Multidimensional filtering of seismic data

Multidimensional filtering has been applied during recording and processing of seismic reflection data since the earliest days of analog recording on paper records. As the state of the art has evolved to digital recording and processing, and acquisition has expanded to include dense spatial sampling over a large number of channels, more sophisticated multichannel filters have been developed. These include simple "mixes" (spatial convolution with small operators), two-dimensional Fourier transforms with appropriate limits in spatial and temporal frequencies, and more geometrically, as well as geophysically, meaningful Radon transform techniques. All multidimensional filtering limits the data in some fashion, be it temporal frequency bandwidth, spatial frequency bandwidth, limits in apparent horizontal phase velocity across a recording array (antenna), or limits in apparent wave-propagation velocity. These limits generally are defined to pass regions of high signal level and reject regions of high noise levels. As more recent techniques have emerged, such as Tau-p transforms (special cases of the Radon transform), filter limits may be described in terms of geophysical knowledge as well as signal characteristics. Thus additional information, derived from regional geophysical knowledge, may be added to the data processing sequence. Many new considerations and potential problems have arisen as new multidimensional filtering techniques have been developed, including spatial sampling, aliasing with different transforms, maintenance of dynamic range, and effects of multidimensional filtering at different points in the processing sequence.