Éditeur(s) : HAL CCSD Ecological Society of America
Résumé : Although niche-based and stochastic processes, including dispersal limitation and demographic stochasticity, can each contribute to community assembly, it is difficult to quantify the relative importance of each process in natural vegetation. Here, we extend Shipley's maxent model (Community Assembly by Trait Selection, CATS) for the prediction of relative abundances to incorporate both trait-based filtering and dispersal limitation from the larger landscape and develop a statistical decomposition of the proportions of the total information content of relative abundances in local communities that are attributable to trait-based filtering, dispersal limitation, and demographic stochasticity. We apply the method to tree communities in a mature, species-rich, tropical forest in French Guiana at 1-, 0.25- and 0.04-ha scales. Trait data consisted of species' means of 17 functional traits measured over both the entire meta-community and separately in each of nine 1-ha plots. Trait means calculated separately for each site always gave better predictions. There was clear evidence of trait-based filtering at all spatial scales. Trait-based filtering was the most important process at the 1-ha scale (34%), whereas demographic stochasticity was the most important at smaller scales (37-53%). Dispersal limitation from the meta-community was less important and approximately constant across scales (similar to 9%), and there was also an unresolved association between site-specific traits and meta-community relative abundances. Our method allows one to quantify the relative importance of local niche-based and meta-community processes and demographic stochasticity during community assembly across spatial and temporal scales.
ISSN: 0012-9658

hal-01032424
https://hal.archives-ouvertes.fr/hal-01032424

Éditeur(s) : HAL CCSD
Résumé : 20 pp
We first analyze some atmospheric parameters measured in 2004 at the top of La Soufrière volcano: wind speed, pressure and temperature. Next, we study the stochastic process of the wind speed modulus which is of interest for prediction of pollution induced by the plume. We fit to the data various models : FARIMA, periodic trend plus multifractional Brownian noise, multifractal continuous cascades. The estimations show that they evoluate during some transition phases in response to environment changes. Thus, we finally suggest, for future works, some settings that should be more appropriate: time series with regime changes and stochastic processes in random environment.
https://hal.archives-ouvertes.fr/hal-00165572

hal-00165572
https://hal.archives-ouvertes.fr/hal-00165572
https://hal.archives-ouvertes.fr/hal-00165572/document
https://hal.archives-ouvertes.fr/hal-00165572/file/Windsouf_v11.pdf

Éditeur(s) : HAL CCSD
Résumé : 15 pages
A Stochastic Differential Equation appearing in the statistical theory of turbulence is extended in random environment by assuming that its two parameters are switched by an unobserved continuoustime Markov chain whose states represent the states of the environment. A Dirichlet process is placed as a prior on the space of the sample paths of this chain, leading to a hierarchical Dirichlet model whose estimation is done both on simulated data and on real data of wind speed measured at the entrance of a mangrove ecosystem.
https://hal.archives-ouvertes.fr/hal-00455050

hal-00455050
https://hal.archives-ouvertes.fr/hal-00455050
https://hal.archives-ouvertes.fr/hal-00455050/document
https://hal.archives-ouvertes.fr/hal-00455050/file/CSDA06_Srik_Hal.pdf

Éditeur(s) : HAL CCSD
Résumé : 27 pages
Cascade Stochastic Differential Equation (SDE), a continuous time model for energy dissipation in turbulence, is a generalization of the Yaglom discrete cascade model. We extend this SDE to a model in random environment by assuming that its two parameters are switched by a continuous time Markov chain whose states represent the states of the environment. Moreover, a Dirichlet process is placed as a prior on the space of sample paths of this chain. We propose a Bayesian estimation method of this model which is tested both on simulated data and on real data of wind speed measured at the entrance of the mangrove ecosystem in Guadeloupe.
https://hal.archives-ouvertes.fr/hal-00286131

hal-00286131
https://hal.archives-ouvertes.fr/hal-00286131
https://hal.archives-ouvertes.fr/hal-00286131/document
https://hal.archives-ouvertes.fr/hal-00286131/file/Srik11_PhysicaDDspace.pdf

