Multichannel z-transforms and minimum-delay

The concept of minimum delay (minimum phase) is an important link in tying together the deterministic and statistical approaches to seismology. It is shown how this concept can be extended to the multichannel case by using multichannel z-transforms. With this approach the theory of multichannel filter can be built up in an analogous manner to single-channel theory. In particular, multichannel predictive deconvolution can be applied to multitrace seismograms to eliminate reverberations. Because multichannel filters can exhibit trace-to-trace and record-to-record correlations, better results could be obtained in many applications where single-channel digital filters are now being used.