Quantified set inversion with applications to control

This paper describes a new reliable method, based on modal interval analysis (MIA) and set inversion (SI) techniques, for the characterization of solution sets defined by quantified constraints satisfaction problems (QCSP) over continuous domains. The presented methodology, called quantified set inversion (QSI), can be used over a wide range of engineering problems involving uncertain nonlinear models. Finally, an application on parameter identification is presented

La nappe du Lebendun entre Alte Kaserne et le Val Cairasca (massif du Simplon): nouvelles observations et interprétations

The lithostratigraphic description of the covers of three Lower Penninic nappes (Monte Leone, Lebendun and Antigorio) allows the comparison of their sedimentary content and their thickness. It has been established that the Lebendun nappe is formed by an ante-Triassic paragneissic core (Valgrande gneiss), and a Mesozoic sedimentary cover in reversed position. The cover series shows a continuous detritic sedimentation, off which the material comes from a continental erosion related to the early Lias rifting phase of the Alpine Tethys. The erosion has reached the basement, resedimented as pebbles and sandstones. This can be observed in both Lebendun and Antigorio covers. The definition of a unit named <<serie intermediaire>> between the Lebendun and the Antigorio covers has important palinspastic implications for both nappes. The unit is composed of a banded marble, a garnet bearing gneiss and a calcschist with great blocks. The comparison between the thickness of Antigorio and Lebendun covers suggests a shoulder position for Antigorio. and a proximal rift basin position tor Lebendun. The general thickness decrease of the series towards the SW points to a NE origin for the Lebendun clastics, taking into account the increase of tectonic deformation in the region trending from east to west. The detritic sedimentation ends with the basin drowning during the Malm, represented by a pure marble sealing the erosive disconformity of the Antigorio cover, and the clastic deposits of Lebendun. Three hypotheses are proposed for the calcschists age and attribution of the <<serie intermediaire>>: A: they belong entirely or partially to the Lebendun cover and correspond to a conglomeratic deposit of Cretaceous-Tertiary Niesen flysch type, of proximal facies. The tectonic limit could be situated in the middle of the calcschists at the level of the huge blocks encountered. B: they belong to Antigorio and correspond to an upper Lias-Dogger synrift deposit, then the marble is liassic. C: they belong to Antigorio and have been deposited following the Lebendun basin inversion (Cretaceous-Tertiary). that generates Tertiary wildflysch deposits, coming from the South for the ultrahelvetic and from the North for the Niesen.

Free-breathing renal magnetic resonance angiography with steady-state free-precession and slab-selective spin inversion combined with radial k-space sampling and water-selective excitation.

The impact of radial k-space sampling and water-selective excitation on a novel navigator-gated cardiac-triggered slab-selective inversion prepared 3D steady-state free-precession (SSFP) renal MR angiography (MRA) sequence was investigated. Renal MRA was performed on a 1.5-T MR system using three inversion prepared SSFP approaches: Cartesian (TR/TE: 5.7/2.8 ms, FA: 85 degrees), radial (TR/TE: 5.5/2.7 ms, FA: 85 degrees) SSFP, and radial SSFP combined with water-selective excitation (TR/TE: 9.9/4.9 ms, FA: 85 degrees). Radial data acquisition lead to significantly reduced motion artifacts (P < 0.05). SNR and CNR were best using Cartesian SSFP (P < 0.05). Vessel sharpness and vessel length were comparable in all sequences. The addition of a water-selective excitation could not improve image quality. In conclusion, radial k-space sampling reduces motion artifacts significantly in slab-selective inversion prepared renal MRA, while SNR and CNR are decreased. The addition of water-selective excitation could not improve the lower CNR in radial scanning.

Régime métropolitain, migrations résidentielles et recompositions urbaines : l'hypothèse de l'inversion du modèle de mobilité

Phénomène resté assez marginal jusqu'aux années quatre-vingt, la gentrification est devenue, dans certaines villes européennes, un principe de production de l'espace urbain. La ville que désertaient les classes moyennes parce qu'elle était associée à une densité excessive et à des nuisances de toutes sortes redevient ainsi le lieu d'une valorisation immobilière renouvelée, mais aussi d'un entre-soi sélectif, du spectacle et du plaisir répondant aux nouveaux styles d'habiter des nouveaux cadres de l'urbain globalisé. Qu'en est-il en Suisse ? L'article présente quelques résultats issus de deux recherches menées à l'échelle du système urbain et de l'agglomération lausannoise. L'observation des dynamiques à l'oeuvre ne permet pas de corroborer la thèse du « retour en ville ».

