Noise Level Of Data Research Articles

Study on terrestiral noise in data of geomagnetic total field in North China

The terrestrial noise in the differencial data of geomagnetic total field recorded at 21h in North China was fitted by using the geomagnetic vector data from Beijing Observatory. The terrestrial noise level and its spatial feature in this region was discussed. A method, which may be useful for justifying the quality of fitting, was provided in this paper. The analysis indicates that the terrestrial noise is one of the important noise in tectonomagnetic study. It is shown that the susceptibility effect is quite small and the orientation effect is the main component in the terrestrial noise in North China. The rough spatial feature of the magnetic anomaly in crustal substance was infered from the spatial feature of terrestrial noise. The measurement precision and the source noise level of data at 21h in this region were obtained in the analysis of residual noise.

A practical method for calculating largest Lyapunov exponents from small data sets

Detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the largest Lyapunov exponent. Lyapunov exponents quantify the exponential divergence of initially close state-space trajectories and estimate the amount of chaos in a system. We present a new method for calculating the largest Lyapunov exponent from an experimental time series. The method follows directly from the definition of the largest Lyapunov exponent and is accurate because it takes advantage of all the available data. We show that the algorithm is fast, easy to implement, and robust to changes in the following quantities: embedding dimension, size of data set, reconstruction delay, and noise level. Furthermore, one may use the algorithm to calculate simultaneously the correlation dimension. Thus, one sequence of computations will yield an estimate of both the level of chaos and the system complexity.

Geostatistical evaluation of satellite radar altimetry for high-resolution mapping of Lambert Glacier, Antarctica

The potential of satellite radar altimetry for high-resolution mapping of Antarctic ice streams is evaluated, using retracked and slope-corrected data from the Lambert Glacier and Amery Ice Shelf area, East Antarctica, acquired by Geosat during the Exact Repeat Mission (ERM), 1986–89. The map area includes lower Lambert Glacier north of 72.18°S, the southern Amery Ice Shelf, and the grounded inland ice sheet on both sides. The Geosat ERM altimetry is found to provide substantially more complete coverage than the 1978 Seasat altimetry, due to improved tracking. Variogram methods are used to estimate the noise levels in the data as a function of position throughout the map area. The spatial structure in the data is quantified by constructing experimental variograms using altimetry from the area of the grounding zone of Lambert Glacier, which is the area chiefly of interest in this topographically complex region. Kriging is employed to invert the along-track height measurements onto a fine-scale 3 km grid. The unsmoothed along-track Geosat ERM altimetry yields spatially continuous maps showing the main topographic features of lower Lambert Glacier, upper Amery Ice Shelf and the adjacent inland ice sheet. The probable position of the grounding line of Lambert Glacier is identified from a break in slope at the grounded ice/floating ice transition. The approximate standard error of the kriged map is inferred from the data noise levels.

Geostatistical evaluation of satellite radar altimetry for high-resolution mapping of Lambert Glacier, Antarctica

The potential of satellite radar altimetry for high-resolution mapping of Antarctic ice streams is evaluated, using retracked and slope-corrected data from the Lambert Glacier and Amery Ice Shelf area, East Antarctica, acquired by Geosat during the Exact Repeat Mission (ERM), 1986–89. The map area includes lower Lambert Glacier north of 72.18°S, the southern Amery Ice Shelf, and the grounded inland ice sheet on both sides. The Geosat ERM altimetry is found to provide substantially more complete coverage than the 1978 Seasat altimetry, due to improved tracking. Variogram methods are used to estimate the noise levels in the data as a function of position throughout the map area. The spatial structure in the data is quantified by constructing experimental variograms using altimetry from the area of the grounding zone of Lambert Glacier, which is the area chiefly of interest in this topographically complex region. Kriging is employed to invert the along-track height measurements onto a fine-scale 3 km grid. The unsmoothed along-track Geosat ERM altimetry yields spatially continuous maps showing the main topographic features of lower Lambert Glacier, upper Amery Ice Shelf and the adjacent inland ice sheet. The probable position of the grounding line of Lambert Glacier is identified from a break in slope at the grounded ice/floating ice transition. The approximate standard error of the kriged map is inferred from the data noise levels.

