Academic literature on the topic 'Errore quadratico medio'

Inversion of reflection traveltimes in anisotropic media can provide estimates of anisotropic coefficients required for seismic processing and lithology discrimination. Nonhyperbolic P-wave moveout for transverse isotropy with a vertical symmetry axis (VTI media) is controlled by the parameter η (or, alternatively, by the horizontal velocity Vhor), which is also responsible for the influence of anisotropy on all time‐processing steps, including dip‐moveout (DMO) correction and time migration. Here, we recast the nonhyperbolic moveout equation, originally developed by Tsvankin and Thomsen, as a function of Vhor and normal‐moveout (NMO) velocity Vnmo and introduce a correction factor in the denominator that increases the accuracy at intermediate offsets. Then we apply this equation to obtain Vhor and η from nonhyperbolic semblance analysis on long common midpoint (CMP) spreads and study the accuracy and stability of the inversion procedure. Our error analysis shows that the horizontal velocity becomes relatively well‐constrained by reflection traveltimes if the spreadlength exceeds twice the reflector depth. There is, however, a certain degree of tradeoff between Vhor and Vnmo caused by the interplay between the quadratic and quartic term of the moveout series. Since the errors in Vhor and Vnmo have opposite signs, the absolute error in the parameter η (which depends on the ratio Vhor/Vnmo) turns out to be at least two times bigger than the percentage error in Vhor. Therefore, the inverted value of η is highly sensitive to small correlated errors in reflection traveltimes, with moveout distortions on the order of 3–4 ms leading to errors in η up to ±0.1—even in the simplest model of a single VTI layer. Similar conclusions apply to vertically inhomogeneous media, in which the interval horizontal velocity can be obtained with an accuracy often comparable to that of the NMO velocity, while the interval values of η are distorted by the tradeoff between Vhor and Vnmo that gets amplified by the Dix‐type differentiation procedure. We applied nonhyperbolic semblance analysis to a walkaway VSP data set acquired at Vacuum field, New Mexico, and obtained a significant value of η = 0.19 indicative of nonnegligible anisotropy in this area. Then we combined moveout inversion results with the known vertical velocity to resolve the anisotropic coefficients ε and δ. However, in agreement with our modeling results, η estimation was significantly compounded by the scatter in the measured traveltimes. Certain instability in η inversion has no influence on the results of anisotropic poststack time migration because all kinematically equivalent models obtained from nonhyperbolic moveout give an adequate description of long‐spread reflection traveltimes. Also, inversion of nonhyperbolic moveout provides a relatively accurate horizontal‐velocity function that can be combined with the vertical velocity (if it is available) to estimate the anisotropic coefficient ε. However, η represents a valuable lithology indicator that can be obtained from surface P-wave data. Therefore, for purposes of lithology discrimination, it is preferable to find η by means of the more stable DMO method of Alkhalifah and Tsvankin.

La interpolación de temperatura en cuerpos de agua permite realizar predicciones de puntos de muestreo que no presentan datos. En la presente investigación se evaluaron 12 métodos de interpolación para estimar la temperatura del reservorio del Centro de Experimentación Académica Salache (CEASA) de la Universidad Técnica de Cotopaxi. Los datos recolectados en campo fueron interpolados aleatoriamente y comparados con los reales en base al error medio (EM), error absoluto medio (MAE), error medio cuadrático (MSE), raíz del error cuadrático (RMSE) y coeficiente de determinación (R2). La interpolación más apropiada para la representación de la variable temperatura en el reservorio fue el del método del Polinomio Local con un MSE de 0,22 y RMSE de 0,47 y R2 de 0,53. Este método se puede utilizar para obtener datos de temperatura del reservorio, disminuyendo costos de tiempo y dinero que demandaría el levantamiento de información en campo. Palabras clave: Interpolación, Temperatura, Polinomio Local, Reservorio CEASA. ABSTRACT The interpolation of temperature in bodies of water allows making predictions of sampling points that do not present data. In the present investigation, 12 interpolation methods were evaluated to estimate the reservoir temperature of the Salache Academic Experimentation Center (CEASA) at the Technical University of Cotopaxi. The data collected in the field were randomly interpolated and compared with the real ones based on the mean error (MS), mean absolute error (MAE), mean square error (MSE), the root of the quadratic error (RMSE) and coefficient of determination (R2). The most appropriate interpolation for the representation of the variable temperature in the reservoir was the Local Polynomial method with an MSE of 0.22 and RMSE of 0.47 and R2 of 0.53. This method can be used to obtain reservoir temperature data, decreasing the time and money costs that gathering information would require in the field require. Key words: Interpolation, Temperature, Local Polynomial, CEASA Reservoir.

