Resolution performance of Wiener filters

When Wiener filters are applied to seismic data, the bandwidth of noise increases along with the bandwidth of the signal. Thus the signal-to-noise ratio is degraded. To reduce signal ambiguity it is common practice to prewhiten the Wiener filter. Prewhitening the filter improves the output signal-to-ambient noise ratio, but reduces resolution. The ability to resolve the temporal separation between events is determined by the resolution time constant which we define as the ratio of signal energy to peak signal power from the filter. For unfiltered wavelets the resolution time constant becomes the reciprocal of resolving power recently described by Widess (1982). For matched filter signals the resolution time constant can be regarded as the inverse of the frequency span of the signal. The resolution time constant definition has two major advantages, it incorporates the effect of filtering; and it is easily generalized to incorporate the effects of noise by assuming that the filter is a Wiener filter. For a given amount of noise the Wiener filter is a generalization of the matched filter. Marine seismic wavelets demonstrate how reducing the noise level improves the resolution of a Wiener filter relative to a matched filter. For these wavelets a point of diminishing return is reached, such that, to realize a further small increase in resolution, a large increase in input signal-to-noise ratio is required to maintain interpretable information at the output.--Modified journal abstract.