Conditioning Surface-Based Geological Models to Well and Thickness Data

Geostatistical simulation methods aim to represent spatial uncertainty through realizations that reflect a certain geological concept by means of a spatial continuity model. Most common spatial continuity models are either variogram, training image, or Boolean based. In this paper, a more recent spatial model of geological continuity is developed, termed the event, or surface-based model, which is specifically applicable to modeling cases with complex stratigraphy, such as in sedimentary systems. These methods rely on a rule-based stacking of events, which are mathematically represented by two-dimensional thickness variations over the domain, where positive thickness is associated with deposition and negative thickness with erosion. Although it has been demonstrated that the surface-based models accurately represent the geological variation present in complex layered systems, they are more difficult to constrain to hard and soft data as is typically required of practical geostatistical techniques. In this paper, we develop a practical methodology for constraining such models to hard data from wells and thickness data interpreted from geophysics, such as seismic data. Our iterative methodology relies on a decomposition of the parameter optimization problem into smaller, manageable problems that are solved sequentially. We demonstrate this method on a real case study of a turbidite sedimentary basin.     

Probabilistic Marcinkiewicz–Zygmund Inequalities on the Rotation Group

Approximation problems on the rotation group SO(3) naturally arise in various fields, like crystallography, chemistry, and biology. For example, in crystallographic texture analysis one is confronted with the problem of evaluating so-called orientation density functions (ODFs). In many situations one only has a finite number of measurements at scattered sampling nodes. In order to reconstruct ODFs over all rotations, so-called Marcinkiewicz–Zygmund inequalities on the rotation group are an important tool. These inequalities provide norm equivalences between polynomials on SO(3) and their sample values. Recently shown equivalences depend on a density parameter of the sampling set and the proven inequalities hold true for polynomials on SO(3) whose degree does not exceed an upper bound which is determined by this density parameter. In this paper, we show that we can enlarge this upper bound for the polynomial degree significantly if we are satisfied by such norm equivalences that hold with a given probability only. Moreover, we show that there are fixed sampling sets for which we get probabilistic Marcinkiewicz–Zygmund inequalities that hold for polynomials on SO(3) of all degrees.     

Seabird aggregative patterns: A new tool for offshore wind energy risk assessment

The emerging development of offshore wind energy has raised public concern over its impact on seabird communities. There is a need for an adequate methodology to determine its potential impacts on seabirds. Environmental Impact Assessments (EIAs) are mostly relying on a succession of plain density maps without integrated interpretation of seabird spatio-temporal variability. Using Taylor’s power law coupled with mixed effect models, the spatio-temporal variability of species’ distributions can be synthesized in a measure of the aggregation levels of individuals over time and space. Applying the method to a seabird aerial survey in the Ebro Delta, NW Mediterranean Sea, we were able to make an explicit distinction between transitional and feeding areas to define and map the potential impacts of an offshore wind farm project. We use the Ebro Delta study case to discuss the advantages of potential impacts maps over density maps, as well as to illustrate how these potential impact maps can be applied to inform on concern levels, optimal EIA design and monitoring in the assessment of local offshore wind energy projects.     

Stochastic downscaling method: application to wind refinement

In this article, we propose a new stochastic downscaling method: provided a numerical prediction of wind at large scale, we aim to improve the approximation at small scales thanks to a local stochastic model. We first recall the framework of a Lagrangian stochastic model borrowed from Pope. Then, we adapt it to our meteorological framework, both from the theoretical and numerical viewpoints. Finally, we present some promising numerical results corresponding to the simulation of wind over the Mediterranean Sea.     

Investigating the effects of a summer storm on the North Sea stratification using a regional coupled ocean-atmosphere model

The influence of a summer storm event in 2007 on the North Sea and its effects on the ocean stratification are investigated using a regional coupled ocean (Regional Ocean Modeling System, ROMS)-atmosphere (Weather Research & Forecasting model, WRF) modeling system. An analysis of potential energy anomaly (PEA, Φ) and its temporal development reveals that the loss of stratification due to the storm event is dominated by vertical mixing in almost the entire North Sea. For specific regions, however, a considerable contribution of depth-mean straining is observed. Vertical mixing is highly correlated with wind induced surface stresses. However, peak mixing values are observed in combination with incoming flood currents. Depending on the phase between winds and tides, the loss of stratification differs strongly over the North Sea. To study the effects of interactive ocean-atmosphere exchange, a fully coupled simulation is compared with two uncoupled ones for the same vertical mixing parameters to identify the impact of spatial resolution as well as of SST feedback. While the resulting new mixed layer depth after the storm event in the uncoupled simulation with lower spatial and temporal resolution of the surface forcing data can still be located in the euphotic zone, the coupled simulation is capable to mix the entire water column and the vertical mixing in the uncoupled simulation with higher resolution of the surface forcing data is strongly amplified. These differences might have notable implications for ecosystem modeling since it could determine the development of new phytoplankton blooms after the storm and for sediment modeling in terms of sediment mobilization. An investigation of restratification after the extreme event illustrates the persistent effect of this summer storm.     