Inversion of crosshole seismic data in heterogenous environments : Comparison of waveform and ray-based approaches

High-resolution tomographic imaging of the shallow subsurface is becoming increasingly important for a wide range of environmental, hydrological and engineering applications. Because of their superior resolution power, their sensitivity to pertinent petrophysical parameters, and their far reaching complementarities, both seismic and georadar crosshole imaging are of particular importance. To date, corresponding approaches have largely relied on asymptotic, ray-based approaches, which only account for a very small part of the observed wavefields, inherently suffer from a limited resolution, and in complex environments may prove to be inadequate. These problems can potentially be alleviated through waveform inversion. We have developed an acoustic waveform inversion approach for crosshole seismic data whose kernel is based on a finite-difference time-domain (FDTD) solution of the 2-D acoustic wave equations. This algorithm is tested on and applied to synthetic data from seismic velocity models of increasing complexity and realism and the results are compared to those obtained using state-of-the-art ray-based traveltime tomography. Regardless of the heterogeneity of the underlying models, the waveform inversion approach has the potential of reliably resolving both the geometry and the acoustic properties of features of the size of less than half a dominant wavelength. Our results do, however, also indicate that, within their inherent resolution limits, ray-based approaches provide an effective and efficient means to obtain satisfactory tomographic reconstructions of the seismic velocity structure in the presence of mild to moderate heterogeneity and in absence of strong scattering. Conversely, the excess effort of waveform inversion provides the greatest benefits for the most heterogeneous, and arguably most realistic, environments where multiple scattering effects tend to be prevalent and ray-based methods lose most of their effectiveness.

Bayesian Markov chain Monte Carlo inversion of geophysical data for the purpose of estimating the hydraulic properties of the unsaturated zone

Ground-penetrating radar (GPR) has the potential to provide valuable information on hydrological properties of the vadose zone because of their strong sensitivity to soil water content. In particular, recent evidence has suggested that the stochastic inversion of crosshole GPR data within a coupled geophysical-hydrological framework may allow for effective estimation of subsurface van-Genuchten-Mualem (VGM) parameters and their corresponding uncertainties. An important and still unresolved issue, however, is how to best integrate GPR data into a stochastic inversion in order to estimate the VGM parameters and their uncertainties, thus improving hydrological predictions. Recognizing the importance of this issue, the aim of the research presented in this thesis was to first introduce a fully Bayesian inversion called Markov-chain-Monte-carlo (MCMC) strategy to perform the stochastic inversion of steady-state GPR data to estimate the VGM parameters and their uncertainties. Within this study, the choice of the prior parameter probability distributions from which potential model configurations are drawn and tested against observed data was also investigated. Analysis of both synthetic and field data collected at the Eggborough (UK) site indicates that the geophysical data alone contain valuable information regarding the VGM parameters. However, significantly better results are obtained when these data are combined with a realistic, informative prior. A subsequent study explore in detail the dynamic infiltration case, specifically to what extent time-lapse ZOP GPR data, collected during a forced infiltration experiment at the Arrenaes field site (Denmark), can help to quantify VGM parameters and their uncertainties using the MCMC inversion strategy. The findings indicate that the stochastic inversion of time-lapse GPR data does indeed allow for a substantial refinement in the inferred posterior VGM parameter distributions. In turn, this significantly improves knowledge of the hydraulic properties, which are required to predict hydraulic behaviour. Finally, another aspect that needed to be addressed involved the comparison of time-lapse GPR data collected under different infiltration conditions (i.e., natural loading and forced infiltration conditions) to estimate the VGM parameters using the MCMC inversion strategy. The results show that for the synthetic example, considering data collected during a forced infiltration test helps to better refine soil hydraulic properties compared to data collected under natural infiltration conditions. When investigating data collected at the Arrenaes field site, further complications arised due to model error and showed the importance of also including a rigorous analysis of the propagation of model error with time and depth when considering time-lapse data. Although the efforts in this thesis were focused on GPR data, the corresponding findings are likely to have general applicability to other types of geophysical data and field environments. Moreover, the obtained results allow to have confidence for future developments in integration of geophysical data with stochastic inversions to improve the characterization of the unsaturated zone but also reveal important issues linked with stochastic inversions, namely model errors, that should definitely be addressed in future research.

