Multichannel Filtering of Seismic Data

Filter systems that have several inputs and one or more outputs are called multichannel filters. Each system output is linked via a more or less complicated filter system with all of the input channels. In contrast to velocity filters, the relationship between the outputs and the inputs of multichannel filters cannot be described by two-dimensional convolution. This is the basic difference between multichannel filters and the multidimensional filters discussed in chapter 24. Two-dimensional filters are characterized by a two-dimensional impulse response function. The response functions of these filters in the frequency-wavenumber and two-dimensional wavenumber domains are obtained using the two-dimensional Fourier transform of the impulse response function. The relationship between filter input and output of a two-dimensional filter is described by two-dimensional convolution. In contrast, multichannel filters have other relationships between filter input and output. These are derived in Sect. 26.1. A general description of the effects of multichannel filters in the frequency-wavenumber domain cannot be made. However, they do have other advantages: 1. Multichannel filters can be used to solve many, quite different kinds of problems, e.g., to separate different types of waves or to improve the signal-to-noise ratio. 2. These filters are designed according to strict mathematical criteria analogous to those for the single-channel optimum filters discussed in chapter 19. They take advantage of redundant information on the different input channels, such as the spatial coherence of the signals in seismics.