Modeling of Wave Dispersion Using Continuous Wavelet Transforms

Abstract

In the estimate of dispersion with the help of wavelet analysis considerable emphasis has been put on the extraction of the group velocity using the modulus of the wavelet transform. In this paper we give an asymptotic expression of the full propagator in wavelet space that comprises the phase velocity as well. This operator establishes a relationship between the observed signals at two different stations during wave propagation in a dispersive and attenuating medium. Numerical and experimental examples are presented to show that the method accurately models seismic wave dispersion and attenuation.

Вейвлет Корреляции Нестационарных Сигналов

“…Этa методика может быть применена для анализа корреляции вспышек на Солнце и ис-следовании сигналов пульсаров. Предлагаемый метод может найти свое применение для описания неравно-весных явлений в теории взаимодействующих когерент-ных пространственно-временных структур, для описания сейсмологических сигналов [45,46]. Особенно важно применение DWC αβ (ν, t) для сред, обладающих сильной дисперсией.…”

Assessment of CO2 dynamics in subsurface atmospheres using the wavelet approach: from cavity–atmosphere exchange to anthropogenic impacts in Rull cave (Vall d′Ebo, Spain)

“…CWT has been applied in multiple research applications, such as the analysis of soil spatial variations (Biswas and Si 2011) and soil hydraulic properties (Si 2003), filtering of multichannel seismic data (Galiana-Merino et al 2013), characterization of surface waves Kulesh et al 2005 and, the study of wave polarization properties (Diallo et al 2006;Kulesh et al 2008) and airborne CO2 measurements over heterogeneous landscapes (Vadrevu and Choi 2011), the evaluation of meteorological data characteristics (Wang and Lu 2010), and studies focusing on the impact of boundary layer dynamics of atmospheric CO2 concentration variability (Lac et al 2013, Pal 2014.…”

Modeling of Wave Dispersion Using Continuous Wavelet Transforms II: Wavelet-based Frequency-velocity Analysis

“…Using the method fully described by KULESH et al (2005), we express the spectral propagator (1) in terms of the wavelet transform of the source signal, W g S k (t, f) and propagated signal, W g S m (t, f).…”

“…In this situation we have shown in KULESH et al (2005), how the wavelet transform of the source and the propagated signals are related through a transformation operator (wavelet propagator) that explicitly incorporates the phase and group velocities as well as the attenuation factor of the medium. In HOLSCHNEIDER et al (2005a), we discuss how minimization of a cost functional based on this transformation operator allows the estimation of the dispersion properties in the case of single-mode signals.…”