Main Harmonic Components Research Articles

Estimation and Removal of Tidal Effects From Pressure Data

Summary We consider field pressure data from two wells, one offshore and one onshore. The onshore well is shut-in and experiences only a very small pressure decline due to interference, whereas in the offshore case, the late time buildup data appear to be severely corrupted by ocean tidal effects. The objectives in both cases are to determine the tidal signal that can be used to estimate formation compressibility and to remove the tidal signal from the measured data. For the onshore well, we use a Savitzky-Golay (SG) filter to smooth the pressure data. Subtracting the smooth data from the measured signal yields a modified signal that ideally represents the earth tidal signal plus measurement error. A s the main harmonic components of the earth tidal signal are known, we perform a least-squares fit of the modified pressure data with a series of sines and cosines that contain only the known frequencies of the earth tide. By subtracting the series obtained by least-squares fitting from the true signal, we remove the effect of the earth tide. In the offshore case, the time span of data that are severely affected by tidal effects is too short to use the SG filter with confidence. As the reservoir pressure change due to the tides is well-approximated by a damped and delayed version of the seafloor response, a least-squares fit of the data with a function that follows the underlying buildup trend plus an attenuated-delayed response of the measured seafloor pressure trace allows one to obtain a good estimate of the attenuation factor and time delay so that the tidal component of the bottomhole pressure change can be determined and removed from the measured pressure.

Modeling hydrodynamics in the Ebrié Lagoon (Côte d’Ivoire)

A two-dimensional depth-averaged model for tide propagation is used to determine the respective impact of several forcings on water mass circulation in the Ebrié lagoon (Côte d’Ivoire). This lagoon is connected to the Atlantic through a narrow artificial channel and supplied with freshwater by a major river. A real tide is imposed at the seaward boundary through the main harmonic components. Tides propagate from the mouth of the channel. The tidal amplitude decreases with distance from the sea connection while the shallow water depth deforms the tidal wave. A large asymmetry in water circulation shows up throughout the lagoon: very limited to the western part of the lagoon, correlated with the freshwater discharge in the eastern part, fully tide-controlled in the central part. The trade winds (south-west direction) have been verified as an important driving force, acting in the whole lagoon and generating a set-up of the tide amplitude in the area of Abidjan harbour.

Harmonic compensation of induction watthour meter performance

Abstract This paper analyzes the variation of the registration error of an induction watthour meter (IWHM) with respect to those parameters concerning the harmonic characteristics of the load and harmonic performance of the IWHM. Based on an analysis of the results of error variation, two types of compensation methods, namely, meter external methods and meter internal methods, are proposed to improve the accuracy of the IWHM when operated in harmonic situations. The meter external methods are related to the harmonic characteristics of the load, while the meter internal methods are associated with the harmonic performance of the IWHM. Each compensation method is comprised of several measures. This paper presents these measures for each compensation method, and gives detailed illustrations of the practical aspects for each measure. The feasibility of each compensation method is assessed, and some useful suggestions for utilities, users and manufacturers of IWHMs are offered. The study results show that the registration error due to constant single power harmonic interference can be fully compensated. When multiple power harmonics exist, however, the compensation, in general, can only focus on the main harmonic component to reduce the registration error to as low as possible. The effectiveness of those compensation methods which are feasible has been confirmed by the experimental results.

Vostok (Antarctica) climate record time-scale deduced from the analysis of a borehole-temperature profile

Several sets of temperature measurements were carried out in 1972- 88 in the Vostok boreholes. They have provided the ice-sheet temperature profile down to a depth of 2000 m. The accuracy of the profile is sufficient to analyze perturbations induced by the surface-temperature variations over the last climatic cycle. The mathematical model developed for the ice-temperature computation is applied to solve an inverse problem. The amplitudes and phase lags of the main harmonic components in the surface-temperature variations are reconstructed on the basis of fitting the calculated ice-temperature profile to the experimental one with the assumption that Milankovich's cycles (100, 41, 23 and 19 kyear) are dominant in the climate oscillations. The paleotemperature record simulated with the inverse procedure is revealed to be insensitive to the model parameters varied within the range of their uncertainty. Minimal standard deviation between calculated and measured temperature profiles is found of the same order as the reproducibility of the temperature measurements (0.005-0.01°C). Although the simulated temperature-time curve obtained in this study does not contain short-term variations, all the main climate events predicted from the ice-core isotope analysis can be recognized. Thus, the age of the events can be verified independently of the ice-sheet dynamics dating. The resultant time-scale for the Vostok record appears to be in good agreement with the dating of climate events recorded in deep-sea sediments.

Vostok (Antarctica) climate record time-scale deduced from the analysis of a borehole-temperature profile

Several sets of temperature measurements were carried out in 1972- 88 in the Vostok boreholes. They have provided the ice-sheet temperature profile down to a depth of 2000 m. The accuracy of the profile is sufficient to analyze perturbations induced by the surface-temperature variations over the last climatic cycle. The mathematical model developed for the ice-temperature computation is applied to solve an inverse problem. The amplitudes and phase lags of the main harmonic components in the surface-temperature variations are reconstructed on the basis of fitting the calculated ice-temperature profile to the experimental one with the assumption that Milankovich's cycles (100, 41, 23 and 19 kyear) are dominant in the climate oscillations. The paleotemperature record simulated with the inverse procedure is revealed to be insensitive to the model parameters varied within the range of their uncertainty. Minimal standard deviation between calculated and measured temperature profiles is found of the same order as the reproducibility of the temperature measurements (0.005-0.01°C). Although the simulated temperature-time curve obtained in this study does not contain short-term variations, all the main climate events predicted from the ice-core isotope analysis can be recognized. Thus, the age of the events can be verified independently of the ice-sheet dynamics dating. The resultant time-scale for the Vostok record appears to be in good agreement with the dating of climate events recorded in deep-sea sediments.

