Amplitudes Of Extrema Research Articles

Technique of Informative Features Selection in Geoacoustic Emission Signals

Studies of geoacoustic emission in a seismically active region in Kamchatka show that geoacoustic signals produce pronounced pulse anomalies during the earthquake preparation and post-seismic relaxation of the local stresses field at the observation point. The qualitative selection of such anomalies is complicated by a strong distortion and weakening of the signal amplitude. A review of existing acoustic emission analysis methods shows that most often researchers turn to the analysis of more accessible to study statistical properties and energy of signals. The distinctive features of the approach proposed by the authors are the extraction of informative features based on the analysis of time and frequency-time structures of geoacoustic signals and the description of various forms of recognizable pulses by a limited pattern set. This study opens up new ideas to develop methods for detecting anomalous behavior of geoacoustic signals, including anomalies before earthquakes.
 The paper describes a technique of information extraction from geoacoustic emission pulse streams of sound frequency range. A geoacoustic pulse mathematical model, reflecting the signal generation process from a variety of elementary sources, is presented. A solution to the problem of detection of geoacoustic signal informative features is presented by the means of description of signal fragments by the matrixes of local extrema amplitude ratios and of interval ratios between them. The result of applying the developed algorithm to describe automatically the structure of the detected pulses and to form a pattern set is shown. The patterns characterize the features of geoacoustic emission signals observed at IKIR FEB RAS field stations. A technique of reduction of the detected pulse set dimensions is presented. It allows us to find patterns similar in structure. A solution to the problem of processing of a large data flow by unifying pulses description and their systematization is proposed. A method to identify a geoacoustic emission pulse model using sparse approximation schemes is suggested. An algorithmic solution of the problem of reducing the computational complexity of the matching pursuit method is described. It is to include an iterative refinement algorithm for the solution at each step in the method. The results of the research allowed the authors to create a tool to investigate the dynamic properties of geoacoustic emission signal in order to develop earthquake prediction detectors.

Katabatic Flow: A Closed-Form Solution with Spatially-Varying Eddy Diffusivities

The Nieuwstadt closed-form solution for the stationary Ekman layer is generalized for katabatic flows within the conceptual framework of the Prandtl model. The proposed solution is valid for spatially-varying eddy viscosity and diffusivity (O’Brien type) and constant Prandtl number (Pr). Variations in the velocity and buoyancy profiles are discussed as a function of the dimensionless model parameters $$z_0 \equiv \hat{z}_0 \hat{N}^2 Pr \sin {(\alpha )} |\hat{b}_\mathrm{s} |^{-1}$$ and $$\lambda \equiv \hat{u}_{\mathrm{ref}}\hat{N} \sqrt{Pr} |\hat{b}_\mathrm{s} |^{-1}$$ , where $$\hat{z}_0$$ is the hydrodynamic roughness length, $$\hat{N}$$ is the Brunt-Vaisala frequency, $$\alpha $$ is the surface sloping angle, $$\hat{b}_\mathrm{s}$$ is the imposed surface buoyancy, and $$\hat{u}_{\mathrm{ref}}$$ is a reference velocity scale used to define eddy diffusivities. Velocity and buoyancy profiles show significant variations in both phase and amplitude of extrema with respect to the classic constant $$\textit{K}$$ model and with respect to a recent approximate analytic solution based on the Wentzel-Kramers-Brillouin theory. Near-wall regions are characterized by relatively stronger surface momentum and buoyancy gradients, whose magnitude is proportional to $$z_0$$ and to $$\lambda $$ . In addition, slope-parallel momentum and buoyancy fluxes are reduced, the low-level jet is further displaced toward the wall, and its peak velocity depends on both $$z_0$$ and $$\lambda $$ .

Efficient method for harmonics estimation of car engine sounds: application to high quality real‐time synthesis

Additive synthesis is the most popular method for the resynthesis of sounds containing slowly evolving harmonics or partials, such as car engine noise and more generally rotating machines sounds. The most important step lies in the estimation of the amplitude and frequency of each sinusoidal component. It appears that insufficiently precise estimation often leads to unsatisfactory results in terms of sound fidelity. A method providing the time and frequency evolution of the amplitude of the harmonics of a recorded sound is presented. This technique is based on a joint time and frequency chaining of amplitude's extrema of amplitudes coming from a short‐time Fourier transform, using forward and backward estimation. The proposed method is compared to a rough estimation, and to an estimation based on measured tachometric data, all carried out over the same car engine sound. This estimation method is implemented into the LEA software, which thus allows fast and precise computations of the parameters. Moreover,...

