the distribution of fragments for fixed ratio of temperature and rate of change of the stress; the interval over which this invariance holds is determined by the force fluctuations at the critical value of the stress.Comment: Revtex, 4 pages, 4 figures available upon reques

A review of selected indicators of particle, nutrient and metal inputs in coral reef lagoon systems

This review presents environmental and biological indicators of the impact of three major categories of inputs in coral reef lagoons i.e. particles, nutrients and metals. Information was synthesized to extract well established indicators together with some interesting new concepts currently under development, and to provide the reader with an assessment of their respective advantages and drawbacks. The paper has been organized according to the capacity of three categories of indicators to respond either in a specific or a non specific way to a given source of input. The first section focuses on abiotic indicators which main interest is to respond instantaneously and in a truly specific way to a given source of input. The second and third sections present informations on bioindicators either at the sub-individual level or at the individual to community level, indicator specificity generally decreasing as a direct function of biological or ecological complexity. This review showed that even though significant work has already been done on coral reef ecosystems, much more scientific studies are still needed to answer the growing local demands for simple and truly validated tools to be used in environmental surveys. It is further stressed that, due to the biological and environmental diversity of coral reef lagoons, a preliminary step of on-site validation must be considered as an absolute prerequisite when indicators are planned to be used in the frame of a local environmental monitoring programme

Origine, transport et devenir des apports naturels et anthropiques dans le lagon sud-ouest de Nouvelle-Calédonie

L’ird (Institut de recherche pour le développement) conduit depuis dix ans un programme pluridisciplinaire sur les effets des apports naturels et anthropiques sur le fonctionnement du lagon de Nouvelle-Calédonie. Celle-ci connaît actuellement une croissance de sa population et un développement de son industrie minière. Trois grands types d’apports sont pris en compte : les particules entraînées par l’érosion des sols et des sous-sols et dont l'accumulation brutale peut être responsable du dépôt de quantités considérables de sédiments, les métaux potentiellement toxiques pour les organismes vivant dans le lagon et les éléments nutritifs susceptibles de conduire les eaux jusqu'à l’eutrophisation (confinement chimique conduisant à l'élimination de nombreuses espèces vivantes et à la dominance d'un petit nombre d'autres). Le présent article offre trois exemples de problématiques environnementales qui n'ont pu être résolues qu’au moyen de la fédération de différentes approches de recherche complémentaires : l’influence des courants sur la dispersion des particules détritiques en provenance de l'île, le devenir des métaux dans le lagon et leur accumulation dans les organismes, les effets des apports en nutriments sur les communautés planctoniques et les risques d'eutrophisation. Les résultats de ces recherches sont présentés tout en conservant à l’esprit les objectifs nécessairement appliqués d’un programme de recherche pour le développement. Il s’agit principalement de définir les bases scientifiques permettant d’identifier certains outils de diagnostic environnemental et de développer des approches de simulation mathématique susceptibles d'offrir une vision synthétique et prévisionnelle de l’état et du devenir des environnements lagonaires sous influence anthropique.For the past ten years, the ird (Institut de recherche pour le développement) has developed a multidisciplinary programme dealing with the effects of natural and anthropogenic terrigenous inputs on the New Caledonia coral reef lagoon which is currently subjected to environmental pressure due to population increase and development of the mining industry. The ongoing study focused on three main categories of inputs: (i) particles generated by erosion processes and responsible for excessive sediment inputs in the lagoon, (ii) metals exhibiting a potentially lethal effect on the lagoon biota, (iii) nutrients responsible for eutrophication. This article presents three examples of environmental issues that could be addressed through complementary research approaches: (i) the dispersion of terrigenous inputs as commended by currents, (ii) the fate of metals in the lagoon and their accumulation in the biota, (iii) the effects of nutrient enrichment on pelagic communities. Results are presented while keeping in mind the necessary applied outcomes requested from a research programme devoted to development issues. Such outcomes are mainly related to the identification of suited environmental diagnostic tools and to the development of modelling approaches yielding synthetic and predictive information on the status and fate of coral reef lagoons subject to anthropogenic stress

Beam Charge Asymmetries for Deeply Virtual Compton Scattering on the Proton at CLAS12