Vostok (Antarctica) climate record time-scale deduced from the analysis of a borehole-temperature profile

Several sets of temperature measurements were carried out in 1972- 88 in the Vostok boreholes. They have provided the ice-sheet temperature profile down to a depth of 2000 m. The accuracy of the profile is sufficient to analyze perturbations induced by the surface-temperature variations over the last climatic cycle. The mathematical model developed for the ice-temperature computation is applied to solve an inverse problem. The amplitudes and phase lags of the main harmonic components in the surface-temperature variations are reconstructed on the basis of fitting the calculated ice-temperature profile to the experimental one with the assumption that Milankovich's cycles (100, 41, 23 and 19 kyear) are dominant in the climate oscillations. The paleotemperature record simulated with the inverse procedure is revealed to be insensitive to the model parameters varied within the range of their uncertainty. Minimal standard deviation between calculated and measured temperature profiles is found of the same order as the reproducibility of the temperature measurements (0.005-0.01°C). Although the simulated temperature-time curve obtained in this study does not contain short-term variations, all the main climate events predicted from the ice-core isotope analysis can be recognized. Thus, the age of the events can be verified independently of the ice-sheet dynamics dating. The resultant time-scale for the Vostok record appears to be in good agreement with the dating of climate events recorded in deep-sea sediments.

Scattering of laser and x-ray radiation by ultrasmooth surfaces formed by diamond turning. Experimental results

An original method was developed for investigating the quality of the surfaces of laser mirrors formed by diamond turning. This method was based on the scattering of laser and x-ray radiation from the mirrors. An analysis of the experimental scattering diagrams made it possible to identify not only the main harmonic component of the microrelief, but also a series of additional long-wavelength harmonics which were not multiples of the main one. A study was made of the influence of the curvature of the surface relief on the shape of the scattering diagram. Criteria were formulated for the relief curvature, which would make it possible to analyze quantitatively the scattering data. The reliability of the results was confirmed by the agreement of the surface data obtained from the laser and x-ray (with wavelengths in the ratio ~ 4000) scattering diagram obtained for different angles of incidence. The proposed method should find applications in quality control of various optical components irrespective of the material of the reflecting or transmitting coating.

Ising model with competing axial interactions in the presence of a field: A renormalization-group treatment.

On the basis of an \ensuremath{\epsilon} expansion, we present a renormalization-group analysis of the anisotropic next-nearest-neighbor Ising model in a field. For small fields, the \ensuremath{\gamma} surface remains XY-like. For larger fields, we confirm the existence of lines of tricritical points which are governed by Gaussian-type exponents. We pay special attention to the many couplings between a two-component critical spin field, associated with the main harmonic component of the magnetization, and several noncritical spin fields, associated with the uniform and the higher harmonic components. We remark that it is necessary to take into account the uniform and the second-harmonic components of the magnetization to describe the tricritical behavior.

Ising model with competing axial interactions in the presence of a field: A mean-field treatment

We study a layered Ising model with competing interactions between nearest and next-nearest layers in the presence of a magnetic field. The analysis is restricted to the mean-field approximation with one effective field for each layer. The high-temperature region is studied analytically. The $\ensuremath{\lambda}$ surface, separating the paramagnetic and the modulated phases, is bounded by two lines of tricritical points which join smoothly at the Lifshitz point and terminate at multicritical points, beyond which lines of critical and double critical end points are expected to appear. The magnetization structure near the $\ensuremath{\lambda}$ surface can be described as having an almost sinusoidal oscillation, with the higher harmonic components contributing as perturbations. Both odd and even higher-harmonic components are present in nonzero fields, and the $n$th harmonic component depends asymptotically on the $n$th power of the main harmonic component. The low-temperature region is studied numerically. We construct $T\ensuremath{-}H$ phase diagrams, which exhibit a variety of modulated phases, for various values of the ratio of the strength of the competing interactions.

Code for electricity meters

This paper analyzes the variation of the registration error of an induction watthour meter (IWHM) with respect to those parameters concerning the harmonic characteristics of the load and harmonic performance of the IWHM. Based on an analysis of the results of error variation, two types of compensation methods, namely, meter external methods and meter internal methods, are proposed to improve the accuracy of the IWHM when operated in harmonic situations. The meter external methods are related to the harmonic characteristics of the load, while the meter internal methods are associated with the harmonic performance of the IWHM. Each compensation method is comprised of several measures. This paper presents these measures for each compensation method, and gives detailed illustrations of the practical aspects for each measure. The feasibility of each compensation method is assessed, and some useful suggestions for utilities, users and manufacturers of IWHMs are offered. The study results show that the registration error due to constant single power harmonic interference can be fully compensated. When multiple power harmonics exist, however, the compensation, in general, can only focus on the main harmonic component to reduce the registration error to as low as possible. The effectiveness of those compensation methods which are feasible has been confirmed by the experimental results.