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Hilbert Transform (hilbert + transform)

Distribution by Scientific Domains

Earth and Environmental Science	42%

Selected Abstracts

System identification of linear structures based on Hilbert,Huang spectral analysis.

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 10 2003
Part 2: Complex modes
Abstract A method, based on the Hilbert,Huang spectral analysis, has been proposed by the authors to identify linear structures in which normal modes exist (i.e., real eigenvalues and eigenvectors). Frequently, all the eigenvalues and eigenvectors of linear structures are complex. In this paper, the method is extended further to identify general linear structures with complex modes using the free vibration response data polluted by noise. Measured response signals are first decomposed into modal responses using the method of Empirical Mode Decomposition with intermittency criteria. Each modal response contains the contribution of a complex conjugate pair of modes with a unique frequency and a damping ratio. Then, each modal response is decomposed in the frequency,time domain to yield instantaneous phase angle and amplitude using the Hilbert transform. Based on a single measurement of the impulse response time history at one appropriate location, the complex eigenvalues of the linear structure can be identified using a simple analysis procedure. When the response time histories are measured at all locations, the proposed methodology is capable of identifying the complex mode shapes as well as the mass, damping and stiffness matrices of the structure. The effectiveness and accuracy of the method presented are illustrated through numerical simulations. It is demonstrated that dynamic characteristics of linear structures with complex modes can be identified effectively using the proposed method. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Improved imaging with phase-weighted common conversion point stacks of receiver functions

GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2010
A. Frassetto
SUMMARY Broad-band array studies frequently stack receiver functions to improve their signal-to-noise ratio while mapping structures in the crust and upper mantle. Noise may produce spurious secondary arrivals that obscure or mimic arrivals produced by P -to- S conversions at large contrasts in seismic impedance such as the Moho. We use a Hilbert transform to calculate phase-weights, which minimize the constructive stacking of erroneous signal in receiver function data sets. We outline this approach and demonstrate its application through synthetic data combined with different types of noise, a previously published example of signal-generated noise, and a large data set from the Sierra Nevada EarthScope Project. These examples show that phase-weighting reduces the presence of signal-generated noise in receiver functions and improves stacked data sets. [source]

Non-uniqueness with refraction inversion , the Mt Bulga shear zone

GEOPHYSICAL PROSPECTING, Issue 4 2010
Derecke Palmer
ABSTRACT The tau-p inversion algorithm is widely employed to generate starting models with many computer programs that implement refraction tomography. However, this algorithm can frequently fail to detect even major lateral variations in seismic velocities, such as a 50 m wide shear zone, which is the subject of this study. By contrast, the shear zone is successfully defined with the inversion algorithms of the generalized reciprocal method. The shear zone is confirmed with a 2D analysis of the head wave amplitudes, a spectral analysis of the refraction convolution section and with numerous closely spaced orthogonal seismic profiles recorded for a later 3D refraction investigation. Further improvements in resolution, which facilitate the recognition of additional zones with moderate reductions in seismic velocity, are achieved with a novel application of the Hilbert transform to the refractor velocity analysis algorithm. However, the improved resolution also requires the use of a lower average vertical seismic velocity, which accommodates a velocity reversal in the weathering. The lower seismic velocity is derived with the generalized reciprocal method, whereas most refraction tomography programs assume vertical velocity gradients as the default. Although all of the tomograms are consistent with the traveltime data, the resolution of each tomogram is comparable only with that of the starting model. Therefore, it is essential to employ inversion algorithms that can generate detailed starting models, where detailed lateral resolution is the objective. Non-uniqueness can often be readily resolved with head wave amplitudes, attribute processing of the refraction convolution section and additional seismic traverses, prior to the acquisition of any borehole data. It is concluded that, unless specific measures are taken to address non-uniqueness, the production of a single refraction tomogram that fits the traveltime data to sufficient accuracy does not necessarily demonstrate that the result is either correct, or even the most probable. [source]

Modelling of GPR waves for lossy media obeying a complex power law of frequency for dielectric permittivity

