Optimal wavelet filter for suppression of coherent noise with an application to seismic data

Wavelet analysis is combined with the Karhunen–Loève (KL) transform into an innovative hybrid method for locally filtering coherent noise. In applying our method, the original time series is first decomposed with wavelet transform, the scales more contaminated with noise are reduced by an attenuation factor AfAf, and the signal is reconstructed using the inverse wavelet transform. Then the KL transform is applied to the reconstructed signal and the behavior of the first energy modes is analyzed as a function of AfAf. The point corresponding to a minimum in the first mode is identified with the maximum extraction of the coherent noise. Our methodology is applied with success to seismic data with the aim of locally extracting the relevant coherent noise, namely the ground roll noise. The procedure can be easily extended to other situations where an undesirable signal is associated with a specific set of energy modes.