Analytic Signal Method Research Articles

USING THE ANALYTIC SIGNAL METHOD OF GRAVITY GRADIENT TENSOR (GGT) TO DETERMINE THE LOCATION AND DEPTH OF THE FAULTS IN THE PRE-CENOZOIC BASEMENT ROCKS OF THE RED RIVER TROUGH

USING THE ANALYTIC SIGNAL METHOD OF GRAVITY GRADIENT TENSOR (GGT) TO DETERMINE THE LOCATION AND DEPTH OF THE FAULTS IN THE PRE-CENOZOIC BASEMENT ROCKS OF THE RED RIVER TROUGH

Rapid Quantification of Melamine in Different Brands/Types of Milk Powders Using Standard Addition Net Analyte Signal and Near-Infrared Spectroscopy.

Multivariate calibration (MVC) and near-infrared (NIR) spectroscopy have demonstrated potential for rapid analysis of melamine in various dairy products. However, the practical application of ordinary MVC can be largely restricted because the prediction of a new sample from an uncalibrated batch would be subject to a significant bias due to matrix effect. In this study, the feasibility of using NIR spectroscopy and the standard addition (SA) net analyte signal (NAS) method (SANAS) for rapid quantification of melamine in different brands/types of milk powders was investigated. In SANAS, the NAS vector of melamine in an unknown sample as well as in a series of samples added with melamine standards was calculated and then the Euclidean norms of series standards were used to build a straightforward univariate regression model. The analysis results of 10 different brands/types of milk powders with melamine levels 0~0.12% (w/w) indicate that SANAS obtained accurate results with the root mean squared error of prediction (RMSEP) values ranging from 0.0012 to 0.0029. An additional advantage of NAS is to visualize and control the possible unwanted variations during standard addition. The proposed method will provide a practically useful tool for rapid and nondestructive quantification of melamine in different brands/types of milk powders.

Integrated geophysical investigation of the Galatian Basin around Seben region, Bolu, Turkey

Abstract The Galatian Basin in the northern part of the Central Anatolia is a large, but insufficiently investigated and unexplored basin because of the volcanic cover on the surface. Its great dimensions can only be noticed when the gravity anomaly map of Turkey is examined. In this paper, it is aimed to investigate the subsurface structure in the western part of the Galatian Basin around Seben region, Bolu. The reason behind the study of only western part of the basin is the existence of seismic and a single borehole data that allow the comparison and control the results of potential field modelling studies in integration. The gravity and aeromagnetic anomaly data were processed with the advance potential field data processing methods. Analytic signal method was performed on the aeromagnetic anomaly data to determine the possible erupsion centers of the volcanic rocks on the surface in and around the Galatian Basin. According to the Analytc Signal transformation results, there are two possible eruptional area; one of them is located to the south of Bolu and the second one is around the W-NW of Ankara, the capital city of Turkey. Three-dimensional (3D) and two-dimensional (2D) modelling studies were constructed on the gravity anomaly data to reveal the basement structure of the basin. Findings were compared with the interpretation of seismic sections. Depth of the western part of the Galatian Basin varies between 3 and 12 km, and the basin deepens through the east encouraging acquisition of new seismic data and drilling wells in the deeper part of the basin to the east. The westernmost part of the basin was divided into two sections by a saddle extending from Seben to Mudurnu in the NW–SE direction and the basin gets deeper again to the south of Mudurnu, down to 6–7 km.

The circular Bedrosian identity for translation‐invariant operators: existence and characterization

The analytic signal method via the circular Hilbert transform is a critical tool in the time–frequency analysis of signals of finite duration. The circular Bedrosian identity is of major theoretical and practical value in the method. The identity holds whenever the Fourier coefficients of f,g∈L2([−π,π]) are respectively supported on A = [−n,m] and for some non‐negative integers 0≤n,m≤+∞. In this note, we investigate the existence of such an identity for a general‐bounded linear translation‐invariant operator on L2([−π,π]d) and for general support sets . We give an insightful geometric characterization of the support sets for the existence. In addition, we find all the support sets for the partial Hilbert transforms. Copyright © 2015 John Wiley & Sons, Ltd.