Éditeur(s) : Elsevier Science Bv
Résumé : Academia and management agencies show a growing interest for ecosystem-based fishery management (EBFM). However, the way to operationalize this approach remains challenging. The present paper illustrates how the concepts of stochastic co-viability, which accounts for dynamic complexities, uncertainties, risk and sustainability constraints, can be useful for the implementation of EBFM. In the present case, this concept is used to identify fishing strategies that satisfy both ecological conservation and economic sustainability in a multi-species, multi-fleet context. Economic Viability Analysis (EVA) and the broader Co-Viability Analysis (CVA), are proposed to expand the usual Population Viability Analysis (PVA) and precautionary approach. An illustration is proposed, using data on the fisheries of Bay of Biscay (France) exploiting the stocks of nephrops and hake. Stochastic simulations show how CVA can guarantee both ecological (stock) and economic (profit) sustainability. Using 2008 as a baseline, the model is used to identify fishing efforts that ensure such co-viability. (C) 2012 Elsevier B.V. All rights reserved.
Ecological Economics (0921-8009) (Elsevier Science Bv), 2012-03 , Vol. 75 , P. 32-42

Droits : 2012 Elsevier Science Bv
http://archimer.ifremer.fr/doc/00074/18571/16153.pdf
DOI:10.1016/j.ecolecon.2012.01.005
http://archimer.ifremer.fr/doc/00074/18571/

Éditeur(s) : HAL CCSD
Résumé : A standard approach for large scale image classification involves high dimensional features and Stochastic Gradient Descent algorithm (SGD) for the minimization of classical Hinge Loss in the primal space. Although complexity of Stochastic Gradient Descent is linear with the number of samples these method suffers from slow convergence. In order to cope with this issue, we propose here a Stochastic Low-Rank Newton Descent SLND for minimization of any calibrated loss in the primal space. SLND approximates the inverse Hessian by the best low-rank approximation according to squared Frobenius norm. We provide core optimization for fast convergence. Theoretically speaking, we show explicit convergence rates of the algorithm using these calibrated losses, which in addition provide working sets of parameters for experiments. Experiments are provided on the SUN, Caltech256 and ImageNet databases, with simple, uniform and efficient ways to tune remaining SLND parameters. On each of these databases, SLND challenges the accuracy of SGD with a speed of convergence faster by order of magnitude.
https://hal.archives-ouvertes.fr/hal-00825414

hal-00825414
https://hal.archives-ouvertes.fr/hal-00825414
https://hal.archives-ouvertes.fr/hal-00825414/document
https://hal.archives-ouvertes.fr/hal-00825414/file/TechnicalReport.pdf

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Predicting the impact of underground engineering on the environment requires the knowledge of natural media at different scales. In particular, understanding basic phenomena controlling the properties of rocks in the presence of complex fluids necessitates a detailed atomic description of the solid/fluid/solid contacts, the subject of Part I of the present study. First, building the solid interspace between two different crystals in a non-periodic situation is achieved using the ab initio and molecular mechanics code GenMol (TM). A description of the fluid confined within the interspace is then derived from the original genetic iterative multi-species (GIMS) algorithm implemented in the same code. This approach consists of equilibrating chemical potentials, cycle after cycle and species after species, between the confined fluid and the free natural fluid. An elementary iteration for a species k consists of different steps incrementing the number N-k of particles k, with other numbers N-k remaining constant. At each step, an optimum fluid composition is obtained by a genetic process distributing the fluid particles on a grid by stochastic shots, followed in fine by a refining process. The effectiveness of the GIMS approach is demonstrated in the case study of a fluid confined between two (0 0 1) kaolinite faces, with apertures h varying between 4 and 10 A. connected to a 9-species external solution [H2O, Cl-, Na+ CO2(aq), NaCl(aq), Ca2+, Mg2+, HCO3-, H3O+] where concentrations are ranging from 55 to 10(-4) mol/L. The results show a drastic variation in the solute/solvent and cations/ions ratios in the confined fluid when aperture h is lowered to less than 1 nm. These results obtained with a very rapid convergence of the iterative algorithm combined with a very competitive genetic optimizer are validated with high precision on a free solution. This description of contacts between crystals is original and unattainable by standard crystal interface approaches. It opens the way to understanding and/or predicting phenomena between crystals in a complex natural environment, such as adhesion or repulsion investigated in the Part II of this study.
ISSN: 0022-0248

hal-00544569
https://hal.archives-ouvertes.fr/hal-00544569
DOI : 10.1016/j.jcrysgro.2010.08.009