An iterative method for inverse scattering problems

An iterative procedure is proposed to solve inverse-scattering problems completely for radiative transfer in a scattering medium by transparent plates. Several numerical simulations have been performed to examine the adequacy of the proposed method. The procedure is stable, even for rather noisy input data, but the accuracy of inverted results deteriorates with increasing magnitude of random errors involved in the input data. However, acceptable results can be obtained as long as the noise level of the input data is of the same degree as that observed in actual light-scattering experiments.

Numerical experiments in broadband receiver function analysis

AbstractThe use of broadband receiver function analysis to estimate the fine-scale S-velocity structure of the lithosphere is becoming increasingly popular. A series of numerical experiments shows several important aspects of this technique, with emphasis on estimation of dipping interfaces. The recent modification introduced to the receiver function analysis technique that preserves absolute amplitudes (Ammon, 1991) is more robust than the previous technique of modeling receiver functions that were normalized to unit amplitude. Using the latter method, shallow (e.g., depths less than ∼2 km) high-velocity contrast interfaces may alter the apparent amplitudes of Ps phases and produce inaccuracies in the Earth model developed. The use of absolute amplitudes minimizes this potential for error. When research targets include deep dipping structure, tight stacking bounds (e.g., ≦ 10° in backazimuth (BAZ) and epicentral distance (Δ)) should be applied to avoid attenuating Ps phases and to aid in the identification of reverberations or scattered energy. Reverberations sample a relatively large lateral range about the recording site (e.g., a radius of 1 to 1.5 times the depth of the reflecting interface) and in the presence of dipping interfaces exhibit drastic variations in amplitude and arrival time as a function of BAZ and Δ. Thus, they cannot readily be used to provide constraints on the Earth structure. Formal inversion techniques, which attempt to match all arrivals in the waveform, must be used with caution when modeling receiver functions from complex regions. Only those phases whose amplitude and arrival-time variations as a function of BAZ and Δ are consistent with those of Ps conversions should be modeled. Forward modeling may resolve, depending upon the data quality and noise level, S-velocity contrasts greater than ∼ 0.2 to 0.4 km / sec. Layers of thickness 2 to 5 km may be accurately imaged, and transition zones may be examined by considering various frequency bands of the data. In order to better understand the resolving power of the data, the averaging functions associated with the receiver functions may be calculated from the observed data and, if desired, used in the forward modeling process.

Unsupervised noise removal algorithms for three-dimensional confocal fluorescence microscopy

Algorithms are presented for effective suppression of the quantum noise artifact that is inherent to three-dimensional confocal fluorescence microscopy images of extended spatial objects such as neurons. The specific advances embodied in these algorithms are as follows: (i) they incorporate an automatic and pattern-constrained three-dimensional segmentation of the image field, and use it to limit any smoothing to the interiors of specified image regions and hence avoid the blurring that is inevitably associated with conventional noise removal algorithms; (ii) they are ‘unsupervised’ in the sense that they automatically estimate and adapt to the unknown spatially and temporally varying noise level in the microscopy data. Fast computation is achieved by parallel computation methods, rather than by algorithmic or modelling compromises. The quantum noise artifact is modelled using a mixture of spatially non-homogeneous Poisson point processes. The intensity of each component process is constrained to lie in specific intervals. A set of segmentation and edge-site variables are used to determine the intensity of the mixture process. Using this model, the noise-removal process is formulated as the joint optimal estimation of the segmentation labels, edge-sites and intensity of the mixture Poisson point process, subject to a combination of stochastic priors and syntactic pattern constraints. The computations proceed iteratively, starting from a set of approximate user-supplied, or default initial guesses of the underlying random process parameters. An Expectation Maximization algorithm is used to obtain a more precise characterization of these parameters, that are then input to a joint estimation algorithm. Stereoscopic renderings of processed three-dimensional images of murine hippocampal neurons are presented to demonstrate the effectiveness of the method. The processed images exhibit increased contrast and significant smoothing and reduction of the background intensity while avoiding any blurring of the foreground neuronal structures.

