Wavelet filtering of tube and surface waves

We apply a B4 wavelet (the wavelet associated with the cubic splines) filtering algorithm to eliminate tube waves in crosshole seismic data and air-waves+surface waves in CDP data. The coherent noise events are first time-shifted in time to be aligned with one another from trace to trace. For each time sample, the shifted data is wavelet transformed along the trace index coordinate to give the B4 wavelet expansion coefficients. It is recognized that tube or surface wave events are almost stationary from trace to trace so that they mostly contribute to the lowest resolution wavelet coefficients (i.e., lowest frequency components), while the other events contribute to the higher resolution wavelet coefficients (i.e., high frequency components). We simply eliminate the low resolution coefficients and reconstruct the signal from the higher resolution coefficients. Limited numerical tests suggest that wavelet filtering of tube waves are superior to filtering by a median filter. In particular, distortion of non-tube wave events by wavelet filtering is much less pronounced than by median-filtering. Also, the choice of the wavelet cut-off level is trivial compared to the variety of parameter choices in median filtering (e.g., the number of points in the median filter, the bandwidth of the bandpass filter applied after the median filter). Filtering of surface waves in CDP data by wavelet filtering also shows promise.