Simultaneous Estimation of Hydrochlorothiazide, Hydralazine Hydrochloride, and Reserpine Using PCA, NAS, and NAS-PCA

In this study, new and feasible UV-visible spectrophotometric and multivariate spectrophotometric methods were described for the simultaneous determination of hydrochlorothiazide (HCTZ), hydralazine hydrochloride (H.HCl), and reserpine (RES) in combined pharmaceutical tablets. Methanol was used as a solvent for analysis and the whole UV region was scanned from 200–400 nm. The resolution was obtained by using multivariate methods such as the net analyte signal method (NAS), principal component analysis (PCA), and net analyte signal-principal component analysis (NAS-PCA) applied to the UV spectra of the mixture. The results obtained from all of the three methods were compared. NAS-PCA showed a lot of resolved data as compared to NAS and PCA. Thus, the NAS-PCA technique is a combination of NAS and PCA methods which is advantageous to obtain the information from overlapping results.

Two-dimensional nonlinear geophysical data filtering using the multidimensional EEMD method

A variety of two-dimensional (2D) empirical mode decomposition (EMD) methods have been proposed in the last decade. Furthermore, the multidimensional EMD algorithm and its parallel class, multivariate EMD (MEMD), are available in recent years. From those achievements, it is possible to design an efficient 2D nonlinear filter for geophysical data processing. We introduce a robust 2D nonlinear filter which can be applied to enhance the signal of 2D geophysical data or to highlight the feature component on an image. We did this by replacing the conventionally used smooth interpolation in the ensemble empirical mode decomposition (EEMD) algorithm with a piecewise interpolation method. The one-dimensional (1D) EEMD procedures were consecutively performed in all directions, and then the comparable minimal scale combination technique was applied to the decomposed components. The theoretical derivation, model simulation, and real data applications are demonstrated in this paper. The proposed filtering method is effective in improving the image resolution by suppressing the random noise added in the simulation example and strong low frequency track corrugation noise bands with background noise in the field example. Furthermore, the algorithm can be easily extended to higher dimensions by repeating the same procedure in the succeeding dimension. To evaluate the proposed method, one data set is processed separately by using the enhanced analytic signal method and the multivariate EMD (MEMD) algorithm, and the results from these two methods are compared with that of the proposed method. A general equation for generating three-dimensional (3D) EEMD components based on the comparable minimal scale combination principle is derived for further applications.

Improved Euler method for the interpretation of potential data based on the ratio of the vertical first derivative to analytic signal

We propose a new automatic method for the interpretation of potential field data, called the RDAS-Euler method, which is based on Euler’s deconvolution and analytic signal methods. The proposed method can estimate the horizontal and vertical extent of geophysical anomalies without prior information of the nature of the anomalies (structural index). It also avoids inversion errors because of the erroneous choice of the structural index N in the conventional Euler deconvolution method. The method was tested using model gravity anomalies. In all cases, the misfit between theoretical values and inversion results is less than 10%. Relative to the conventional Euler deconvolution method, the RDAS-Euler method produces inversion results that are more stable and accurate. Finally, we demonstrate the practicability of the method by applying it to Hulin Basin in Heilongjiang province, where the proposed method produced more accurate data regarding the distribution of faults.

Edge Detection in Potential-Field Gradient Tensor Data by Use of Improved Horizontal Analytical Signal Methods

Potential-field gradient tensor data contain nine signal components. They include higher-frequency signals than potential field data, which can help delineation of small-scale features of the sources. Edge-detection technology has been widely used to delineate the edges of the sources. We need to develop a new edge detector to process gradient tensor data. Many methods are used to recognize the edges of data. The analytical signal method is a widely used edge-detection filter. We make some improvements to the analytical signal method so it can process potential-field gradient tensor data. We define new filters based on the horizontal directional analytical signal and the second-order horizontal directional analytical signal. To display the large and small amplitude edges simultaneously, we present two normalization methods: use of the maxima of nearby values to normalize the center point in a moving window and use of different orders of vertical derivatives to normalize the new filters. The methods were tested on synthetic and real potential-field gradient tensor data to verify their feasibility. Compared with other balance filters, the normalized second-order horizontal directional analytical signal and true vertical derivatives of the directional analytical signal normalized by use of the vertical derivative of vertical gravity gradient furnish better results and reveal more detail.

