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.

A sequential model for older workers' labor transitions after a health shock

In this work we study older workers'(50-64) labor force transitions after a health/disability shock. We find that the probability of keeping working decreases with both age and severity of the shock. Moreover, we find strong interactions between age and severity in the 50-64 age range and none in the 30-49 age range. Regarding demographics we find that being female and married reduce the probability of keeping work. On the contrary, being main breadwinner, education and skill levels increase it. Interestingly, the effect of some demographics changes its sign when we look at transitions from inactivity to work. This is the case of being married or having a working spouse. Undoubtedly, leisure complementarities should play a role in the latter case. Since the data we use contains a very detailed information on disabilities, we are able to evaluate the marginal effect of each type of disability either in the probability of keeping working or in returning back to work. Some of these results may have strong policy implications.

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.

High-dose sequential chemotherapy (ICE) under circulating progenitor cells (CPC) protection in patients with small cell lung carcinoma (SCLC). Preliminary report on a multicentric study

Starting in February 1994, 20 patients (pt) with a median age of 50 years(range 41-63) from 7 European centers have been included. Completedata were obtained in 16 patients so far. CPC were mobilized with chemo(Epirubicine 75 mg/m2 /d, 01 + 02) followed by G-CSF 5 p.gfkg/d for14 days. HD chemo consisted in 3 sequential courses of ICE regimen(UOs. 10 g/m2 , Carbo. 1200 mg/m2 and Etop. 1200 mg/m2 ) underCPC protection and G-CSF 5 p.g/kg/d. Out of the 16 pt, 12 completedfull program (3 cycles). One pt died of septic shock before receivingany ICE course. One pt died during the first ICE of renal insufficiency.Two pt had only 2 courses because of toxicity. Among the 16 pt, responserate (RR) was: 7 CR, 6 PR, 1 PO; 3 pt are not evaluable dueto early withdrawal (overall RR: 13/16 = 81 %). Thirty-nine cycles ofHD chemo were given with a median hematological recovery of 9 days(range 7-12) until neutro. counts> 1.0 x 109 /1 and 9 days (range 717)until thrombo. > 20 x 109 /1. No cumulative, hematological toxicitywas seen. Accrual of patients is still ongoing and updated results will bepresented.

Bundling and competition for slots: Sequential pricing

In this paper we study, as in Jeon-Menicucci (2009), competition between sellerswhen each of them sells a portfolio of distinct products to a buyer having limitedslots. This paper considers sequential pricing and complements our main paper (Jeon-Menicucci, 2009) that considers simultaneous pricing.First, Jeon-Menicucci (2009) find that under simultaneous individual pricing, equilibriumoften does not exist and hence the outcome is often inefficient. By contrast,equilibrium always exists under sequential individual pricing and we characterize it inthis paper. We find that each seller faces a trade-off between the number of slots heoccupies and surplus extraction per product, and there is no particular reason thatthis leads to an efficient allocation of slots.Second, Jeon-Menicucci (2009) find that when bundling is allowed, there alwaysexists an efficient equilibrium but inefficient equilibria can also exist due to purebundling (for physical products) or slotting contracts. Under sequential pricing,we find that all equilibria are efficient regardless of whether firms can use slottingcontracts, and both for digital goods and for physical goods. Therefore, sequentialpricing presents an even stronger case for laissez-faire in the matter of bundling thansimultaneous pricing.

Hot vs. cold: Sequential responses and preference stability in experimental games

In experiments with two-person sequential games we analyzewhether responses to favorable and unfavorable actions dependon the elicitation procedure. In our hot treatment thesecond player responds to the first player s observed actionwhile in our cold treatment we follow the strategy method and have the second player decide on a contingent action foreach and every possible first player move, without firstobserving this move. Our analysis centers on the degree towhich subjects deviate from the maximization of their pecuniaryrewards, as a response to others actions. Our results show nodifference in behavior between the two treatments. We also findevidence of the stability of subjects preferences with respectto their behavior over time and to the consistency of theirchoices as first and second mover.

Strategies for sequential prediction of stationary time series

We present simple procedures for the prediction of a real valued sequence. The algorithms are based on a combinationof several simple predictors. We show that if the sequence is a realization of a bounded stationary and ergodic random process then the average of squared errors converges, almost surely, to that of the optimum, given by the Bayes predictor. We offer an analog result for the prediction of stationary gaussian processes.

A sequential model for older workers’ labor transitions after a health shock

In this work we study older workers (50 64) labor force transitions after a health/disability shock. We find that the probability of keeping working decreases with both age and severity of the shock. Moreover, we find strong interactions between age and severity in the 50 64 age range and none in the 30 49 age range. Regarding demographics we find that being female and married reduce the probability of keeping work. On the contrary, being main breadwinner, education and skill levels increase it. Interestingly, the effect of some demographics changes its sign when we look at transitions from inactivity to work. This is the case of being married or having a working spouse. Undoubtedly, leisure complementarities should play a role in the latter case. Since the data we use contains a very detailed information on disabilities, we are able to evaluate the marginal effect of each type of disability either in the probability of keeping working or in returning back to work. Some of these results may have strong policy implications.

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.

Choice by sequential procedures

We propose a rule of decision-making, the sequential procedure guided byroutes, and show that three influential boundedly rational choice models can be equivalentlyunderstood as special cases of this rule. In addition, the sequential procedure guidedby routes is instrumental in showing that the three models are intimately related. We showthat choice with a status-quo bias is a refinement of rationalizability by game trees, which, inturn, is also a refinement of sequential rationalizability. Thus, we provide a sharp taxonomyof these choice models, and show that they all can be understood as choice by sequentialprocedures.