The parameterization of the nucleon structure through Generalized Parton Distributions (GPDs) shed a new light on the nucleon internal dynamics. For its direct interpretation, Deeply Virtual Compton Scattering (DVCS) is the golden channel for GPDs investigation. The DVCS process interferes with the Bethe-Heitler (BH) mechanism to constitute the leading order amplitude of the $eN \to eN\gamma$ process. The study of the $ep\gamma$ reaction with polarized positron and electron beams gives a complete set of unique observables to unravel the different contributions to the $ep \gamma$ cross section. This separates the different reaction amplitudes, providing a direct access to their real and imaginary parts which procures crucial constraints on the model dependences and associated systematic uncertainties on GPDs extraction. The real part of the BH-DVCS interference amplitude is particularly sensitive to the $D$-term which parameterizes the Gravitational Form Factors of the nucleon. The separation of the imaginary parts of the interference and DVCS amplitudes provides insights on possible higher-twist effects. We propose to measure the unpolarized and polarized Beam Charge Asymmetries (BCAs) of the $\vec{e}^{\pm}p \to e^{\pm}p \gamma$ process on an unpolarized hydrogen target with {\tt CLAS12}, using polarized positron and electron beams at 10.6~GeV. The azimuthal and $t$-dependences of the unpolarized and polarized BCAs will be measured over a large $(x_B,Q^2)$ phase space using a 100 day run with a luminosity of 0.66$\times 10^{35}$cm$^{-2}\cdot$s$^{-1}$.Comment: Proposal to the Jefferson Lab Program Advisory Committee (PAC51

Impact of the spatial resolution of satellite remote sensing sensors in the quantification of total suspended sediment concentration: A case study in turbid waters of Northern Western Australia

The impact of anthropogenic activities on coastal waters is a cause of concern because such activities add to the total suspended sediment (TSS) budget of the coastal waters, which have negative impacts on the coastal ecosystem. Satellite remote sensing provides a powerful tool in monitoring TSS concentration at high spatiotemporal resolution, but coastal managers should be mindful that the satellite-derived TSS concentrations are dependent on the satellite sensor's radiometric properties, atmospheric correction approaches, the spatial resolution and the limitations of specific TSS algorithms. In this study, we investigated the impact of different spatial resolutions of satellite sensor on the quantification of TSS concentration in coastal waters of northern Western Australia. We quantified the TSS product derived from MODerate resolution Imaging Spectroradiometer (MODIS)-Aqua, Landsat-8 Operational Land Image (OLI), and WorldView-2 (WV2) at native spatial resolutions of 250 m, 30 m and 2 m respectively and coarser spatial resolution (resampled up to 5 km) to quantify the impact of spatial resolution on the derived TSS product in different turbidity conditions. The results from the study show that in the waters of high turbidity and high spatial variability, the high spatial resolution WV2 sensor reported TSS concentration as high as 160 mg L-1 while the low spatial resolution MODIS-Aqua reported a maximum TSS concentration of 23.6 mg L-1. Degrading the spatial resolution of each satellite sensor for highly spatially variable turbid waters led to variability in the TSS concentrations of 114.46%, 304.68% and 38.2% for WV2, Landsat-8 OLI and MODIS-Aqua respectively. The implications of this work are particularly relevant in the situation of compliance monitoring where operations may be required to restrict TSS concentrations to a pre-defined limit

GLORIA - A globally representative hyperspectral in situ dataset for optical sensing of water quality

The development of algorithms for remote sensing of water quality (RSWQ) requires a large amount of in situ data to account for the bio-geo-optical diversity of inland and coastal waters. The GLObal Reflectance community dataset for Imaging and optical sensing of Aquatic environments (GLORIA) includes 7,572 curated hyperspectral remote sensing reflectance measurements at 1 nm intervals within the 350 to 900 nm wavelength range. In addition, at least one co-located water quality measurement of chlorophyll a, total suspended solids, absorption by dissolved substances, and Secchi depth, is provided. The data were contributed by researchers affiliated with 59 institutions worldwide and come from 450 different water bodies, making GLORIA the de-facto state of knowledge of in situ coastal and inland aquatic optical diversity. Each measurement is documented with comprehensive methodological details, allowing users to evaluate fitness-for-purpose, and providing a reference for practitioners planning similar measurements. We provide open and free access to this dataset with the goal of enabling scientific and technological advancement towards operational regional and global RSWQ monitoring