Characterization of dispersive surface waves using continuous wavelet transforms

Abstract

S U M M A R YIn this paper, we propose a method of surface waves characterization based on the deformation of the wavelet transform of the analysed signal. An estimate of the phase velocity (the group velocity) and the attenuation coefficient is carried out using a model-based approach to determine the propagation operator in the wavelet domain, which depends nonlinearly on a set of unknown parameters. These parameters explicitly define the phase velocity, the group velocity and the attenuation. Under the assumption that the difference between waveforms observed at a couple of stations is solely due to the dispersion characteristics and the intrinsic attenuation of the medium, we then seek to find the set of unknown parameters of this model. Finding the model parameters turns out to be that of an optimization problem, which is solved through the minimization of an appropriately defined cost function. We show that, unlike time-frequency methods that exploit only the square modulus of the transform, we can achieve a complete characterization of surface waves in a dispersive and attenuating medium. Using both synthetic examples and experimental data, we also show that it is in principle possible to separate different modes in both the time domain and the frequency domain.

Wavelet-based multiscale analysis of geomagnetic disturbance

“…The most recent justification of this change of variables is given by Holschneider et al (2005). Using this change of variables, the CWT is performed in the time-frequency domain and not in the time-scale one.…”

Inverse Problems and Parameter Identification in Image Processing

“…If only one single phase is observed in all the traces S k (t), it will be enough to minimize a cost function that involves some selected seismic traces in order to estimate the attenuation and phase velocity using the modulus and the phase of the wavelet transforms correspondingly, see [38]:…”

“…The optimization is carried out over the whole frequency range of the signal. In order to reduce the effect of uncorrelated noise in our estimates, it is preferable to use a propagator based on the cross-correlations, see [38].…”

Nonlinear Analysis of Multi-Dimensional Signals: Local Adaptive Estimation of Complex Motion and Orientation Patterns

“…[46]). A seismic signal typically contains several superposed propagation modes, each with its own dispersion and attenuation characteristics.…”

“…There are several existing approaches to solving the Multiple Modes problem, e.g., by estimating a wavelet operator [46]. We have developed a solution that is based on the technique of harmonic inversion by filter diagonalization [64,65].…”