GEOPHYSICAL PROSPECTING, Issue 1 2004
Maksim Bano
ABSTRACT The attenuation of ground-penetrating radar (GPR) energy in the subsurface decreases and shifts the amplitude spectrum of the radar pulse to lower frequencies (absorption) with increasing traveltime and causes also a distortion of wavelet phase (dispersion). The attenuation is often expressed by the quality factor Q. For GPR studies, Q can be estimated from the ratio of the real part to the imaginary part of the dielectric permittivity. We consider a complex power function of frequency for the dielectric permittivity, and show that this dielectric response corresponds to a frequency-independent- Q or simply a constant- Q model. The phase velocity (dispersion relationship) and the absorption coefficient of electromagnetic waves also obey a frequency power law. This approach is easy to use in the frequency domain and the wave propagation can be described by two parameters only, for example Q and the phase velocity at an arbitrary reference frequency. This simplicity makes it practical for any inversion technique. Furthermore, by using the Hilbert transform relating the velocity and the absorption coefficient (which obeys a frequency power law), we find the same dispersion relationship for the phase velocity. Both approaches are valid for a constant value of Q over a restricted frequency-bandwidth, and are applicable in a material that is assumed to have no instantaneous dielectric response. Many GPR profiles acquired in a dry aeolian environment have shown a strong reflectivity inside dunes. Changes in water content are believed to be the origin of this reflectivity. We model the radar reflections from the bottom of a dry aeolian dune using the 1D wavelet modelling method. We discuss the choice of the reference wavelet in this modelling approach. A trial-and-error match of modelled and observed data was performed to estimate the optimum set of parameters characterizing the materials composing the site. Additionally, by combining the complex refractive index method (CRIM) and/or Topp equations for the bulk permittivity (dielectric constant) of moist sandy soils with a frequency power law for the dielectric response, we introduce them into the expression for the reflection coefficient. Using this method, we can estimate the water content and explain its effect on the reflection coefficient and on wavelet modelling. [source]

Dynamics of human neocortex that optimizes its stability and flexibility

INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 9 2006
Walter J. Freeman
The electroencephalogram (EEG) in states of awake, sleep, and seizure in a patient with intractable partial complex seizures was recorded through a 1- × 1-cm microgrid of 64 electrodes on the right inferior temporal gyrus during a week-long neurosurgical evaluation. Comparisons with a normal intracranial EEG were perforce from animals. Analytic phase and amplitude from the Hilbert transform gave the temporal resolution needed to resolve EEG spatiotemporal structure. The rest state revealed multiple overlapping patterns of high-frequency coherent oscillations resembling bubbles in boiling water. Bubble diameters gave estimates of the distances across the cortex over which the cortical oscillations were synchronized. Superimposed on these bubbles were large-sized epochs of phase locking with briefly constant frequency and high amplitude. These coordinated analytic phase differences occurred between short periods of high phase variance. The variance gave evidence for state transitions between transiently stable states with constant phase gradients. In sleep these phase patterns persisted with reduced amplitude, occasionally interrupted by long-lasting (,1 s) epochs with no spatial textures in phase and amplitude despite a large increase in amplitude. Seizures had high amplitude 3/s spikes with steep spatial gradients. Onset occurred after pre-ictal reduction in bubble diameters as evidence for large-scale cortical disintegration preceding loss of stability. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 881,901, 2006. [source]

A limiting absorption principle for scattering problems with unbounded obstacles

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 14 2001
Anne-Sophie Bonnet-Bendhia
Abstract A generalized mode matching method that applies to a wide class of scattering problems is developed in the time harmonic two-dimensional Helmholtz case. This method leads by variational means to an integro-differential formulation whose unknown is the trace of the field on an unbounded one-dimensional interface. The well-posedness is proved after a careful study of the rather original functional framework. Owing to a fundamental density result,based upon some properties of a singular integral operator similar to the Hilbert transform,the limiting absorption principle related to this original formulation is established. Finally, two other situations are emphasized. Copyright © 2001 John Wiley & Sons, Ltd. [source]

The correct form of the Raman scattering tensor

JOURNAL OF RAMAN SPECTROSCOPY, Issue 1 2004
Dr S. Hassing
Abstract In the literature about Raman scattering, an unsatisfactory ambiguity exists in the basic Kramers,Heisenberg formula. The sign in front of the damping constant ,, appears to be arbitrary. In the present paper we show that the correct form is the one where ,, has the same sign as the excitation frequency ,. The argument is based on the causality principle, leading to the requirement that the real and imaginary parts of the scattering tensor constitute a pair of Hilbert transforms. Copyright © 2004 John Wiley & Sons, Ltd. [source]