Geophysical wavelet library: Applications of the continuous wavelet transform to the polarization and dispersion analysis of signals

In the present paper, we consider and summarize applications of the continuous wavelet transform to 2C and 3C polarization analysis and filtering, modeling the dispersed and attenuated wave propagation in the time–frequency domain, and estimation of the phase and group velocity and the attenuation from a seismogram. Along with a mathematical overview of each of the presented methods, we show that all these algorithms are logically combined into one software package “Geophysical Wavelet Library” developed by the authors. The novelty of this package is that we incorporate the continuous wavelet transform into the library, where the kernel is the time–frequency polarization and dispersion analysis. This library has a wide range of potential applications in the field of signal analysis and may be particularly suitable in geophysical problems that we illustrate by analyzing synthetic, geomagnetic and real seismic data.