Removing spatially aliased tube waves in cross‐well data

Abstract

Seismic data collected in a cross-well experiment often contain steep linear events generated by tube waves that propagate vertically along wells where sources and receivers are positioned. Because these linear events are spatially aliased, trace interpolation is necessary before they can be removed through dip-filtering. One of existing methods for trace interpolation is the linear two-step method. The method first finds prediction filters from known traces, and then estimates missing traces by minimizing the energy of prediction errors. I have developed an improved method for finding prediction filters from known, spatially-aliased data. With this method, the prediction filter at one frequency is obtained from the component of data at that frequency; no squeezing or stretching of the filter is required. The effects of aliased data on the prediction filters are removed by selecting the zeros of the prediction filters with a neural net. Consequently, this method can correctly interpolate data whose dip structure varies with respect to frequencies. It does not require the amplitudes of the wavelets along an event to be constant. And furthermore, it correctly determines prediction filters even when data are completely aliased. An example with field data shows that after trace interpolation, tube waves are removed much more effectively than before.