Seismic forward modeling in tilted transverse isotropic (TTI) media is crucial for the application of reverse time migration and full-waveform inversion. Modeling based on conventional coupled pseudoacoustic wave equations not only generates SV-wave artifacts, but it also suffers from instabilities in which the anisotropy parameter [Formula: see text]. To address these issues, we have started with the exact vertical transversely isotropic phase velocity formula and developed novel pure qP- and qSV-wave governing equations in TTI media by using the optimal quadratic approximation. For the convenience of using finite-difference (FD) method to solve the new pure qP- and qSV-wave wave equations, we decompose the equations into a combination of a time-space-domain wave equation that can be solved by the FD method and a Poisson equation that can be solved by the pseudospectral method. We find that the high-frequency errors caused by the pseudospectral method and the usual truncation errors in FD schemes may be responsible for the instability of the numerical simulations. To stabilize the computation, we design a 2D low-pass filtering operator to eliminate severe high-frequency numerical noise. Several numerical examples demonstrate that modeling using the new pure qP-wave equations does not have qSV-wave artifacts interference and is stable for [Formula: see text]. Our results indicate that our method can achieve highly accurate and stable modeling results even in extremely complex TTI media.

One of the most serious problems in anisotropic velocity analysis is the trade-off between anisotropy and lateral heterogeneity, especially if velocity varies on a scale smaller than the maximum offset. We have developed a P-wave MVA (migration velocity analysis) algorithm for transversely isotropic (TI) models that include layers with small-scale lateral heterogeneity. Each layer is described by constant Thomsen parameters [Formula: see text] and [Formula: see text] and the symmetry-direction velocity [Formula: see text] that varies as a quadratic function of the distance along the layer boundaries. For tilted TI media (TTI), the symmetry axis is taken orthogonal to the reflectors. We analyzed the influence of lateral heterogeneity on image gathers obtained after prestack depth migration and found that quadratic lateral velocity variation in the overburden can significantly distort the moveout of the target reflection. Consequently, medium parameters beneath the heterogeneous layer(s) are estimated with substantial error, even when borehole information (e.g., check shots or sonic logs) is available. Because residual moveout in the image gathers is highly sensitive to lateral heterogeneity in the overburden, our algorithm simultaneously inverts for the interval parameters of all layers. Synthetic tests for models with a gently dipping overburden demonstrate that if the vertical profile of the symmetry-direction velocity [Formula: see text] is known at one location, the algorithm can reconstruct the other relevant parameters of TI models. The proposed approach helps increase the robustness of anisotropic velocity model-building and enhance image quality in the presence of small-scale lateral heterogeneity in the overburden.

The paper considers the problem of determining the local inhomogeneity of the medium from the natural frequencies of string oscillation. The inhomogeneity is modeled in three sections: in the first and third sections medium is homogeneous, and on average section the elastic characteristics are modeled by a quadratic function. This model is implemented using the conjugation conditions at boundary between media. It is shown that to identify the center of an inhomogeneity and determine its size, two natural frequencies are enough, and in the case of rigid fixing of both ends of the string, the solution of the problem is dual. The problem is solved by expanding the fundamental system of solutions into a power series in the variables x and λ. The estimates of the error of the method are given.