Obtaining Earth surface gravity disturbances from a GPS-based ‘high-low’ satellite-to-satellite tracking experiment

A ‘high-low’ satellite-to-satellite tracking measurement process, involving a single low orbiter (300 km altitude) and the GPS constellation (20 189 km altitude), has been proposed by Jekeli & Upadhyay (1990) to estimate Earth surface gravity disturbances. This paper examines the potentiality of such a mission by initially conducting an error analysis based on signal-to-noise ratios of the spectra of intersatellite line-of-sight (los) accelerations possessing an assumed white noise process. Using a 60 day mission duration, los acceleration data rates ranging from 1 to 60s and data noise levels from 0.1 to 0.3 mGal, corresponding errors of commission and omission propagating into the spectrum of a desired set of 1° and/or 2° mean Earth surface vertical gravity disturbances (residual to harmonic degree and order n=m=6) were obtained. The resulting total estimated errors (in a global average sense) of the 1° mean disturbances ranged from 6 to 12 mGal, and for 2° values the range was 1.5 to 6 mGal, the lower error bounds corresponding to a 1 s data rate and a 0.1 mGal data noise level. An optimal least-squares collocation simulation was next carried out. The simulated los accelerations reflected all gravimetric perturbations due to an adopted true gravity field extending to n=m= 180. A downward continuation approach was used in conjunction with singular value decomposition techniques to predict 1° mean disturbances over two separate regions on the Earth's surface. For a 10° by 10° region possessing a fairly tranquil local gravity field, the overall RMS of 100 ‘true-predicted’ mean differences, using the aforementioned los data rates and noise levels, ranged from 5 to 9 mGal and was only 1 mGal when the data were noise-free. For a more turbulent 15° by 20° region, the RMS of 300 differences was 1.5 mGal using perfect data and was in the 6 to 11 mGal range using noisy data. Again, the lower error bounds corresponded to 1 s and 0.1 mGal data rate and noise levels. If the low satellite takes on a polar orbit one could therefore obtain respectable 1° mean disturbances and highly reliable 2° mean values over all previously inaccessible Earth surface areas.

Diagnosing Noisy Process Data using Neural Networks

An account of the application of neural networks for detecting and diagnosing faults during process transients in the presence of random measurement noise is presented The approach employs a feedforward neural network with backpropagation as the learning algorithm. Two representation techniques for capturing dynamic process trend data in the form of a timeseries as well as in the form of a moving average have been developed and used for training the network. Networks with various number of hidden units have been tested and compared with respect to their performance in recall and generalization. The time required for training increases substantially when the level of noise in the training data increases. Trained networks have excellent recall performance even in the presence of noise, in both steady state and dynamic processes. The networks are successful in diagnosing untrained, noisy single fault patterns in a large majority of the steady state and dynamic cases tested.

On ISCPPandpPdata and their use in delay-time tomography of the Caribbean region

Summary A major problem in P delay-time tomography is the inhomogeneous sampling of mantle structure by the P-wave ray paths resulting in low resolution in images of large regions of the upper mantle. Incorporation of PP and pP phases can improve the quality and reliability of tomographic images because they: (1) sample Earth structure not ordinarily sampled by direct P phases; (2) add rays that are oblique to rays of direct phases, which is especially important where the latter sample mantle structure in selected directions; and (3) pP data better constrain the earthquake focal depths. PP traveltimes have often been used in combination with P data in differential traveltime studies. We show that the assumptions and approximations necessary for this approach are problematic, and that they can be avoided when the P, PP and P data are used in tomographic inversion. We investigated the applicability of PP and pP delay times to the tomographic study of the aspherical mantle structure below the Caribbean region. The success of the application of data of the later arriving reflected waves depends critically on the quality of these data. We examined possible sources of error in the ISC PP and pP data and assessed the contribution to the delay times used in this study. For the Caribbean region, analyses of the ISC PP and pP delay times do not reveal biases due to effects of PP-waveform distortions, the asymmetry of the reflections, or due to misidentifications of phases that reflect at a surface other than that assumed. The noise level of PP and pP data is high with respect to data of the direct P-wave. This is accommodated by weighting with the inverse of the variance of the data of each of the three phases. The independent information that is revealed from the PP and pP data results in modifications of tomographic images based solely on P data. These modifications are important if the tomographic images are being used to understand the geodynamical history of convergent margins in the Caribbean region. We investigated the effect of adding data of later arriving phases to the ISC P data with sensitivity tests: we inverted synthetic delay times to which we added Gaussian noise with a standard error typical for the data of the three seismic phases. These tests demonstrate that the image resolution of shallow mantle structure is enhanced significantly by the incorporation of later arriving phases. Due to the absence of seismicity below 200 km the resolution improved less at deeper levels below the Caribbean region. In some poorly constrained parts of the solution the test results even indicate an apparent decrease of resolution. This is explained by changes in the rate of convergence of the inversion algorithm: in mantle regions where the effective sampling of structure improved by the addition of PP- and pP-wave ray paths, the convergence was speeded up at the expense of the convergence rate in regions where fewer or no PP- or pP-wave ray paths were added. A shortcoming of the resolution tests used in our study is that some specific problems of reported delay times are not reflected in synthetic data. We observe that ISC delay times of later arriving phases are not necessarily consistent with the reported hypocentral parameters, as most ISC-reported earthquake locations are computed from direct P-wave data. For the pP data, the inconsistency with event location not only results in a decrease of focal depths during relocation, but in a bias of the imaged velocity perturbations as well. This property of reported data is not modelled in resolution tests.

