Space-varying FIR filter design for nonuniformly sampled seismic data

Since the early days of exploration seismology seismic receiver field arrays have been employed for purposes such as suppressing high wavenumbers present in wavefield, reducing the volume of recorded data and improving its signal-to-noise ratio. These receiver field arrays rely on the receivers being placed on a predetermined geometric layout, a condition which is not always met in the field. Misplacing receivers can have a detrimental effect on the performance of the field array. Fortunately, advances in seismic acquisition now enable a) recording the output of individual receivers and b) knowing with high (but limited) accuracy the actual location of each receiver. It is possible then to form arrays digitally on a computer, a process known as group forming. Group forming can be viewed as a combination of filtering and resampling. We propose two algorithms that take advantage of the positional information available about the receivers and generate a linear space-varying (LSV) filter. The LSV filter is suitable for filtering the nonuniformly sampled data, generating the filtered output on the nominal grid. We examine the relation of our algorithms with other algorithms from the bibliography and investigate their performance on synthetic data.