Interpretation of marine magnetic anomalies. Part I. A survey of existing methods and analysis of the analytic signal method

In this work, the problem of interpreting linear marine magnetic anomalies in the context of the spreading model is considered. Analysis and a comparison of the methods proposed earlier for solving this problem are carried out and the analytic signal method is considered in detail. In terms of a simplest example, it is shown that the AS method has significant restrictions associated primarily with the size and/or occurrence depth of the bodies.

Multidimensional Analytic Signals and the Bedrosian Identity

The analytic signal method via the Hilbert transform is a key tool in signal analysis and processing, especially in the time–frequency analysis. Imaging and other applications to multidimensional signals call for extension of the method to higher dimensions. We justify the usage of partial Hilbert transforms to define multidimensional analytic signals from both engineering and mathematical perspectives. The important associated Bedrosian identity T(fg) = fTg for partial Hilbert transforms T is then studied. Characterizations and several necessity theorems are established. We also make use of the identity to construct basis functions for the time–frequency analysis.

The Applications of Analytic Signal Method in Archaeological Investigations of Part of Lejja Pre-historic Site, South-Eastern Nigeria

,Nigeria. Authorscontributions ABSTRACT The attempt to properly date the iron -age Lejja site has been the concern of some archaeologists for the past few decades. The latest archaeological investigations of the area revealed that artefacts could be found at depths below one metre. Excavation o f such completely concealed features may involve much futiledigging which is prohibited at most locations in the community. To avoid discontinuity of the research resulting from environmental restrictions, we have adopted a more environmentally friendly a pproach;

Direct analytic signal (DAS) method in the interpretation of magnetic data

Abstract We presented a new method for interpreting 2D magnetic data, called direct analytic signal (DAS) method, which directly used the analytic signal of magnetic anomaly to compute the depth and the structural index of the source. The DAS method needs only the computation of the first order derivatives of magnetic anomaly, so that the inversion results are more stable than the results obtained by the other existing analytic signal methods. The DAS method is tested on synthetic magnetic data with and without noise, and the DAS method can successfully obtain the depth and the structural index of the source. We also applied the DAS method to interpret a real magnetic data over a shallow geological source whose source parameters are known from closely drilling information, and the inversion results are in accord with the true values.

Geophysical investigations on the gravity and aeromagnetic anomalies of the region between Sapanca and Duzce, along the North Anatolian Fault, Turkey

In this paper, it is aimed to model subsurface structures to the east of the Gulf of Izmit through Duzce by using the gravity and aeromagnetic anomaly data. 1/500.000 scaled gravity anomaly map of the area was taken from the General Directorate of Mineral Research and Exploration (MTA) and it was digitized. The aeromagnetic anomaly data were obtained in the digital form. 3D and 2D models were constructed to reveal the subsurface structure in two different inset regions in the study area including most important negative and positive gravity anomalies. Seismic velocities obtained from the deep seismic recordings were converted to densities. In addition, density information from a previous research was also taken. These densities were used for construction of 3D and 2D gravity models where it was shown that there are narrow and long sedimentary basins and depressions with 0.5–3km depths. These sedimentary basins with the shape of negative flower structures indicating pull-apart basins are controlled by the active fault segments of the North Anatolian Fault (NAF). Earthquake epicenter data were also correlated with the constructed models from the gravity anomalies. Positive gravity anomalies are also caused by very shallow (about 2km) masses that are accepted as the crustal origin intrusions into the fractures of the NAF and, ophiolites and gabbro outcropping on the surface of the studied regions. These intrusives and remnants of the Tethys Ocean are located between the fault segments where the fault bifurcates and they also constitute barriers for straight extension of the NAF. Analytic signal method was applied to the aeromagnetic anomaly data to determine the locations and boundaries of the causative bodies. Those bodies are observed around Duzce, and to the E-SE of it, to the NW of Golyaka and a large mass between Adapazari and Sapanca. Shallow settlement of these magmatics was confirmed by the second vertical derivative of the aeromagnetic data. An anti-clockwise block rotation is evident in the northeast of the study area from the polarity changes of the magnetic anomalies.

