Parametric

Keywords deterministic methods, STOllP, GllP, reserves, ultimate recovery, net oil sands, area-depth and area-thickness methods, gross rock volume, expectation curves, probability of excedence curves, uncertainty, probability of success, annual reporting requirements, Monte-Carlo simulation, parametric method... 

Figure 6.11 Schematic of Monte Carlo simulation 6.2.5 The parametric method...

The parametric method is an established statistical technique used for combining variables containing uncertainties, and has been advocated for use within the oil and gas industry as an alternative to Monte Carlo simulation. The main advantages of the method are its simplicity and its ability to identify the sensitivity of the result to the input variables. This allows a ranking of the variables in terms of their impact on the uncertainty of the result, and hence indicates where effort should be directed to better understand or manage the key variables in order to intervene to mitigate downside and/or take advantage of upside in the outcome. 

One significant feature of the Parametric Method is that it indicates, through the (1 + K 2) value, the relative contribution of each variable to the uncertainty in the result. Subscript i refers to any individual variable. (1 + K ) will be greater than 1.0 the higher the value, the more the variable contributes to the uncertainty in the result. In the following example, we can rank the variables in terms of their impact on the uncertainty in UR. We could also calculate the relative contribution to uncertainty. 

It enables first to explain the phenomena that happen in the thin-skin regime concerning the electromagnetic skin depth and the interaetion between induced eddy eurrent and the slots. Modelling can explain impedance signals from probes in order to verify experimental measurements. Parametric studies can be performed on probes and the defect in order to optimise NDT system or qualify it for several configurations. 

The development and validation of UTDefect has now progressed so far so that the program can be of real help in the development of testing procedures, in parametric and sensitivity studies and in such technical justifications that are used for qualifications of testing procedures. 

The parameters of equivalent planar OSD are then obtained by iterative minimization of a specifie dissimilarity eriterion measuring the degree of matching between the parametric descriptions of the observed segmented Bscan image Y° = s" = n = 1,..,jV and... 

I m = 1,.., m, viewed as two sets of planar parametric line segments. Figure 2 shows the schematic flow chart of the identification method for determining the parameters of an OSD. 

Etude et realisation de sondes pour la caracterisation non destructive par courants de Foucault de couches de cementation des aciers. Les proprietes electromagnetiques des aciers dependent de leur composition, de leurs microstructures et des contraintes appliquees. II est done naturel d essayer d utiliser les parametres electriques et magnetiques des aciers pour evaluer leur microstructure. 

La sensibilite aux defauts et autres parametres de controle peut etre amelioree par le choix optimal de la sonde. II apparait, apres etudes des differents types de sondes (ferritiques, acier doux, isolant) avec des geometries differentes (plate, conique,. ..), necessaires de souligner que le succes d une recherche de faisabilite depend en grande partie de la bonne definition des capteurs de mesure, de telle sorte que ceux-ci soient adaptes au probleme considere. 

To describe the X-ray imaging system the projection of 3D object points onto the 2D image plane, and nonlinear distortions inherent in the image detector system have to, be modelled. A parametric camera model based on a simple pinhole model to describe the projection in combination with a polynomal model of the nonlinear distortions is used to describe the X-ray imaging system. The parameters of the model are estimated using a two step approach. First the distortion parameters for fixed source and detector positions are calculated without any knowledge of the projection parameters. In a second step, the projection parameters are calculated for each image taken with the same source and detector positions but with different sample positions. 

The kinetics of crystal growth has been much studied Refs. 98-102 are representative. Often there is a time lag before crystallization starts, whose parametric dependence may be indicative of the nucleation mechanism. The crystal growth that follows may be controlled by diffusion or by surface or solution chemistry (see also Section XVI-2C). 

The potential fiinctions for the mteractions between pairs of rare-gas atoms are known to a high degree of accuracy [125]. Flowever, many of them use ad hoc fiinctional fonns parametrized to give the best possible fit to a wide range of experimental data. They will not be considered because it is more instmctive to consider representations that are more finnly rooted in theory and could be used for a wide range of interactions with confidence. 

Parametrized representations of individual damping dispersion functions were first obtained [127] by fitting ab initio damping functions [74] for Ft-Fl interactions. The one-parameter dampmg fiinctions of Douketis et al are [127] ... 