Éditeur(s) : HAL CCSD Springer Verlag (Germany) Springer Verlag
Résumé : Production rates in horizontal shale gas wells display declines that are controlled by the low permeability and the intrinsic heterogeneity of the shale matrix. We present an original multi-continuum approach that yields a physical model able to reproduce the complexity of the decreasing gas rates. The model describes the dynamics of gas rate as function of the physical reservoir parameters and geometry, while the shale matrix heterogeneity is accounted for by a stochastic description of transmissivity field. From the 3D (Dimensional) problem setting, including the heterogeneous shale matrix, the fractures generated by the hydrofracking operations, as well as the production well characteristics, we establish an effective upscaled 1D model for the gas pressures in fracture and matrix as well as the volumetric flux. We analyse the decline curves behaviour, and we identify the time scales that characterize the dynamics of the gas rate decline using explicit analytical Laplace space solutions of the upscaled process model. Asymptotically, the flux curves decrease exponentially, while in an intermediate regime we find a power-law behaviour, in which the flux scales with a power law in time as (t^{-beta }), where (beta ) reflects the medium heterogeneity. We use this solution to fit a set of real data displaying distinctly different decline trends and study the sensitivity of the model to the reservoir parameters in order to identify their respective controls at the different stages of the decline curve dynamics. Results indicate that the initial value of the gas rate is determined by the transmissivity of the fractures and the initial pressure of the gas in the shale matrix. The latter causes mainly a shift in the entire decline curve. The early time of decline curve shape is primarily controlled by the fracture properties (compressibility and transmissivity). During the main part of the economically valuable production times, i.e. before the production rate drops exponentially, the decline curve is strongly controlled by the properties of the shale rocks including their heterogeneity, which is modelled by two parameters describing the non-Fickian pressure diffusion effects in a stochastic framework.
ISSN: 0169-3913

hal-01217247
https://hal.archives-ouvertes.fr/hal-01217247
DOI : 10.1007/s11242-015-0504-y

Éditeur(s) : HAL CCSD American Physical Society (APS)
Résumé : International audience
Diffusion in natural and engineered media is quantified in terms of stochastic models for the heterogeneity-induced fluctuations of particle motion. However, fundamental properties such as ergodicity and self-averaging and their dependence on the disorder distribution are often not known. Here, we investigate these questions for diffusion in quenched disordered media characterized by spatially varying retardation properties, which account for particle retention due to physical or chemical interactions with the medium. We link self-averaging and ergodicity to the disorder sampling efficiency Rn, which quantifies the number of disorder realizations a noise ensemble may sample in a single disorder realization. Diffusion for disorder scenarios characterized by a finite mean transition time is ergodic and self-averaging for any dimension. The strength of the sample to sample fluctuations decreases with increasing spatial dimension. For an infinite mean transition time, particle motion is weakly ergodicity breaking in any dimension because single particles cannot sample the heterogeneity spectrum in finite time. However, even though the noise ensemble is not representative of the single-particle time statistics, subdiffusive motion in q≥2 dimensions is self-averaging, which means that the noise ensemble in a single realization samples a representative part of the heterogeneity spectrum.
ISSN: 2470-0053

hal-01622668
https://hal.archives-ouvertes.fr/hal-01622668
https://hal.archives-ouvertes.fr/hal-01622668v2/document
https://hal.archives-ouvertes.fr/hal-01622668/file/russian2017.pdf
DOI : 10.1103/PhysRevE.96.022156

