We present a new method of surface-wave mitigation using polarization filtering. The method evolves from the polarization-analysis technique developed by Diallo et al., (2006) and introduces new constraints to effectively detect and mitigate surface waves without damaging the signal. Straightforward application of polarization filtering without these constraints results in ineffective filtering or damage to the signal, due to the complexity of surface-wave wavetrains. We illustrate the performance of the method with examples from multicomponent seismic data, and demonstrate the superiority of the filtering compared to the unconstrained approach.
Polarization filtering exploits the fact that P-waves, S-Waves, Love and Rayleigh waves have distinct polarization patterns, which can be used to discriminate these different wave types. In practice, this turns out to be quite challenging because, in heterogeneous media, surface waves are strongly dispersive, and their polarization attributes are time, frequency and mode dependent. Furthermore, because of interferences, it is very difficult to recover the polarization attributes of individual wave types in either the time or the frequency domain. To overcome some of these limitations, Diallo et al., (2006) derived analytical expressions that relate the multicomponent signal to its polarization attributes in the time-frequency domain using the wavelet transform. A method using these expressions can effectively separate signal from surfacewave noises when clear time-frequency boundaries exist between these wave types. Often, however, it is not the case that such clear boundaries exist. We use an improved method to attenuate surface-wave noises without damaging the signal. The method combines information, including polarization attributes, amplitude, and velocity, to analytically constrain the application of polarization filtering to the part of the time-frequency domain most dominated by surface waves. We demonstrate the effectiveness of the method using field data.
In this section, we highlight some key results from Diallo et al., (2006), which uses complex trace analysis.
We now develop an extension to the method described above. The extension automatically determines a zone in the time-frequency domain where polarization filtering is to be applied, thus constraining the filter and improving protection of signal. We propose two schemes to delineate the time-frequency domain where the surface waves are predominant.
From the modulus of the wavelet transform of the complex seismic trace, we identify the portion of the T-F domain that corresponds to surface-wave arrivals. An initial step in detecting the boundary, referred to here as a ridge (which should not be confused with rigorous definition of the ridge as known in the wavelet community), consists of scanning the frequency axis for each given time to find the maximum of the wavelet transform modulus. The resulting curve R(t) represents the frequency f at which the modulus of the wavelet transform is maximum for each time t. At far offsets where surface waves are weak, the curve R(t) is associated with the reflection arrivals. At the near offset where surface wave energy is predominant the curve R(t) gives the frequency of maximum amplitude of the predominant, surface-wave arrivals at each time.