Finite element approximation of electromagnetic fields using nonfitting meshes for Geophysics

We analyze the use of nonfitting meshes for simulating the propagation of electromagnetic waves inside the earth with applications to borehole logging. We avoid the use of parameter homogenization and employ standard edge finite element basis functions. For our geophysical applications, we consider a 3D Maxwell’s system with piecewise constant conductivity and globally constant permittivity and permeability. The model is analyzed and discretized using both the Eand H-formulations. Our main contribution is to develop a sharp error estimate for both the electric and magnetic fields. In the presence of singularities, our estimate shows that the magnetic field approximation is converging faster than the electric field approximation. As a result, we conclude that error estimates available in the literature are sharp with respect to the electric field error but provide pessimistic convergence rates for the magnetic field in our geophysical applications. Another surprising consequence of our analysis is that nonfitting meshes deliver the same convergence rate as fitting meshes to approximate the magnetic field. Our theoretical results are numerically illustrated via 2D experiments. For the analyzed cases, the accuracy loss due to the use of nonfitting meshes islimited, even for high conductivity contrasts

Adjoint-based formulation for computing derivatives with respect to bed boundary positions in resistivity geophysics

In inverse geophysical resistivity problems, it is common to optimize for specific resistivity values and bed boundary positions, as needed, for example, in geosteering applications. When using gradient-based inversion methods such as Gauss-Newton, we need to estimate the derivatives of the recorded measurements with respect to the inversion parameters. In this article, we describe an adjoint-based formulation for computing the derivatives of the electromagnetic fields withrespect to the bed boundary positions. The key idea to obtain this adjoint-based formulation is to separate the tangential and normal components of the field, and treat them differently. We then apply this method to a 1.5D borehole resistivity problem. We illustrate its accuracy and some of its convergence properties via numerical experimentation by comparing the results obtained with our proposed adjoint-based method vs. both the analytical results when available and a finite differences approximation of the derivative

Optical determination and identification of organic shells around nanoparticles: application to silver nanoparticles

We present a simple method to prove the presence of an organic shell around silver nanoparticles. This method is based on the comparison between optical extinction measurements of isolated nanoparticles and Mie calculations predicting the expected wavelength of the Localized Surface Plasmon Resonance of the nanoparticles with and without the presence of an organic layer. This method was applied to silver nanoparticles which seemed to be well protected from oxidation. Further experimental characterization via Surface Enhanced Raman Spectroscopy (SERS) measurements allowed to identify this protective shell as ethylene glycol. Combining LSPR and SERS measurements could thus give proof of both presence and identification for other plasmonic nanoparticles surrounded by organic shells

Finite Element Simulations of Logging-While-Drilling and Extra-Deep Azimuthal Resistivity Measurements using Non-Fitting Grids

We propose a discretization technique using non-fitting grids to simulate magnetic field-based resistivity logging measurements. Non-fitting grids are convenient because they are simpler to generate and handle than fitting grids when the geometry is complex. On the other side, fitting grids have been historically preferred because they offer additional accuracy for a fixed problem size in the general case. In this work, we analyse the use of non-fitting grids to simulate the response of logging instruments that are based on magnetic field resistivity measurements using 2.5D Maxwell’s equations. We provide various examples demonstrating that, for these applications, if the finite element matrix coefficients are properly integrated, the accuracy loss due to the use of non-fitting grids is negligible compared to the case where fitting grids are employed

An ensemble approach to assess hydrological models’ contribution to uncertainties in the analysis of climate change impact on water resources

Over the recent years, several research efforts investigated the impact of climate change on water resources for different regions of the world. The projection of future river flows is affected by different sources of uncertainty in the hydro-climatic modelling chain. One of the aims of the QBic3 5 project (Que´bec-Bavarian International Collaboration on Climate Change) is to assess the contribution to uncertainty of hydrological models by using an ensemble of hydrological models presenting a diversity of structural complexity (i.e. lumped, semi distributed and distributed models). The study investigates two humid, mid-latitude catchments with natural flow conditions; one located in 10 Southern Que´bec (Canada) and one in Southern Bavaria (Germany). Daily flow is simulated with four different hydrological models, forced by outputs from regional climate models driven by a given number of GCMs’ members over a reference (1971–2000) and a future (2041–2070) periods. The results show that the choice of the hydrological model does strongly affect the climate change response of selected hydrological indicators, especially those related to low flows. Indicators related to high flows seem less sensitive on the choice of the hydrological model. Therefore, the computationally less demanding models (usually simple, lumped and conceptual) give a significant level of trust for high and overall mean flows

On the need for bias correction in regional climate scenarios to assess climate change impacts on river runoff