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
The objectives are to study and model the aggregate wind power fluctuations dynamics in the multifractal framework. We present here the analysis of aggregate power output sampled at 1 Hz during three years. We decompose the data into several Intrinsic Mode Functions (IMF) using Empirical Mode Decomposition (EMD). We use a new approach, arbitrary order Hilbert spectral analysis, a combination of EMD approach with Hilbert spectral analysis (or Hilbert Huang Transform) and the classical structure function analysis to extract the scaling exponents or multifractal spectrum $zeta(q)$: this function provides a full characterization of a process at all intensities and all scales. The application of both methods, i.e. structure function and arbitrary-order Hilbert spectral analyses, give similar results indicating that the aggregate power output from a wind farm, possesses intermittent and multifractal properties. In order to check this result, we generate stochastic simulations of a Multifractal Random Walk (MRW) using a log-normal stochastic equation. We show that the simulation results are fully compatible with the experimental results.
Physica A

hal-01527887
https://hal.archives-ouvertes.fr/hal-01527887
DOI : 10.1016/j.physa.2013.04.038

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Wind energy production is very sensitive to turbulent wind speed. Thus rapid variation of wind speed due to changes in the local meteorological conditions can lead to electrical power variations of the order of the nominal power output, in particular when wind power variations on very short time scales, range at few seconds to 1 h, are considered. In small grid as they exist on islands (Guadeloupean Archipelago: French West Indies) such fluctuations can cause instabilities in case of intermediate power shortages. The developed analysis in [14] reveals three main classes of time series for the wind speed fluctuations. In this work, Probability Density Functions (PDFs) are proposed to fit the wind speed fluctuations distributions in each class. After, to simulate wind speed fluctuations sequences, we use a stochastic differential equation, the Langevin equation considering Gaussian turbulence PDF (class I), Gram–Charlier PDF (class II) and a mixture of gaussian PDF (class III). The statistical and dynamical properties of simulated wind sequences are close to those of measured wind sequences, for each class
ISSN: 0306-2619

hal-01527885
https://hal.archives-ouvertes.fr/hal-01527885
DOI : 10.1016/j.apenergy.2012.05.007

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Joint inversions are now commonly used in the earth sciences. They have been developed to better understand the structure of the earth, since they provide more constraints on the inverted parameters. We propose a new process to simultaneously invert several data sets in order to better image 3D crustal and upper mantle structures. Our inversion uses three kinds of data that present good complementarity: (1) P-wave receiver functions to provide Moho depth variations, (2) teleseismic delay times of P-waves to retrieve velocity anomalies in the crust and the upper mantle, and (3) gravity anomalies to image density variations at the lithospheric scale. We use a stochastic scheme, where receiver functions are first inverted. The interpolated resulting Moho depths are incorporated as a priori information into the joint inversion of teleseismic delay times and gravity anomalies process. Moreover, velocity and density can be linked by empirical relationships, which justifies the joint inversion of those parameters. In our stochastic approach, we perform a model space search for Moho variations, P-velocity, and density structure to find an acceptable fit to the three data sets. In order to preferentially sample the good data fit regions, we chose the neighborhood algorithm of Sambridge to optimistically survey the model space. We model the delay times with 3D raytracing using evenly spaced velocity-density nodes. We present here the first results given by this method on synthetic tests. (C) 2011 Elsevier Ltd. All rights reserved.
ISSN: 0098-3004

hal-00643158
https://hal.archives-ouvertes.fr/hal-00643158
DOI : 10.1016/j.cageo.2010.11.017

Éditeur(s) : HAL CCSD
Résumé : International audience
We are interested in the e ect of some types of events on dispersion indexes such as the mean crowding. From a mathematical point of view, we consider that a distribution of individuals is a realization of a point process and we study the consequences of a stochastic point thinning on the model distributional properties. A case study is provided from counting of aphids of the cotton plant carried out before and after thunderstorm. The mortality rate due to the thunderstorm is analyzed according to characteristics of thunderstorms, leaf strata and larvae stages.
SSC Meeting