Hilbert transform methods for nonparametric identification of nonlinear time varying vibration systems

The objective of this paper is to demonstrate a Hilbert transform (HT) method for identification of mechanical time-varying vibration systems under free and forced vibration regimes. This special kind of non-stationarity arises in experimental vibration analysis and in engineering practice. The method is based on the HT of input/output signals in a time domain to extract instantaneous dynamic structure characteristics, such as natural frequencies, stiffness, damping, and their variations in time.The HT assigns a complementary imaginary part to a given real signal part, or vice versa, by shifting each component of the signal by a quarter of a period. Thus, the HT pair provides a method for determining the instantaneous amplitude and the instantaneous frequency of a signal.For general non-stationary vibration signals, the analytic signal method does a good job of simultaneous time-frequency localization of the main signal components.The paper focuses on HT signal processing techniques and identifies three groups of dynamics time-varying SDOF systems: slow varying quasi-periodic modulation of stiffness under free and forced vibration, slow varying quasi-periodic modulation of nonlinear stiffness under free vibration, and fast inter-wave parametric stiffness modulation (Mathieu equation).

Determination of the Acidity Constant of Drugs Using the Hard–Soft Net Analyte Signal Method

The newly proposed hard–soft net analyte signal (HS-NAS) method was employed to determine the acidity constants of drugs. The spectrophotometric data obtained through monitoring of the pH-metric titrations of the acids (both experimental and simulated data) were analyzed by the HS-NAS method, and accurate results were obtained. As experimental data sets, tetracycline as a triprotic acid and p-aminobenzoic acid, m-aminobenzoic acid, and piroxicam as diprotic acids were studied. In addition, the acidity constants of the drugs were determined in the presence of Triton X-100 as an inert light-absorbing interference. The data for such systems, which are rank-deficient in nature, were successfully analyzed by the HS-NAS method. This method is based on changing the acidity constants of the drugs to maximize the correlation coefficient between the NAS vector obtained for one species of the reaction and the theoretical concentration profile of that species. Unlike existing methods, it needs neither previous inform...

Phase-amplitude investigation of spontaneous low-frequency oscillations of cerebral hemodynamics with near-infrared spectroscopy: A sleep study in human subjects

We have investigated the amplitude and phase of spontaneous low-frequency oscillations (LFOs) of the cerebral deoxy- and oxy-hemoglobin concentrations ([Hb] and [HbO]) in a human sleep study using near-infrared spectroscopy (NIRS). Amplitude and phase analysis was based on the analytic signal method, and phasor algebra was used to decompose measured [Hb] and [HbO] oscillations into cerebral blood volume (CBV) and flow velocity (CBFV) oscillations. We have found a greater phase lead of [Hb] vs. [HbO] LFOs during non-REM sleep with respect to the awake and REM sleep states (maximum increase in [Hb] phase lead: ~π/2). Furthermore, during non-REM sleep, the amplitudes of [Hb] and [HbO] LFOs are suppressed with respect to the awake and REM sleep states (maximum amplitude decrease: 87%). The associated cerebral blood volume and flow velocity oscillations are found to maintain their relative phase difference during sleep, whereas their amplitudes are attenuated during non-REM sleep. These results show the potential of phase-amplitude analysis of [Hb] and [HbO] oscillations measured by NIRS in the investigation of hemodynamics associated with cerebral physiology, activation, and pathological conditions.