The relation between the significant factors and the combustion temperature (T) of Liquid Petroleum Gas (LPG) on the spherical packed-bed porous burner is investigated. Alumina-Cordierite ceramic balls having the average diameter (d) of 3 mm. and the porosity (ε) of 0.322 are employed as porous media. The multiple-linear and multiple-quadratic regressions are used to analyze the data at the equivalence ratio (F) of 0.58 – 0.66 and volumetric premixed-gas flow rate (Vmix) in a range of 10 – 25 m3/h. The porous thickness (H) is in the range of 2.5 – 7.5 cm. Thus, independent variables are F, Vmix and H. The dependent variable is the maximum temperature (T) of combustion LPG on the porous burner. For statistical analysis, both main and interaction of independent variables effecting to the combustion temperature are investigated. The results showed that, for the case of multiple-linear regression, an equations recommended in prediction of the T on porous burner is T = 1375.603(F) +179.636(H) – 295.028(FH) – 9.628(HVmix) + 16.368(FVmixH) with a coefficient of determination (R2) of 0.998 and the standard error of the estimation of 42.7365. In the case of multiple- quadratic regression, a proper equation used in predicting T on porous burner is T = 2133.184(F)2 + 1.247(Vmix)2 + 17.248(H)2 – 2.916(FVmix )2 – 42.107(FH)2 – 0.049(VmixH)2 + 0.123(FVmixH)2 with R2 of 0.997 and standard error of the estimation of 44.2979. In addition, the comparison between the experimental results and the predicted estimation is reported that different percentage of both regressions and experimental results is satisfied.

To compute the phase velocities in the weakly anisotropic media, we propose to transform the Christoffel matrix K into an adapted coordinate system, and, then, apply the perturbation theory to the resulting matrix X. For a weakly anisotropic medium, the off-diagonal elements of the matrix X are small compared to the diagonal ones, and two of them are equal to 0. The diagonal elements of the matrix X are initial approximations of the phase velocities squared. To refine them, it is proposed to use either iterative schemes or Taylor series expansions. The initial terms of the series and the formulas of iterative schemes are expressed through the elements of the matrix X and have a compact analytical representation. The odd-order terms in the series are equal to 0. To approximate the phase velocities of the S1 and S2 waves, a stable method is proposed based on solving a quadratic equation with the coefficients being expressed in terms of the matrix elements and the precomputed value of the qP wave phase velocity squared. For all iterative schemes and series, the convergence conditions are derived. The polarization vector of the wave with the square of the phase velocity is defined as the column with maximum modulus of cofactor of the matrix K-I. The group velocities vectors are computed based on the known components of the polarization vector, the directional vector, and the density-normalized stiffness coefficients. The computational accuracy is demonstrated for the standard orthorhombic model. It is shown how the perturbation theory can be applied to media with strong anisotropy. To do this, first we need to apply several QR transforms or Jacobi rotations of the Christoffel matrix, and then use the perturbation theory. This method with four Jacobi rotations is applied to the calculation of the phase velocities squared for a triclinic medium with a maximum number (32) of singularity points. In this case, the phase velocities are computed with a relative error less than 0,004 %.