hal-00684234
https://hal.archives-ouvertes.fr/hal-00684234

Éditeur(s) : Université des Antilles et de la Guyane
Résumé : The need for an integrated approach to fisheries is now widely affirmed, including the FAO, in particular in the context of tropical artisanal fisheries. These small-scale fisheries, often multispecies are very important in terms of production, employment and food security. However these fisheries and the exploited resources are often characterized by a lack of data making difficult their management within an ecosystem approach, and by the ecological and economic system complexities including trophic and technological interactions. This thesis aims to contribute to the development of bioeconomic tools for small tropical fisheries in a sustainable management perspective based on the ecosystem approach. In this perspective, the French Guiana coastal fishery constitutes an interesting case study. The thesis proposes multi-criteria evaluations, complex bioeconomic models and viable management scenarios for this fishery. At first, multivariate statistical analysis suggests a satisfactory overall status of the fishery in terms of sustainability. However, some performance differences are noted within the fishery, particularly at border areas. Also, management improvements are proposed. Then, through bioeconomic modeling, projections of different fishing scenarios show that, in the long-term, the current exploitation level may not be consistent with the future increase of local demand and a loss of biodiversity may occur. A scenario called "co-viability" reconciling ecological, economic and social objectives, with a high probability of achievement is exhibited. Finally, the comparison of optimal behavior in cooperative and non-cooperative conditions, confirms that harvest levels are greater when actors do not cooperate. Furthermore, it is shown that the state of the ecosystem depends on the fishing strategies and the type of interaction between species. Beyond the diagnosis made for the case study, the method is promising in the context of small tropical fisheries, while the co-viability approach allows finding the exploitation conditions under which ecological and socio-economic sustainability are meet, what the conventional fisheries management generally do not allow.
La nécessité d’une approche intégrée des pêches est actuellement largement affirmée, notamment par la FAO, en particulier dans le contexte des pêcheries artisanales tropicales. Ces pêcheries à petites échelles, souvent multi-spécifiques sont très importantes en termes d’emploi et de production, y compris pour la sécurité alimentaire. Néanmoins ces pêcheries et la biodiversité exploitées sont souvent marquées, d’une part, par le manque de données rendant difficile leur gestion dans le cadre d’une approche écosystémique, d’autre part, par la complexité des systèmes écologiques et économiques sous-jacents incluant interactions trophiques et techniques. Cette thèse contribue à la mise au point d’outils bioéconomiques adaptés aux petites pêcheries tropicales dans la perspective d’une gestion durable des pêches fondée sur l’approche écosystémique. Dans cette perspective, la pêcherie côtière en Guyane Française constitue un cas d’étude particulièrement fécond. La thèse propose ainsi des évaluations multi-critères, des modèles bioéconomiques complexes et des scénarios de gestion viable pour cette pêcherie. Dans un premier temps l’analyse statistique multivariée suggère un statut global satisfaisant de la pêcherie en termes de durabilité. Cependant des différences de performance sont notées au sein de la pêcherie, notamment au niveau des zones frontalières. Aussi des améliorations dans le mode de gestion sont proposées. Ensuite, à travers la modélisation bioéconomique, les projections des différents scénarios de pêche montrent qu’à long terme le niveau d’exploitation actuel peut ne pas être en adéquation avec la future augmentation de la demande locale et qu’une perte de biodiversité peut avoir lieu. Un scenario dit de "co-viabilité" conciliant des objectifs à la fois écologique, économique et social, avec une probabilité de réalisation satisfaisante, est mis en exergue. Enfin, la comparaison des comportements optimaux en situation coopératif et non coopératif, montre dans quelle mesure la viabilité est favorisée quand les acteurs coopèrent. Au-delà du diagnostic apporté pour le cas d’étude, la méthode utilisée s’avère prometteuse dans le contexte des petites pêcheries tropicales, tandis que l’approche de co-viabilité permet de trouver les modalités d’exploitation dans le cadre de compromis entre durabilité écologique et socio-économique, ce que les principes de gestion halieutiques traditionnels ne permettent généralement pas.