Contrast enhancement of noisy images by windowing: Limitations due to the finite dynamic range of the display system

A theoretical model has been developed to explain the effects of simple linear windowing on the apparent contrasts of signals in displayed digital images. The model predicts, and experimental results demonstrate, that the effective displayed contrast of a digital radiographic signal depends in a complex way upon interactions among the endpoints of the display scale, the signal contrast and noise level of the original data, the window center and display center selected, and the contrast enhancement factor applied. The results obtained from this work apply quantitatively to the highly idealized situation in which (i) a uniform signal is superimposed on a uniform background containing Gaussian pixel-value noise, and (ii) a linear (or exponential) relationship exists between the optical density of a film display (or the light intensity of a luminous display) and pixel value in some finite range. However, the qualitative effects demonstrated here may be expected to arise in a broad variety of situations involving strong digital contrast enhancement.

Reseating of ecological gradients. III. The effect of scale and niche breath measurements

Abundances of eleven Sphagnum species in 800 sample plots are used to investigate the effect of DCA rescaling on Levins' measure of niche breadth relative to three partitions of the water‐table gradient in a boreal Norwegian mire: (1) sample plots classified into 15 categories, each spanning an interval of 2 cm vertical extent, (2) as (1), but sequence of categories rescaled by DCA and sample plots reorganized into 15 categories with uniform beta diversity, and (3), sample plots ordinated by DCA and classified into 15 categories with uniform beta diversity by subdivision of an ordination axis highly correlated with median water‐table. Habitat niche breadth is shown to be dependent on four issues (in order of supposedly decreasing importance): (1) scale, (2) noise level of data, (3) homogeneity of individual samples, and (4), weighting function. Six problems relevant to interpretation of measurements of niche breadth are discussed: (1) range of measures, (2) spacing of categories, (3) scale, (4) choice of gradients, (5) number of samples, and (6), comparability of studies. For measures of habitat niche breadth to be biologically meaningful, four conditions have to be satisfied: (1) the gradients studied have important impact on the studied species, (2) sampling is adequate, (3) scaling of gradients is in compositional turnover, and (4), comparability is demonstrated prior to comparison with other studies. Revisions of current methods are proposed. The role of DCA in niche studies is particularly emphasized.

Resolution in seismic trace inversion by parameter estimation

An alternative to the conventional time series approach to single‐trace modeling and inversion by convolution and inverse filtering is a parametric approach. To obtain insight into the potential of the parametric approach, the solution of the single‐trace forward problem is formulated in matrix terms. For the nonlinear reflector lag time parameters this is achieved by linearization, which is shown to be a valid approximation over a sufficiently large region. The matrix forward operators are analyzed by means of the singular value decomposition (SVD). The SVD can be considered a generalization of the Fourier transform of convolution operators. On the basis of the SVD analysis, inverse operators are designed which combine stability with high resolving power. A method to determine the resolving power of the parametric inverse operators is presented. Several examples show how wavelet bandwidth, data noise level, and model complexity influence the resolving power of the data for the reflection coefficient and the lag‐time parameters. The most important result is that the resolution obtained in parametric inversion is, in most cases, superior to and, at worst, equal to the resolution obtained with wavelet inverse filtering. The explanation is that in parametric inversion a different representation of the reflectivity function is used which, in practical situations, involves fewer unknowns. In wavelet inverse filtering the reflectivity function is represented as a regularly sampled function where every sample point represents an unknown. In practical applications of parametric inversion the reflectivity function is represented as a model with a limited number of reflectors as unknowns. To formulate parametric models, a priori information is required. The effort of collecting sufficient a priori information is the cost of increasing resolution beyond the resolution offered by wavelet inverse filtering.