Converted wave AVO inversion for average velocity ratio and shear wave reflection coefficient

Based on the empirical Gardner equation describing the relationship between density and compressional wave velocity, the converted wave reflection coefficient extrema attributes for AVO analysis are proposed and the relations between the extrema position and amplitude, average velocity ratio across the interface, and shear wave reflection coefficient are derived. The extrema position is a monotonically decreasing function of average velocity ratio, and the extrema amplitude is a function of average velocity ratio and shear wave reflection coefficient. For theoretical models, the average velocity ratio and shear wave reflection coefficient are inverted from the extrema position and amplitude obtained from fitting a power function to converted wave AVO curves. Shear wave reflection coefficient sections have clearer physical meaning than conventional converted wave stacked sections and establish the theoretical foundation for geological structural interpretation and event correlation. The method of inverting average velocity ratio and shear wave reflection coefficient from the extrema position and amplitude obtained from fitting a power function is applied to real CCP gathers. The inverted average velocity ratios are consistent with those computed from compressional and shear wave well logs.

Interstimulus interval dependence of the auditory vertex response and its magnetic counterpart: Implications for their neural generation

Auditory vertex responses elicited by short tone bursts were compared with their magnetic counterparts. Special attention was paid to the behaviour of the N100 deflection of the response. Electrical responses were recorded from scalp locations Fp2, Fz, Cz, Pz, C4 and T4 and the magnetic responses half way between P4 and T6, at a point where the response has one of its amplitude extrema. Different ISIs (from 1 to 16 sec) were applied in order to differentiate specific and nonspecific evoked potential components from each other. The main results were as follows: 1. (1) The scalp distribution of the electrical vertex response depends on the ISI used: with frequent stimulation there are no marked differences in the amplitudes of N100 between frontal and central areas but with long ISIs the amplitude maxima move to the vertex. 2. (2) The magnetic responses also show a clear ISI dependence. The magnetic counterpart of N100 saturates at shorter ISIs than N100 recorded from the vertex. Independent of the ISI the magnetic counterpart of P200 is constantly very small. On the basis of the different sensitivities of the EEG and MEG to current sources of different orientations it is concluded that the auditory vertex response contains both modality specific and nonspecific components. Experimental conditions, especially the ISI used, determine the relative contributions of these components to the potential recorded on the scalp.

The shape of modulation-broadened, unsaturated Lorentzian magnetic resonance transitions. IV. Dispersion, dnL( n = 0, I, II)

The effect of modulation broadening on the shape of unsaturated, Lorentzian dispersion lines is examined. The closed, analytic expressions for the Fourier coefficients d n L due to Buckmaster (1) and Evans and Brey (2) are employed to derive exact formulas relating the location and amplitude of the extrema, the amplitude extrema ratio, the location and amplitude of the slope extrema, the slope extrema ratio, and the location of the zeros of the observed d nn L ( n = 0, I, II) to the true half-width for arbitrary modulation amplitude [normalized modulation amplitude ( 1 β )]. Graphs of the various results of experimental interest in determining the line width and the number of paramagnetic spins present are included.

Shape of Modulation-Broadened Unsaturated Lorentzian Magnetic Resonance Transitions. III. Absorption, aIIIL (Third Harmonic)

The effect of modulation broadening on the shape of unsaturated Lorentzian absorption lines is examined. The closed analytic expression for the Fourier coefficients anL due to Wahlquist [H. Wahlquist, J. Chem. Phys. 35, 1708 (1961)] is employed to derive exact formulas relating the location and amplitude of the extrema, the amplitude extrema ratio, the location and amplitude of the slope extrema, the slope extrema ratios and the location of the zeros of the observed aIIIL to the true half-width for arbitrary modulation amplitude [normalized modulation amplitude (1/β)]. This Fourier coefficient is recorded when synchronous demodulation is employed at the third harmonic of the magnetic-field modulation frequency. It is of considerable experimental interest since it has two zeros symmetrically located with respect to a central zero and the total amplitude of the pairs of antisymmetric peaks is approximately the same as for the two antisymmetric peaks of aIL when the modulation amplitude is near optimum. It is shown that linewidth measurements can be made more precisely and easily under conditions of near-maximum sensitivity using aIIIL than either aIL or aIIL since zero crossings can be located more accurately than the amplitude extrema. Graphs of the various results of experimental interest are included.

The Shape of Modulation-Broadened, Unsaturated, Lorentzian Magnetic Resonance Transitions

The effect of modulation broadening on the shape of unsaturated, Lorentzian absorption lines is examined. The closed, analytic expressions for the Fourier coefficients anL due to Wahlquist are employed to derive exact formulas relating the location and amplitude of the extrema, the location and amplitude of the slope extrema, the slope extrema ratio, and the location of the zeros of the observed a2L to the true half-width for arbitrary modulation amplitude [normalized modulation amplitude (1/β)]. Wahlquist's results for a1L are extended to include the location and amplitude of the slope extrema. It is shown that simultaneous measurement of a1L and a2L, when the normalized modulation amplitude is near unity, can be employed to determine if the lineshape is Lorentzian. For a Lorentzian lineshape, these measurements can be used to determine the linewidth and the number of paramagnetic spins under conditions of near-maximum sensitivity. Graphs and tables of the various results of experimental interest in making these determinations and calculations are included.