Nucleotide, cytogenetic and expression impact of the human chromosome 8p23.1 inversion polymorphism

Background: The human chromosome 8p23.1 region contains a 3.8–4.5 Mb segment which can be found in different orientations (defined as genomic inversion) among individuals. The identification of single nucleotide polymorphisms (SNPs) tightly linked to the genomic orientation of a given region should be useful to indirectly evaluate the genotypes of large genomic orientations in the individuals. Results: We have identified 16 SNPs, which are in linkage disequilibrium (LD) with the 8p23.1 inversion as detected by fluorescent in situ hybridization (FISH). The variability of the 8p23.1 orientation in 150 HapMap samples was predicted using this set of SNPs and was verified by FISH in a subset of samples. Four genes (NEIL2, MSRA, CTSB and BLK) were found differentially expressed (p<0.0005) according to the orientation of the 8p23.1 region. Finally, we have found variable levels of mosaicism for the orientation of the 8p23.1 as determined by FISH. Conclusion: By means of dense SNP genotyping of the region, haplotype-based computational analyses and FISH experiments we could infer and verify the orientation status of alleles in the 8p23.1 region by detecting two short haplotype stretches at both ends of the inverted region, which are likely the relic of the chromosome in which the original inversion occurred. Moreover, an impact of 8p23.1 inversion on gene expression levels cannot be ruled out, since four genes from this region have statistically significant different expression levels depending on the inversion status. FISH results in lymphoblastoid cell lines suggest the presence of mosaicism regarding the 8p23.1 inversion.

Source wavelet estimation for waveform inversion of crosshole georadar data

AbstractFor a wide range of environmental, hydrological, and engineering applications there is a fast growing need for high-resolution imaging. In this context, waveform tomographic imaging of crosshole georadar data is a powerful method able to provide images of pertinent electrical properties in near-surface environments with unprecedented spatial resolution. In contrast, conventional ray-based tomographic methods, which consider only a very limited part of the recorded signal (first-arrival traveltimes and maximum first-cycle amplitudes), suffer from inherent limitations in resolution and may prove to be inadequate in complex environments. For a typical crosshole georadar survey the potential improvement in resolution when using waveform-based approaches instead of ray-based approaches is in the range of one order-of- magnitude. Moreover, the spatial resolution of waveform-based inversions is comparable to that of common logging methods. While in exploration seismology waveform tomographic imaging has become well established over the past two decades, it is comparably still underdeveloped in the georadar domain despite corresponding needs. Recently, different groups have presented finite-difference time-domain waveform inversion schemes for crosshole georadar data, which are adaptations and extensions of Tarantola's seminal nonlinear generalized least-squares approach developed for the seismic case. First applications of these new crosshole georadar waveform inversion schemes on synthetic and field data have shown promising results. However, there is little known about the limits and performance of such schemes in complex environments. To this end, the general motivation of my thesis is the evaluation of the robustness and limitations of waveform inversion algorithms for crosshole georadar data in order to apply such schemes to a wide range of real world problems.One crucial issue to making applicable and effective any waveform scheme to real-world crosshole georadar problems is the accurate estimation of the source wavelet, which is unknown in reality. Waveform inversion schemes for crosshole georadar data require forward simulations of the wavefield in order to iteratively solve the inverse problem. Therefore, accurate knowledge of the source wavelet is critically important for successful application of such schemes. Relatively small differences in the estimated source wavelet shape can lead to large differences in the resulting tomograms. In the first part of my thesis, I explore the viability and robustness of a relatively simple iterative deconvolution technique that incorporates the estimation of the source wavelet into the waveform inversion procedure rather than adding additional model parameters into the inversion problem. Extensive tests indicate that this source wavelet estimation technique is simple yet effective, and is able to provide remarkably accurate and robust estimates of the source wavelet in the presence of strong heterogeneity in both the dielectric permittivity and electrical conductivity as well as significant ambient noise in the recorded data. Furthermore, our tests also indicate that the approach is insensitive to the phase characteristics of the starting wavelet, which is not the case when directly incorporating the wavelet estimation into the inverse problem.Another critical issue with crosshole georadar waveform inversion schemes which clearly needs to be investigated is the consequence of the common assumption of frequency- independent electromagnetic constitutive parameters. This is crucial since in reality, these parameters are known to be frequency-dependent and complex and thus recorded georadar data may show significant dispersive behaviour. In particular, in the presence of water, there is a wide body of evidence showing that the dielectric permittivity can be significantly frequency dependent over the GPR frequency range, due to a variety of relaxation processes. The second part of my thesis is therefore dedicated to the evaluation of the reconstruction limits of a non-dispersive crosshole georadar waveform inversion scheme in the presence of varying degrees of dielectric dispersion. I show that the inversion algorithm, combined with the iterative deconvolution-based source wavelet estimation procedure that is partially able to account for the frequency-dependent effects through an "effective" wavelet, performs remarkably well in weakly to moderately dispersive environments and has the ability to provide adequate tomographic reconstructions.