Droits : 2013 Université des Antilles et de la Guyane
http://archimer.ifremer.fr/doc/00144/25492/23646.pdf
http://archimer.ifremer.fr/doc/00144/25492/

Éditeur(s) : HAL CCSD Intech
Résumé : International audience
The massive integration of sustainable energies into electrical grids (non-interconnectedor connected) is a major problem due to their stochastic character revealed by strongfluctuations at all scales. In this paper, the scaling behaviour or power law correlationsand the nature of scaling behaviour of sustainable resource data such as flow velocity,atmospheric wind speed, solar global solar radiation and sustainable energy such as,wind power output, are highlighted. For the first time, Fourier power spectral densitiesare estimated for each dataset. We show that the power spectrum densities obtained areclose to the 5/3 Kolmogorov spectrum. Furthermore, the multifractal and intermittentproperties of sustainable resource and energy data have been revealed by the concavityof the scaling exponent function. The proposed analysis frame allows a full descriptionof fluctuations of processes considered. A good knowledge of the dynamic of fluctua-tions is crucial to management of the integration of sustainable energies into a grid.
Sustainable Energy - Technological Issues, Applications and Case Studies

hal-01528087
https://hal.archives-ouvertes.fr/hal-01528087
DOI : 10.5772/106341

Éditeur(s) : Wiley-blackwell
Résumé : 1. Approximately 300 pelagic fish species naturally aggregate around floating objects (FOBs) at the surface of the oceans. Currently, more than 50% of the world catch of tropical tuna comes from the industrial tuna fisheries around drifting FOBs. Greater understanding of the complex decision-making processes leading to this aggregation pattern and the impact of the massive release of artificial FOBs by fishermen on the spatial distribution and management of tuna is needed. 2. We analyse how the interplay between social (relationships between individuals) and non-social (responses to the environment) behaviours may affect the spatial distribution of a population in a multi-FOB environment. Taking the example of tropical tunas associating with FOBs and using differential equations and stochastic simulations, we examine how, when increasing the number of FOBs, fish aggregation dynamics and the distribution of the population among patches are affected by the population size, level of sociality and the natural retentive and/or attractive forces of FOBs on individual tuna. 3. Our model predicts that, depending on the species' level of sociality, fish will be scattered among FOBs or aggregated around a single FOB based on the number of FOBs deployed in a homogeneous oceanic region. 4. For social species, we demonstrated that the total fish catch is reduced with increasing FOBs number. Indeed, for each size of population, there are a number of FOBs minimizing the total population of fish associated with FOBs and another number of FOBs maximizing the total population of associated fish. 5. Synthesis and applications. In terms of fisheries management, the total catch volume is directly linked to the total number of floating objects (FOBs) for non-social species, and any limit on the number of sets would then result in a limit on the total catch. For social species (e.g. tuna), however, increasing the number of FOBs does not necessarily lead to an increase in the total catch, which is a non-intuitive result. Indeed, our model shows that, for specific values of the parameters, deploying a greater number of FOBs in the water (all other parameters being constant) does not necessarily help fishermen to catch more tuna, but does increase the level of fishing effort and bycatch.
Journal Of Applied Ecology (0021-8901) (Wiley-blackwell), 2013-10 , Vol. 50 , N. 5 , P. 1081-1092

Droits : 2013 The Authors. Journal of Applied Ecology, 2013 British Ecological Society
http://archimer.ifremer.fr/doc/00151/26275/24439.pdf
DOI:10.1111/1365-2664.12140
http://archimer.ifremer.fr/doc/00151/26275/

Éditeur(s) : Elsevier
Résumé : Overexploitation of marine resources remains a problem worldwide. Many works advocate for the use of marine reserves as a central element of future stock management in a sustainable perspective. In the present paper, we address the influence of protected areas upon fisheries sustainability within an eco-systemic framework through a dynamic bio-economic model integrating a trophic web, catches and environmental uncertainties. The model is spatially implicit. The evaluation of the ecosystem is designed through the respect along time of constraints of both conservation and guaranteed captures. Using the mathematical concept of invariance kernel in a stochastic context, we define different MPA effects according to biodiversity catches or mixed points of view. Numerical simulations inspired from data of Abore coral reef reserve in New Caledonia illustrate the main concepts. In this case, it is pointed out how MPA conservation effect is not necessarily conflicting with MPA catches effect. it is shown that such a co-viability requires medium exploitation rate. Moreover, the climatic changes represented by rise in cyclonic events seem to reinforce these assertions. (C) 2007 Elsevier B.V. All rights reserved.
Ecological Modelling (0304-3800) (Elsevier), 2007-11 , Vol. 208 , N. 2-4 , P. 353-366

