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.

Parameter estimation for the distribution of single cell lag times.

In Quantitative Microbial Risk Assessment, it is vital to understand how lag times of individual cells are distributed over a bacterial population. Such identified distributions can be used to predict the time by which, in a growth-supporting environment, a few pathogenic cells can multiply to a poisoning concentration level. We model the lag time of a single cell, inoculated into a new environment, by the delay of the growth function characterizing the generated subpopulation. We introduce an easy-to-implement procedure, based on the method of moments, to estimate the parameters of the distribution of single cell lag times. The advantage of the method is especially apparent for cases where the initial number of cells is small and random, and the culture is detectable only in the exponential growth phase.

Panel index VAR models: Specification, Estimation, Testing and Leading Indicators

This paper proposes a method to conduct inference in panel VAR models with cross unit interdependencies and time variations in the coefficients. The approach can be used to obtain multi-unit forecasts and leading indicators and to conduct policy analysis in a multiunit setups. The framework of analysis is Bayesian and MCMC methods are used to estimate the posterior distribution of the features of interest. The model is reparametrized to resemble an observable index model and specification searches are discussed. As an example, we construct leading indicators for inflation and GDP growth in the Euro area using G-7 information.

Transmission Fourier transform infrared microspectroscopy allows simultaneous assessment of cutin and cell-wall polysaccharides of Arabidopsis petals.

A procedure for the simultaneous analysis of cell-wall polysaccharides, amides and aliphatic polyesters by transmission Fourier transform infrared microspectroscopy (FTIR) has been established for Arabidopsis petals. The combination of FTIR imaging with spectra derivatization revealed that petals, in contrast to other organs, have a characteristic chemical zoning with high amount of aliphatic compounds and esters in the lamina and of polysaccharides in the stalk of the petal. The hinge region of petals was particular rich in amides as well as in vibrations potentially associated with hemicellulose. In addition, a number of other distribution patterns have been identified. Analyses of mutants in cutin deposition confirmed that vibrations of aliphatic compounds and esters present in the lamina were largely associated with the cuticular polyester. Calculation of spectrotypes, including the standard deviation of intensities, allowed detailed comparison of the spectral features of various mutants. The spectrotypes not only revealed differences in the amount of polyesters in cutin mutants, but also changes in other compound classes. For example, in addition to the expected strong deficiencies in polyester content, the long-chain acyl CoA synthase 2 mutant showed increased intensities of vibrations in a wavelength range that is typical for polysaccharides. Identical spectral features were observed in quasimodo2, a cell-wall mutant of Arabidopsis with a defect in pectin formation that exhibits increased cellulose synthase activity. FTIR thus proved to be a convenient method for the identification and characterization of mutants affected in the deposition of cutin in petals.

Simultaneous determination of plasma levels of fluvoxamine and of the enantiomers of fluoxetine and norfluoxetine by gas chromatography-mass spectrometry.

A gas chromatographic-mass spectrometric method is presented which allows the simultaneous determination of the plasma concentrations of fluvoxamine and of the enantiomers of fluoxetine and norfluoxetine after derivatization with the chiral reagent, (S)-(-)-N-trifluoroacetylprolyl chloride. No interference was observed from endogenous compounds following the extraction of plasma samples from six different human subjects. The standard curves were linear over a working range of 10 to 750 ng/ml for racemic fluoxetine and norfluoxetine and of 50 to 500 ng/ml for fluvoxamine. Recoveries ranged from 50 to 66% for the three compounds. Intra- and inter-day coefficients of variation ranged from 4 to 10% for fluvoxamine and from 4 to 13% for fluoxetine and norfluoxetine. The limits of quantitation of the method were found to be 2 ng/ml for fluvoxamine and 1 ng/ml for the (R)- and (S)-enantiomers of fluoxetine and norfluoxetine, hence allowing its use for single dose pharmacokinetics. Finally, by using a steeper gradient of temperature, much shorter analysis times are obtained if one is interested in the concentrations of fluvoxamine alone.

Estimation du débit de filtration glomérulaire par la formule DFG = K x T/Pcr [Estimation of glomerular filtration rate by the formula GFR = K x T/Pc].

BACKGROUND: Creatinine clearance is the most common method used to assess glomerular filtration rate (GFR). In children, GFR can also be estimated without urine collection, using the formula GFR (mL/min x 1.73 m2) = K x height [cm]/Pcr [mumol/L]), where Pcr represents the plasma creatinine concentration. K is usually calculated using creatinine clearance (Ccr) as an index of GFR. The aim of the present study was to evaluate the reliability of the formula, using the standard UV/P inulin clearance to calculate K. METHODS: Clearance data obtained in 200 patients (1 month to 23 years) during the years 1988-1994 were used to calculate the factor K as a function of age. Forty-four additional patients were studied prospectively in conditions of either hydropenia or water diuresis in order to evaluate the possible variation of K as a function of urine flow rate. RESULTS: When GFR was estimated by the standard inulin clearance, the calculated values of K was 39 (infants less than 6 months), 44 (1-2 years) and 47 (2-12 years). The correlation between the values of GFR, as estimated by the formula, and the values measured by the standard clearance of inulin was highly significant; the scatter of individual values was however substantial. When K was calculated using Ccr, the formula overestimated Cin at all urine flow rates. When calculated from Ccr, K varied as a function of urine flow rate (K = 50 at urine flow rates of 3.5 and K = 64 at urine flow rates of 8.5 mL/min x 1.73 m2). When calculated from Cin, in the same conditions, K remained constant with a value of 50. CONCLUSIONS: The formula GFR = K x H/Pcr can be used to estimate GFR. The scatter of values precludes however the use of the formula to estimate GFR in pathophysiological studies. The formula should only be used when K is calculated from Cin, and the plasma creatinine concentration is measured in well defined conditions of hydration.