Despite the presence of glycogen and triglycerides as energy reserves in bovine embryos, the viability of embryonic cells in culture is maintained primarily by energetic substrates present in the culture medium. The aim of this experiment was evaluate the embryo metabolism during three important stages of development: Days 1 to 3, Days 3 to 5, and Days 5 to 7; before the formation of Barr body, before the differentiation into ICM and trophectoderm, and during the blastocyst formation, respectively. In this study, we evaluated some energetic substrates (Krebs cycle intermediates). For these analyses we chose to use proton magnetic resonance (H1-NMR) spectroscopy. Matured oocytes were purchased from DeSoto Biosciences (Seymour, TN, USA). The matured cumulus-oocyte complexes were fertilized in vitro according to our standard procedures (Rubessa et al. 2011 Theriogenology 76, 1347–1355). For each group (Days 1–3, 3–5, and 5–7), the zygotes were place in individual drops, and after 48 h of culture, they were placed into well of the well (WOW) culture. For the 3–5 and 5–7 groups, the zygotes were first place in 400 μL of SOF and then moved in a single drop. The 5–7 group was not placed in the WOW system. Zygotes were incubated in a humidified mixture of 5% CO2, 6% O2, and 88% N2 in air at 39°C. The embryos were scored for quality on the basis of morphological criteria. Samples of media (40 μL) were added to 560 μL of a stock solution prepared by dissolving 5.0 mg of sodium 3-(trimethylsilyl)-2,2′,3,3′-tetradeuteropropionate (TSP) in 50 mL of deuterium oxide. The TSP acted both as a chemical shift reference and as an internal standard for the purposes of quantitation. The resulting diluted samples were transferred to a 5-mm NMR tube. Samples were analysed on a Varian VNS-750 NB (750 MHz) spectrometer (Agilent Technologies, Santa Clara, CA, USA). A total of 30 embryos were evaluated, 10 per stage. Data were statistically analysed through an analysis of variance using the Generalized Linear Model (GLM) procedure (SPSS, version 18, 2009). Bonferroni’s post-hoc test was used to perform statistical multiple comparison. The α level was set at 0.05. All data were expressed as quadratic mean and mean standard error. The results, reported in Table 1, show that there was no statistical difference when we compare the lactate, myo-inositol, and pyruvate concentrations. However, there were significant differences when we focused on acetate and formate levels: after Day 3 the production of these two substrates significantly increased. Formate and acetate are important metabolites of the Krebs cycle. The changes of these two substrates are important signs that embryos start glycolysis after Day 3. Table 1.Quadratic means and mean standard errors of formate, lactate, myo-inositol, pyruvate, and acetate for Day 1–3, 3–5, 5–7, and control groups

The existence of a TPG can generate a relatively high pressure gradient in the process of fluid flow in porous media in low-permeable reservoirs, and neglecting the QPGTs in the governing equations, by assuming a small pressure gradient for such a problem, can cause a significant error in predicting the formation pressure. Based on these concerns, in consideration of the QPGT, a moving boundary model of radial flow in low-permeable reservoirs with the TPG for the case of a constant flow rate at the inner boundary is constructed. Due to strong nonlinearity of the mathematical model, a numerical method is presented: the system of partial differential equations for the moving boundary problem is first transformed equivalently into a closed system of partial differential equations with fixed boundary conditions by a spatial coordinate transformation method; and then a stable, fully implicit finite difference method is used to obtain its numerical solution. Numerical result analysis shows that the mathematical models of radial flow in low-permeable reservoirs with TPG must take the QPGT into account in their governing equations, which is more important than those of Darcy’s flow; the sensitive effects of the QPGT for the radial flow model do not change with an increase of the dimensionless TPG.

To develop a preantral follicular culture system that will support follicular growth and result in fertilizable oocytes, we conducted an experiment designed to determine the best medium for culture. In our preliminary experiment, we compared 2 common base media used for porcine oocytes: α-minimal essential medium and NCSU-23. Ovaries were collected from prepubertal gilts at a local abattoir and transported to the laboratory in saline solution (0.9% NaCl) maintained at 30–35°C. The ovaries were cut into small pieces (1–3 mm), and preantral follicles were isolated mechanically. Preantral follicles from 280 to 300 μm in diameter were collected into a small dish containing medium TCM199 (Lonza 12–117F) supplemented with 5% fetal bovine serum. The follicles were transferred from the collecting medium to the culture medium that consisted of base medium (NCSU23 or α-minimal essential medium) supplemented with 3.5 μg mL–1 of insulin, 10 μg mL–1 of transferrin, 100 μg mL–1 of l-ascorbic acid, 7.5% porcine serum, and 1.5 ng mL–1 of FSH. The follicles were randomly distributed to the different experimental treatments and cultured for 6 days in 24-well cell culture plates, with 3 follicles per well in 280 μL of culture medium. The culture was carried out at 38.5°C in 5% CO2 in air. Culture medium was changed every 2 days with freshly prepared medium. The diameters of follicles were measured every 2 days, and each follicle was photographed and evaluated at 20× magnification. Forty-two follicles per group were analysed and collected in 4 replicates. Data were statistically analysed with ANOVA using the Generalized Linear Model (GLM) procedure (SPSS, version 18, SPSS Inc., Chicago, IL, USA), where the independent variable was the sample (group and day of culture). Tukey's post hoc test was used to perform multiple comparisons; the α level was set at 0.05. All data were expressed as quadratic means with standard error of the means. Only the antrum formation was evaluated by chi-square test. The results, reported in Table 1, show that there was no statistical differences between follicle size between NCSU23 or α-minimal essential media, but at Day 6 there was a positive trend (P = 0.08). Otherwise, when we compared the size inside the groups, we observed that the preantral follicles grew more in α-minimal essential media than in NCSU23. The percentages of antrum formation were 65 v. 76% (NCSU23 and α-minimal essential media, respectively). These results support the use of α-minimal essential media because it had a positive effect on the antrum formation, and that after Day 4 some follicles could undergo a regression phase. Future studies will be necessary to evaluate the molecular status and the hormone production. Table 1.Follicle size (μm) from Day 0 to Day 6