Droits : 2007 Elsevier B.V. All rights reserved.
http://archimer.ifremer.fr/doc/2007/publication-3510.pdf
DOI:10.1016/j.ecolmodel.2007.06.018
http://archimer.ifremer.fr/doc/00000/3510/

Éditeur(s) : HAL CCSD Springer
Résumé : The analysis of gamma ray measurements provides valuable information about the basement's lithospherical model and the radioactive elements contained in the subsurface. To be exploited, the raw data need pre-processing operations which consist of corrections of the Compton effect, altimetry and the aircraft background, and 2D interpolations. These transformations may modify the data's stochastic component which reflects heterogeneities of the investigated medium. In this study, a fractal analysis is carried out on airborne gamma ray data measured in the Hoggar's area (Algeria). First, it is shown that the analyzed data exhibit fractal properties. Due to the dependence of the latter on the spatial location of the measures, the data can be considered as paths of multifractional Brownian motions. Another result worth noting is that the fractal nature of the raw data is not modified by the pre-processing operations. The fractal analysis can be then performed on the raw spectrometric measurements without submitting them to any pre-processing; thus, the stochastic component of the measurements is kept intact.
ISSN: 1866-7411

hal-00817494
https://hal.archives-ouvertes.fr/hal-00817494
DOI : 10.1007/s12517-011-0407-3