Focused time-lapse inversion of radio and audio magnetotelluric data

Geoelectrical techniques are widely used to monitor groundwater processes, while surprisingly few studies have considered audio (AMT) and radio (RMT) magnetotellurics for such purposes. In this numerical investigation, we analyze to what extent inversion results based on AMT and RMT monitoring data can be improved by (1) time-lapse difference inversion; (2) incorporation of statistical information about the expected model update (i.e., the model regularization is based on a geostatistical model); (3) using alternative model norms to quantify temporal changes (i.e., approximations of l(1) and Cauchy norms using iteratively reweighted least-squares), (4) constraining model updates to predefined ranges (i.e., using Lagrange Multipliers to only allow either increases or decreases of electrical resistivity with respect to background conditions). To do so, we consider a simple illustrative model and a more realistic test case related to seawater intrusion. The results are encouraging and show significant improvements when using time-lapse difference inversion with non l(2) model norms. Artifacts that may arise when imposing compactness of regions with temporal changes can be suppressed through inequality constraints to yield models without oscillations outside the true region of temporal changes. Based on these results, we recommend approximate l(1)-norm solutions as they can resolve both sharp and smooth interfaces within the same model. (C) 2012 Elsevier B.V. All rights reserved.

Selective coronary artery plaque visualization and differentiation by contrast-enhanced inversion prepared MRI.

AIMS: We sought to evaluate the utility of contrast-enhanced coronary magnetic resonance imaging (CE-MRI) for selective visualization and non-invasive differentiation of atherosclerotic coronary plaque in humans. METHODS AND RESULTS: Nine patients with coronary artery disease (CAD) as confirmed by X-ray angiography and multidetector computed tomography (MDCT) were studied by T1-weighted black blood inversion recovery coronary MRI before (N-IR) and after administration of Gd-DTPA (CE-IR). Plaques were categorized as calcified, non-calcified, and mixed based on their Hounsfield number derived from MDCT. With MDCT, a total of 29 plaques were identified, including calcified (n=6), non-calcified (n=6), and mixed calcified/non-calcified (n=17). On N-IR MRI, 26 plaques (90%) were dark, whereas three plaques (two non-calcified and one mixed) appeared bright. On CE-MRI, 13/29 (45%) plaques, 11 of which were mixed, one non-calcified, and one calcified showed contrast uptake. All others remained dark. CONCLUSION: In this preliminary study, we demonstrate the potential utility of CE-IR MRI for selective plaque visualization and differentiation of plaque types. The observed contrast uptake may be associated with endothelial dysfunction, neovascularization, inflammation, and/or fibrosis.

Positive contrast visualization of iron oxide-labeled stem cells using inversion-recovery with ON-resonant water suppression (IRON)

In proton magnetic resonance imaging (MRI) metallic substances lead to magnetic field distortions that often result in signal voids in the adjacent anatomic structures. Thus, metallic objects and superparamagnetic iron oxide (SPIO)-labeled cells appear as hypointense artifacts that obscure the underlying anatomy. The ability to illuminate these structures with positive contrast would enhance noninvasive MR tracking of cellular therapeutics. Therefore, an MRI methodology that selectively highlights areas of metallic objects has been developed. Inversion-recovery with ON-resonant water suppression (IRON) employs inversion of the magnetization in conjunction with a spectrally-selective on-resonant saturation prepulse. If imaging is performed after these prepulses, positive signal is obtained from off-resonant protons in close proximity to the metallic objects. The first successful use of IRON to produce positive contrast in areas of metallic spheres and SPIO-labeled stem cells in vitro and in vivo is presented.

Structural joint inversion of time-lapse crosshole ERT and GPR traveltime data

Time-lapse geophysical monitoring and inversion are valuable tools in hydrogeology for monitoring changes in the subsurface due to natural and forced (tracer) dynamics. However, the resulting models may suffer from insufficient resolution, which leads to underestimated variability and poor mass recovery. Structural joint inversion using cross-gradient constraints can provide higher-resolution models compared with individual inversions and we present the first application to time-lapse data. The results from a synthetic and field vadose zone water tracer injection experiment show that joint 3-D time-lapse inversion of crosshole electrical resistance tomography (ERT) and ground penetrating radar (GPR) traveltime data significantly improve the imaged characteristics of the point injected plume, such as lateral spreading and center of mass, as well as the overall consistency between models. The joint inversion method appears to work well for cases when one hydrological state variable (in this case moisture content) controls the time-lapse response of both geophysical methods. Citation: Doetsch, J., N. Linde, and A. Binley (2010), Structural joint inversion of time-lapse crosshole ERT and GPR traveltime data, Geophys. Res. Lett., 37, L24404, doi: 10.1029/2010GL045482.