Characterization of polarization attributes of seismic waves using continuous wavelet transforms

Abstract

Complex-trace analysis is the method of choice for analyzing polarized data. Because particle motion can be represented by instantaneous attributes that show distinct features for waves of different polarization characteristics, it can be used to separate and characterize these waves. Traditional methods of complex-trace analysis only give the instantaneous attributes as a function of time or frequency. However, for transient wave types or seismic events that overlap in time, an estimate of the polarization parameters requires analysis of the time-frequency dependence of these attributes. We propose a method to map instantaneous polarization attributes of seismic signals in the wavelet domain and explicitly relate these attributes with the wavelettransform coefficients of the analyzed signal. We compare our method with traditional complex-trace analysis using numerical examples. An advantage of our method is its possibility of performing the complete wave-mode separation/ filtering process in the wavelet domain and its ability to provide the frequency dependence of ellipticity, which contains important information on the subsurface structure. Furthermore, using 2-C synthetic and real seismic shot gathers, we show how to use the method to separate different wave types and identify zones of interfering wave modes.

Seismic wave characterization using complex trace analysis in the stationary wavelet packet domain

“…The proposed method presents some advantages relative to other methods based on the CWT (Diallo et al 2005;Diallo et al, 2006;Kulesh et al, 2007). The signal can be very accurately recovered from the time-frequency domain to the time domain, while any real mother wavelet can be used.…”

“…This is the reason why a time-frequency polarization analysis seems to be a more appropriate alternative in order to separate the different phases in the wavefield. A similar aim guided the studies of Diallo et al (2005Diallo et al ( , 2006 and Kulesh et al (2007Kulesh et al ( , 2008, where the time-frequency polarization analysis is carried out using the Continuous Wavelet Transform (CWT).…”

“…In the present study, we aim at estimating the instantaneous polarization parameters in the time-frequency domain, and thus any phase variation of the wavelet coefficients would lead to erroneous results. Diallo et al (2006) used a complex wavelet as the mother wavelet, which has the advantage, compared with the real ones, that it does not introduce any phase distortion. Specifically, they used the complex Morlet wavelet.…”

“…In fact, although the definition of the inverse transform is well established, with its expression and its applicability conditions, it is not possible to recover the original signal when only a discrete set of scales and translation values has been applied for obtaining the CWT coefficients. In this situation, some approximated inversion methods can be applied for returning to the time-domain, as explained in Diallo et al (2006).…”

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.…”