Magnitude <Emphasis Type="Italic">M</Emphasis><Subscript>w</Subscript> in metropolitan France

The recent seismicity catalogue of metropolitan France Sismicité Instrumentale de l’Hexagone (SI-Hex) covers the period 1962–2009. It is the outcome of a multipartner project conducted between 2010 and 2013. In this catalogue, moment magnitudes (M _w) are mainly determined from short-period velocimetric records, the same records as those used by the Laboratoire de Détection Géophysique (LDG) for issuing local magnitudes (M _L) since 1962. Two distinct procedures are used, whether M _L-LDG is larger or smaller than 4. For M _L-LDG >4, M _w is computed by fitting the coda-wave amplitude on the raw records. Station corrections and regional properties of coda-wave attenuation are taken into account in the computations. For M _L-LDG ≤4, M _w is converted from M _L-LDG through linear regression rules. In the smallest magnitude range M _L-LDG <3.1, special attention is paid to the non-unity slope of the relation between the local magnitudes and M _w. All M _w determined during the SI-Hex project is calibrated according to reference M _w of recent events. As for some small events, no M _L-LDG has been determined; local magnitudes issued by other French networks or LDG duration magnitude (M _D) are first converted into M _L-LDG before applying the conversion rules. This paper shows how the different sources of information and the different magnitude ranges are combined in order to determine an unbiased set of M _w for the whole 38,027 events of the catalogue.     

Evolution of particle size and concentration in the Rhône river mixing zone: : influence of salt flocculation

The salt induced flocculation phenomenon is often proposed as a major mechanism influencing the deposition of the suspended matter near the mouth of major rivers. However, depending on the particular mixing conditions between fresh water and marine water and on suspended solids (SS) reactivity, salt induced aggregation may be a minor factor controlling fast deposition of SS. This work combines field studies and laboratory experiments in order to assess the importance of salt induced flocculation in the case of the saltwedge estuary of the Rhône river. Sampling of the mixing zone has been performed in contrasted hydrodynamic conditions from a low water discharge period (500 m³ s⁻¹) to a small flood event (2400 m³ s⁻¹) for particle counting and salinity measurements. Through laboratory experiments, it is shown that the Rhône river particulate matter has a poor average reactivity regarding salt induced flocculation. Considering the hydrodynamics of the estuary, we show that the evolution of the concentration of larger particles (>5 μm) can be explained by settling and dilution. In contrast, the smallest measured fraction (2–5 μm) shows a more complex behavior and settling processes alone cannot explain the observed particle concentrations during the field studies. Four hypotheses are discussed for explaining the 2–5 μm particle concentration evolutions.     

Mesoscale variability in the Bransfield Strait region (Antarctica) during Austral summer

The Bransfield Strait is one the best-known areas of Antarctica’s oceanic surroundings. In spite of this, the study of the mesoscale variability of its local circulation has been addressed only recently.This paper focuses on the mesoscale structure of local physical oceanographic conditions in the Bransfield Strait during the Austral summer as derived from the BIOANTAR 93 cruise and auxiliary remote sensing data. Moreover, data recovered from moored current meters allow identification of transient mesoscale phenomena.     

Estimation of crack opening from a two‐dimensional continuum‐based finite element computation

Damage models are capable of representing crack initiation and mimicking crack propagation within a continuum framework. Thus, in principle, they do not describe crack openings. In durability analyses of concrete structures however, transfer properties are a key issue controlled by crack propagation and crack opening. We extend here a one‐dimensional approach for estimating a crack opening from a continuum‐based finite element calculation to two‐dimensional cases. The technique operates in the case of mode I cracking described in a continuum setting by a nonlocal isotropic damage model. We used the global tracking method to compute the idealized crack location as a post‐treatment procedure. The original one‐dimensional problem devised in Dufour et al. [4] is recovered as profiles of deformation orthogonal to the idealized crack direction are computed. An estimate of the crack opening and an error indicator are computed by comparing finite element deformation profiles and theoretical profiles corresponding to a displacement discontinuity. Two estimates have been considered: In the strong approach, the maxima of the profiles are assumed to be equal; in the weak approach, the integrals of each profile are set equal. Two‐dimensional numerical calculations show that the weak estimates perform better than do the strong ones. Error indicators, defined as the distance between the numerical and theoretical profiles, are less than a few percentages. In the case of a three‐point bending, test results are in good agreement with experimental data, with an error lower than 10% for widely opened crack (> 40µm). Copyright © 2011 John Wiley & Sons, Ltd.