Intermediate‐wavelength magnetic anomalies over the central Pacific

We have extracted the intermediate‐wavelength magnetic anomaly field from the marine survey data of the central Pacific in the band pass of 4000–400 km (spherical harmonic degree 10–100). Our technique minimizes the effects of external field sources, secular variation, and strike aliasing. The objective of this paper is to demonstrate this capability, compare the derived sea surface field to the equivalent MAGSAT data set, and demonstrate that anomalies observed in both fields are correctable to geologic features within the oceanic lithosphere. As expected, the sea surface field exhibits a strong spatial correlation to and a better resolution than the MAGSAT field. However, the MAGSAT field also displays a diminished resolution for wavelengths less than 1900 km when compared to the upward continued sea surface data. Two reasons are likely for this diminished resolution: (1) differences in the resolution of the spherical harmonic reference fields and (2) an increased noise level in the MAGSAT data at the shorter wavelengths. Other sources of error are also considered. We also demonstrate that the remanent magnetization of the central Pacific seamounts produces negative magnetic anomalies which are observed at satellite altitude. Other sources including the thickened crust of the oceanic plateaus and regional petrologic variations can be associated with intermediate‐wavelength anomalies observed in both the MAGSAT and the sea surface fields.

Calculating a relaxation spectrum from experimental data via quadratic programming with and without regularization

Abstract The regularization quadratic programming approach to infer relaxation spectra from experimental mechanical data was studied. It was found that the inferior of the sum of the squared difference between the input data and the back-calculated values did not yield a satisfactory relaxation spectrum as the regularization weighting parameter α was increased. A modification was made to the function to be minimized so that all data points were equally weighted. Quadratic programming was then found to be sufficient to infer a reliable relaxation spectrum if the input experimental data had a high degree of accuracy. When the experimental data were not sufficiently accurate, regularization over-regularized the high-value region of the solution spectrum before it could improve the low-value region. Decreasing the number of sought-after points in the solution spectrum can compensate for the noise level in the input experimental data and will allow inferring a reliable relaxation spectrum from the experimental...

Resolution Beyond the Diffraction Limit for Regularized Object Restoration

We propose a new formulation of Miller's regularization theory, which is particularly suitable for object restoration problems. By means of simple geometrical arguments, we obtain upper and lower bounds for the errors on regularized solutions. This leads to distinguish between ‘Hölder continuity’ which is quite good for practical computations and ‘logarithmic continuity’ which is very poor. However, in the latter case, one can reconstruct local weighted averages of the solution. This procedure allows for precise valuations of the resolution attainable in a given problem. Numerical computations, made for object restoration beyond the diffraction limit in Fourier optics, show that, when logarithmic continuity holds, the resolution is practically independent of the data noise level.

Period analysis at high noise level

Analytical expressions are derived for the variances of some types of the periodograms due to normal-distributed noise present in the data. The equivalence of the Jurkevich and the Warner and Robinson methods is proved. The optimum phase cell number of the Warner and Robinson method is given; this number depends on the data length, signal form and noise level. The results are illustrated by numerical examples.

Estimation of the Parameters of the Earth's Polar Motion

The parameters of the Earth's polar motion have been estimated by a method which accounts for observational error and which treats two possible statistical models for the polar motion excitation process. Both a 100 year and a 78 year long polar motion series have been used to estimate the Chandler wobble frequency, Fc, and quality factor, Qc; the noise level in the polar motion data; and the magnitude of the excitation process. Discussion of the annual component of polar motion has been omitted because its frequency (1 cycle per year (cpy)) and cause (annual motion of air and water) are presumed known.

Dynamic characteristics of the renal arterial microvasculature of the dog obtained by simulation.

To develop a measurement technique for microvascular stiffness and resistance, an iterative algorithm (NOLESQ) combining steepest descent and Taylor series (Gauss-Newton) methods was used to estimate model parameters to provide a minimal least squares error at 5-ms intervals of the predicted blood flow to the measured flow. Renal arterial pressure and flow data of high dynamic and static accuracy were used. The data were in blocks of 2500 values each (12.5-s samples). A reasonable fit was obtained with only three parameters: arterial conductance, compliance, and a steady pressure at or just beyond the glomerulae. Other models, incorporating large artery resistance, blood mass, pressure dependent conductance, and pressure dependent compliance were studied. Criteria for acceptance were reasonable values from prior knowledge of biological materials, similarity of parameter values between consecutive samples and between animals, convergence, and error of fit reduced to the noise level of the input data.