Spectrophotometric study of complex formation equilibria in the presence of interference using hard–soft net analyte signal method: Application to drug–metal complexation

In this article, the ability of a new and efficient hard–soft method, previously proposed by our research group, is reported for modeling of the complex formation equilibria in the presence of interferences. This method is based on the net analyte signal (NAS) concept, which is a part of total signal that is directly related to the concentration of the component of interest. It monitors the concentration changes of any chemical species involved in the evolutionary process without requiring any pure spectra or having previous knowledge about the presence of the interferences. The proposed hard–soft method based on net analyte signal (HS-NAS) only needs a chemical model for one of the species involved in the reaction under study. The reliability of the method was examined by applying it to the measured data and spectrum of the known real systems of Fe 2+–azithromycin and Ca 2+–tetracycline.

Aeromagnetic anomaly modeling of central zone structure and magnetic sources in the Chicxulub crater

The analytic signal method and forward modeling in three dimensions are applied to magnetic field data over the Chicxulub crater in order to determine and document the main magnetic anomaly sources and crater structure in the central zone. Aeromagnetic data over the structure reveal three strong, well-defined concentric patterns, with a central 40-km diameter zone of high amplitude anomalies. Magnetic anomalies are interpreted to be associated with the melt sheet, upper breccias and central uplift, which present three to four orders of magnitude contrasts with the surrounding carbonate units. The limited number of magnetic property measurements, apparent wide range in the remanent intensity and susceptibility in the upper breccias and possible yet unconstrained zones of hydrothermal systems have restricted our ability to determine the characteristics and distribution of major structural elements of the Chicxulub crater. The amplitude of the analytic signal produces maxima over magnetization contrasts, independent of the direction of magnetization. Interpretation of maxima location and depth distribution is used, in a second stage, as a priori information in the construction of an input prism assemblage magnetic configuration and its properties for three-dimensional forward modeling. Results indicate that magnetic sources extend to a radial distance of ∼45 km from the center of the structure with average depths ranging between 2 and 4 km. The magnetic anomaly sources in the central structural uplift zone are located in the range from 3.5 to 8 km depth, with dominant contributions from an apparent large body forming the basement uplift.

Interpretation of magnetic anomalies using the horizontal gradient analytic signal

In recent years the analytic signal method has been of great utility in the interpretation of potential field data. The amplitude of the 3D analytic signal of magnetic data yields information on the location of the edges of the sources in both the horizontal and vertical dimensions, with the main advantage that the magnetic field and magnetic source parameters need not be known or assumed. Accurate detection of source body coordinates is becoming the main goal for interpreters and therefore enhanced techniques are acquiring an increasing revival in data interpretation. This paper presents a high-resolution approach for detecting source boundaries. These boundaries can be determined from the maxima of the analytic signal computed from the horizontal gradient of the field, defined here as a vector, the components of which are the analytic signals of x- and y-horizontal derivatives, respectively. Synthetic examples have shown the high resolving power of the proposed technique. This approach has also given very good results when applied to real data.

Fast Determination of the Release Degree of Compound Sulfamethoxazole Tablets by Using Circulation Release System Combined with Ultraviolet Spectral Net Analyte Signal Method

Based on ultraviolet spectral net analyte signals, this research has studied the determination of the two effective components, sulfamethoxazole (SMZ) and trimethoprim (TMP), contained in compound sulfamethoxazole tablets in acid environment. The linear ranges of SMZ and TMP were 0.48-7.84 microg/ml (the regression correlation coefficient r = 0.9981) and 0.12-1.5 microg/ml (r = 0.9986), the corresponding average recoveries were 99.5 and 101.0%, respectively, and the relative standard deviations were 1.87 and 3.60%, respectively. The method was simple, fast and accurate. A circulation release system for the determination of the tablet release degree has been built, and the on-line filtering and small-volume sampling could thus be carried out. Thanks to the combination of the circulation release system and the determination method of SMZ and TMP in acid environment, the determination of release degree for compound sulfamethoxazole tablets was fast and accurate, especially for the early time of rapid release.