Éditeur(s) : HAL CCSD
Résumé : Point processes are often used as spatial or spatio-temporal distribution models of occurrences. In this PhD dissertation, we focus first on Cox processes driven by a hidden process associated with a Dirichlet process. This model corresponds to hidden occurrences influencing the stochastic intensity of observed occurrences. We generalize the notion of "Shot noise Cox process" introduced by M{o}ller and develop its bayesian analysis by a Gibbs sampler combined with a Metropolis-Hastings algorithm. We show that our MCMC method is a reversible jump one. The model takes into account a random number of hidden contributions producing effects on the observed point process intensity. Therefore the parameter space has a variable dimension. We focus the statistical inference on the estimation of the hidden contribution expected value, the hidden contribution expected number, the spatial influence and correlation parameters. The contribution equality test and contribution independence test are proposed. Applications in epidemiology and ecology are shown from extit{Rubus fruticosa} data, extit{Ibicella lutea} data and death number data in counties of Georgia, USA. Two situations are considered with respect to available data~: firstly, the spatial positions of occurrences are observed between several pairs of consecutive dates; secondly, counts are carried out over a fixed time interval in several spatial sampling units. Secondly, we focus on point processes with memory introduced by Kagan, Ogata and Vere-Jones, pioneers in statistical seismology. In fact, spatio-temporal point processes play an important role in the studies of earthquake catalogs since they consist of seismic events with their dates and spatial locations. We studied an ETAS (Epidemic Type Aftershock Sequence) model with time independent background intensity and several triggering functions taking into account previous events. We illustrate our approach with a seismicity study of the Lesser Antilles arc. A comparaison study of Gamma, Weibull, Log-Normal and modified Omori law triggering function models is also carried out. We show that the modified Omori law does not fit the Lesser Antilles seismic data and the best adjusted triggering function is the Weibull model. Consequently, the waiting time between aftershocks is weaker in the Lesser Antilles zone compared to the one in regions with seismicity described by the modified Omori law. In other words, aftershock aggregativity is higher in the Lesser Antilles region. The stochastic background intensity following a Dirichlet process centered on a spatial log-normal process is discussed.
Les processus ponctuels sont souvent utilisés comme modèles de répartitions spatiales ou spatio-temporelles d'occurrences. Dans cette thèse, nous nous intéressons tout d'abord à des processus de Cox dirigés par un processus caché associé à un processus de Dirichlet. Ce modèle correspond à des occurrences cachées influençant l'intensité stochastique des occurrences observées. Nous généralisons la notion de " Shot noise Cox process " introduite par Moller et développons le traitement bayésien par un échantillonneur de Gibbs combiné à un algorithme de Metropolis-Hastings. Nous montrons que cette méthode MCMC est à sauts réversibles. Le modèle prend en compte, en effet, un nombre aléatoire de contributions cachées influençant l'intensité du processus ponctuel observé donc a un espace paramétrique de dimension variable. Nous focalisons l'inférence statistique sur l'estimation de la valeur espérée de chaque contribution cachée, le nombre espéré de contributions cachées, le degré d'influence spatiale de ces contributions et leur degré de corrélation. Le test d'égalité des contributions et celui de leur indépendance sont ainsi développés. L'utilité en épidémiologie et en écologie est alors démontrée à partir de données de Rubus fruticosa, Ibicella lutea et de mortalité dans les cantons de Georgia, USA. En termes de données observées, deux situations sont considérées: premièrement, les positions spatiales des occurrences sont observées entre plusieurs paires de dates consécutives; deuxièmement, des comptages sont effectués, au cours d'une période fixée, dans des unités d'échantillonnage spatiales. D'autre part, nous nous intéressons aux processus ponctuels à mémoire introduits par Kagan, Ogata et Vere-Jones, précurseurs de la statistique sismologique. En effet, les processus ponctuels spatio-temporels ont une place importante dans l'étude des catalogues sismiques puisque ces derniers sont généralement constitués d'événements sismiques datés et géo-référencés. Nous avons étudié un modèle ETAS (Epidemic Type Aftershock Sequence) avec une intensité d'arrière-plan indépendante du temps et plusieurs fonctions déclenchantes permettant d'intégrer les événements antérieurs récents. Cette approche est utilisée pour étudier la sismicité de l'arc des Petites Antilles. Une étude comparative des modèles Gamma, Weibull, Log-Normal et loi d'Omori modifiée pour les fonctions déclenchantes est menée. Nous montrons que la loi d'Omori modifiée ne s'ajuste pas aux données sismiques des Petites Antilles et la fonction déclenchante la plus adaptée est le modèle de Weibull. Cela implique que le temps d'attente entre répliques dans la zone des Petites Antilles est plus faible que celui des régions à sismicité décrite par la loi d'Omori modifiée. Autrement dit, l'agrégation des répliques après un événement majeur est plus prononcée dans la zone des Petites Antilles. La possibilité d'inclure une intensité d'arrière-plan suivant un processus de Dirichlet centré sur un processus spatial log-gaussien est discutée.
https://tel.archives-ouvertes.fr/tel-00841146

Droits : info:eu-repo/semantics/OpenAccess
NNT : 2012AGUY0555
tel-00841146
https://tel.archives-ouvertes.fr/tel-00841146
https://tel.archives-ouvertes.fr/tel-00841146/document
https://tel.archives-ouvertes.fr/tel-00841146/file/these_VALMY.pdf

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
The objectives are to study and model the aggregate wind power fluctuations dynamics in the multifractal framework. We present here the analysis of aggregate power output sampled at 1 Hz during three years. We decompose the data into several Intrinsic Mode Functions (IMFs) using Empirical Mode Decomposition (EMD). We use a new approach, arbitrary order Hilbert spectral analysis, a combination of the EMD approach with Hilbert spectral analysis (or Hilbert-Huang Transform) and the classical structure-function analysis to extract the scaling exponents or multifractal spectrum ζ(q)ζ(q): this function provides a full characterization of a process at all intensities and all scales. The application of both methods, i.e. structure-function and arbitrary-order Hilbert spectral analyses, gives similar results indicating that the aggregate power output from a wind farm, possesses intermittent and multifractal properties. In order to check this result, we generate stochastic simulations of a Multifractal Random Walk (MRW) using a log-normal stochastic equation. We show that the simulation results are fully compatible with the experimental results
Physica A

hal-00846643
https://hal.archives-ouvertes.fr/hal-00846643
DOI : 10.1016/j.physa.2013.04.038