In climate change impact research, the assessment of future river runoff as well as the catchment scale water balance is impeded by different sources of modeling uncertainty. Some research has already been done in order to quantify the uncertainty of climate 5 projections originating from the climate models and the downscaling techniques as well as from the internal variability evaluated from climate model member ensembles. Yet, the use of hydrological models adds another layer of incertitude. Within the QBic3 project (Qu´ebec-Bavaria International Collaboration on Climate Change) the relative contributions to the overall uncertainty from the whole model chain (from global climate 10 models to water management models) are investigated using an ensemble of multiple climate and hydrological models. Although there are many options to downscale global climate projections to the regional scale, recent impact studies tend to use Regional Climate Models (RCMs). One reason for that is that the physical coherence between atmospheric and land-surface 15 variables is preserved. The coherence between temperature and precipitation is of particular interest in hydrology. However, the regional climate model outputs often are biased compared to the observed climatology of a given region. Therefore, biases in those outputs are often corrected to reproduce historic runoff conditions from hydrological models using them, even if those corrections alter the relationship between temperature and precipitation. So, as bias correction may affect the consistency between RCM output variables, the use of correction techniques and even the use of (biased) climate model data itself is sometimes disputed among scientists. For those reasons, the effect of bias correction on simulated runoff regimes and the relative change in selected runoff indicators is explored. If it affects the conclusion of climate change analysis in 25 hydrology, we should consider it as a source of uncertainty. If not, the application of bias correction methods is either unnecessary in hydro-climatic projections, or safe to use as it does not alter the change signal of river runoff. The results of the present paper highlight the analysis of daily runoff simulated with four different hydrological models in two natural-flow catchments, driven by different regional climate models for a reference and a future period. As expected, bias correction of climate model outputs is important for the reproduction of the runoff regime of the 5 past regardless of the hydrological model used. Then again, its impact on the relative change of flow indicators between reference and future period is weak for most indicators with the exception of the timing of the spring flood peak. Still, our results indicate that the impact of bias correction on runoff indicators increases with bias in the climate simulations

Quantization Watermarking for Joint Compression and Data Hiding Schemes

International audienceEnrichment and protection of JPEG2000 images is an important issue. Data hiding techniques are a good solution to solve these problems. In this context, we can consider the joint approach to introduce data hiding technique into JPEG2000 coding pipeline. Data hiding consists of imperceptibly altering multimedia content, to convey some information. This process is done in such a way that the hidden data is not perceptible to an observer. Digital watermarking is one type of data hiding. In addition to the imperceptibility and payload constraints, the watermark should be robust against a variety of manipulations or attacks. We focus on trellis coded quantization (TCQ) data hiding techniques and propose two JPEG2000 compression and data hiding schemes. The properties of TCQ quantization, defined in JPEG2000 part 2, are used to perform quantization and information embedding during the same time. The first scheme is designed for content description and management applications with the objective of achieving high payloads. The compression rate/imperceptibility/payload trade off is our main concern. The second joint scheme has been developed for robust watermarking and can have consequently many applications. We achieve the better imperceptibility/robustness trade off in the context of JPEG2000 compression. We provide some experimental results on the implementation of these two schemes

Ordering intermetallic alloys by ion irradiation: a way to tailor magnetic media

Combining He ion irradiation and thermal mobility below 600K, we both trigger and control the transformation from chemical disorder to order in thin films of an intermetallic ferromagnet (FePd). Kinetic Monte Carlo simulations show how the initial directional short range order determines order propagation. Magnetic ordering perpendicular to the film plane was achieved, promoting the initially weak magnetic anisotropy to the highest values known for FePd films. This post-growth treatment should find applications in ultrahigh density magnetic recording.Comment: 7 pages, 3 Figure

A Painless Automatic hp-Adaptive Strategy for Elliptic Problems

In this work, we introduce a novel hp-adaptive strategy. The main goal is to minimize the complexity and implementational efforts hence increasing the robustness of the algorithm while keeping close to optimal numerical results. We employ a multi-level hierarchical data structure imposing Dirichlet nodes to manage the so-called hanging nodes. The hp-adaptive strategy is based on performing quasi-optimal unre finements. Taking advantage of the hierarchical structure of the basis functions both in terms of the element size h and the polynomial order of approximation p, we mark those with the lowest contributions to the energy of the solution and remove them. This straightforward unrefi nement strategy does not need from a fi ne grid or complex data structures, making the algorithm flexible to many practical situations and existing implementations. On the other side, we also identify some limitations of the proposed strategy, namely: (a) data structures only support isotropic h-re nements (although p-anisotropic re nements are enabled), (b) we assume certain quasi-orthogonality properties of the basis functions in the energy norm, and (c) in this work, we restrict to symmetric and positive defi nite problems. We illustrate these and other advantages and limitations of the proposed hp-adaptive strategy with several one-, two- and three-dimensional Poisson examples