Simultaneous determination of antidementia drugs in human plasma: Procedure transfer from HPLC-MS to UPLC-MS/MS.

A previously developed high performance liquid chromatography mass spectrometry (HPLC-MS) procedure for the simultaneous determination of antidementia drugs, including donepezil, galantamine, memantine, rivastigmine and its metabolite NAP 226-90, was transferred to an ultra performance liquid chromatography system coupled to a tandem mass spectrometer (UPLC-MS/MS). The drugs and their internal standards ([(2)H(7)]-donepezil, [(13)C,(2)H(3)]-galantamine, [(13)C(2),(2)H(6)]-memantine, [(2)H(6)]-rivastigmine) were extracted from 250μL human plasma by protein precipitation with acetonitrile. Chromatographic separation was achieved on a reverse phase column (BEH C18 2.1mm×50mm; 1.7μm) with a gradient elution of an ammonium acetate buffer at pH 9.3 and acetonitrile at a flow rate of 0.4mL/min and an overall run time of 4.5min. The analytes were detected on a tandem quadrupole mass spectrometer operated in positive electrospray ionization mode, and quantification was performed using multiple reaction monitoring. The method was validated according to the recommendations of international guidelines over a calibration range of 1-300ng/mL for donepezil, galantamine and memantine, and 0.2-50ng/mL for rivastimgine and NAP 226-90. The trueness (86-108%), repeatability (0.8-8.3%), intermediate precision (2.3-10.9%) and selectivity of the method were found to be satisfactory. Matrix effects variability was inferior to 15% for the analytes and inferior to 5% after correction by internal standards. A method comparison was performed with patients' samples showing similar results between the HPLC-MS and UPLC-MS/MS procedures. Thus, this validated UPLC-MS/MS method allows to reduce the required amount of plasma, to use a simplified sample preparation, and to obtain a higher sensitivity and specificity with a much shortened run-time.

Simultaneous determination of antidementia drugs by HPLC-MS: validation data of the method and plasma level determinations in 300 patients

Aims: A rapid and simple HPLC-MS method was developed for the simultaneousdetermination of antidementia drugs, including donepezil, galantamine, rivastigmineand its major metabolite NAP 226 - 90, and memantine, for TherapeuticDrug Monitoring (TDM). In the elderly population treated with antidementiadrugs, the presence of several comorbidities, drug interactions resulting frompolypharmacy, and variations in drug metabolism and elimination, are possiblefactors leading to the observed high interindividual variability in plasma levels.Although evidence for the benefit of TDM for antidementia drugs still remains tobe demonstrated, an individually adapted dosage through TDM might contributeto minimize the risk of adverse reactions and to increase the probability of efficienttherapeutic response. Methods: A solid-phase extraction procedure with amixed-mode cation exchange sorbent was used to isolate the drugs from 0.5 mL ofplasma. The compounds were analyzed on a reverse-phase column with a gradientelution consisting of an ammonium acetate buffer at pH 9.3 and acetonitrile anddetected by mass spectrometry in the single ion monitoring mode. Isotope-labeledinternal standards were used for quantification where possible. The validatedmethod was used to measure the plasma levels of antidementia drugs in 300patients treated with these drugs. Results: The method was validated accordingto international standards of validation, including the assessment of the trueness(-8 - 11 %), the imprecision (repeatability: 1-5%, intermediate imprecision:2 - 9 %), selectivity and matrix effects variability (less than 6 %). Furthermore,short and long-term stability of the analytes in plasma was ascertained. Themethod proved to be robust in the calibrated ranges of 1 - 300 ng/mL for rivastigmineand memantine and 2 - 300 mg/mL for donepezil, galantamine and NAP226 - 90. We recently published a full description of the method (1). We found ahigh interindividual variability in plasma levels of these drugs in a study populationof 300 patients. The plasma level measurements, with some preliminaryclinical and pharmacogenetic results, will be presented. Conclusion: A simpleLC-MS method was developed for plasma level determination of antidementiadrugs which was successfully used in a clinical study with 300 patients.

Improved estimation of the covariance matrix of stock returns with an application to portofolio selection

This paper proposes to estimate the covariance matrix of stock returnsby an optimally weighted average of two existing estimators: the samplecovariance matrix and single-index covariance matrix. This method isgenerally known as shrinkage, and it is standard in decision theory andin empirical Bayesian statistics. Our shrinkage estimator can be seenas a way to account for extra-market covariance without having to specifyan arbitrary multi-factor structure. For NYSE and AMEX stock returns from1972 to 1995, it can be used to select portfolios with significantly lowerout-of-sample variance than a set of existing estimators, includingmulti-factor models.

Using composite estimators to improve both domain and total area estimation

In this article we propose using small area estimators to improve the estimatesof both the small and large area parameters. When the objective is to estimateparameters at both levels accurately, optimality is achieved by a mixed sampledesign of fixed and proportional allocations. In the mixed sample design, oncea sample size has been determined, one fraction of it is distributedproportionally among the different small areas while the rest is evenlydistributed among them. We use Monte Carlo simulations to assess theperformance of the direct estimator and two composite covariant-freesmall area estimators, for different sample sizes and different sampledistributions. Performance is measured in terms of Mean Squared Errors(MSE) of both small and large area parameters. It is found that the adoptionof small area composite estimators open the possibility of 1) reducingsample size when precision is given, or 2) improving precision for a givensample size.