Il mio lavoro ha l'intento di esporre alcuni aspetti del filtro di Kalman. Una prima parte è dedicata alla sua contestualizzazione storica, mentre successivamente l'attenzione si sposta sugli aspetti tecnici e, in particolare, all'interpretazione probabilistica delle equazioni matematiche che lo costituiscono. Vengono esposti risultati fondamentali per la derivazione di tali equazioni, i quali permettono di interpretare la stima fornita dal filtro in termini di attesa condizionata. In conclusione sono esposte due applicazioni, al fine di mostrare la concreta applicabilità del filtro di Kalman.

Orientador: Jose Maria Campos dos Santos
Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica
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Resumo: Neste trabalho foi estudado o controle ativo de ruído em dutos usando técnicas de filtragem adaptativa. Foi utilizado o método de controle adaptativo do Mínimo Erro Médio Quadrático (Least Mean Square - LMS) normalizado com sinal de referência filtrado, NFXLMS. Três geometrias de dutos montados em uma bancada experimental para os casos de controle monocanal, multierro e multiexcitação foram verificados. Os sinais de perturbação investigados foram: tonal (seno), aleatório e uma com composição de duas senoidais no caso multiexcitação. Avaliações das impedâncias analíticas e experimentais foram verificadas no estudo de uma configuração do duto para o caso de controle monocanal. Simulações e experimentos foram realizados para diversas geometrias de dutos e diferentes tipos de excitação. Parâmetros do algoritmo, como o número de pesos do filtro adaptativo, faixa de frequência de perturbação, fator de convergência do algoritmo e freqüência de amostragem foram investigados nos casos tratados. Os resultados encontrados nos experimentos realizados para o controlador monocanal e multierro confirmaram as avaliações efetuadas nas simulações. Para o caso multiexcitação, limitações da placa de processamento de sinal não permitiram a obtenção de resultados conclusivos
Abstract: In this work was investigated the active control of noise in ducts using the techniques of adaptive filtering. The normalized, filtered reference Least Mean Square algorithm control method - NXLMS was used. Three shapes of duct system in a supported experimental test rig for the cases of control mono-channel, multi-error, and multi-input were verified. The investigated disturbance signals were: tonal (sine), random, and a composition of two sinusoids for the case of multi-input. Evaluations of analytical and experimental impedances were verified in a configuration study of mono-channel duct contraI case. Simulations and experiments were accomplished for several duct shapes and different types of excitations. AIgorithm parameters, such as the weight number of adaptive filter, the disturbance frequency range, the convergence factor of the algorithm, and the sampling frequency were investigated in the treated cases. The experimental results obtained for the mono-channel and multi-error controller confirm the evaluations obtained in the simulations. For the multi-input case, limitations of the DSP board didn't allow to obtain conclusive results
Mestrado
Mecanica dos Sólidos e Projeto Mecanico
Mestre em Engenharia Mecânica