Su T and Chesnavich W J 1982 Parametrization of the ion-poiar moiecuie coiiision rate constant by tra]ectory caicuiations J. Chem. Phys. 76 5183-5... 

Light sources can either be broadband, such as a Globar, a Nemst glower, an incandescent wire or mercury arc lamp or they can be tunable, such as a laser or optical parametric oscillator (OPO). In the fomier case, a monocln-omator is needed to achieve spectral resolution. In the case of a tunable light source, the spectral resolution is detemiined by the linewidth of the source itself In either case, the spectral coverage of the light source imposes limits on the vibrational frequencies that can be measured. Of course, limitations on the dispersing element and detector also affect the overall spectral response of the spectrometer. 

In order to achieve a reasonable signal strength from the nonlinear response of approximately one atomic monolayer at an interface, a laser source with high peak power is generally required. Conuuon sources include Q-switched ( 10 ns pulsewidth) and mode-locked ( 100 ps) Nd YAG lasers, and mode-locked ( 10 fs-1 ps) Ti sapphire lasers. Broadly tunable sources have traditionally been based on dye lasers. More recently, optical parametric oscillator/amplifier (OPO/OPA) systems are coming into widespread use for tunable sources of both visible and infrared radiation. 

These limitations have recently been eliminated using solid-state sources of femtosecond pulses. Most of the femtosecond dye laser teclmology that was in wide use in the late 1980s [11] has been rendered obsolete by tliree teclmical developments the self-mode-locked Ti-sapphire oscillator [23, 24, 25, 26 and 27], the chirped-pulse, solid-state amplifier (CPA) [28, 29, 30 and 31], and the non-collinearly pumped optical parametric amplifier (OPA) [32, 33 and 34]- Moreover, although a number of investigators still construct home-built systems with narrowly chosen capabilities, it is now possible to obtain versatile, nearly state-of-the-art apparatus of the type described below Ifom commercial sources. Just as home-built NMR spectrometers capable of multidimensional or solid-state spectroscopies were still being home built in the late 1970s and now are almost exclusively based on commercially prepared apparatus, it is reasonable to expect that ultrafast spectroscopy in the next decade will be conducted almost exclusively with apparatus ifom conmiercial sources based around entirely solid-state systems. 

Figure B2.1.1 Femtosecond light source based on an amplified titanium-sapphire laser and an optical parametric amplifier. Symbols used P, Brewster dispersing prism X, titanium-sapphire crystal OC, output coupler B, acousto-optic pulse selector (Bragg cell) FR, Faraday rotator and polarizer assembly DG, diffraction grating BBO, p-barium borate nonlinear crystal.

Perhaps the ultimate femtosecond light source, the OPA exploits a nonlinear parametric process to amplify a portion of... 

The OPA should not be confiised with an optical parametric oscillator (OPO), a resonant-cavity parametric device that is syncln-onously pumped by a femtosecond, mode-locked oscillator. 14 fs pulses, tunable over much of the visible regime, have been obtained by Hache and co-workers [49, with a BBO OPO pumped by a self-mode-locked Ti-sapphire oscillator. 

Wilhelm T, Piel J and Riedle E 1997 Sub-20 fs pulses tunable across the visible from a blue-pumped single-pass noncollinear parametric converter Opt. Lett. 22 1494-6... 

Shirakawa A, Sakane I and Kobayasi T 1998 Pulse-front-matched optical parametric amplification for sub-10 fs pulse generation tunable in the visible and near infrared Opt. Lett. 23 1292-4... 

Cerullo G, Nisoli M, Stagira S and De Silvestri S 1998 Sub-8 fs pulses from an ultrabroadband optical parametric amplifier in the visible Opt. Lett. 23 1283-5... 

Yakovlev V V, Kohler B and Wilson K R 1994 Broadly tunable 30 fs pulses produced by optical parametric generation Opt. Lett. 19 2000-2... 

Reed M K, Steiner-Shepard M K and Negus D K 1994 Widely tunable femtosecond optical parametric amplifier at 250 kHz with a Ti sapphire regenerative amplifier Opt. Lett. 19 1855-7... 

Greenfield S R and Wasielewski M R 1995 Near-transform-limited visible and near-IR femtosecond pulses from optical parametric amplification using Type II p-barium borate Opt. Lett. 20 1394-6... 

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