Abstract

The classical fan filtering method can be time-consuming on the digital computer. This is because one must perform M/2 convolutions on a set of M input traces in order to obtain one output trace, where M is any convenient even integer. It is possible to manipulate the filter equations into a different form such that only one convolution per output trace is required, no matter what the value of M may be. The algorithm found in this manner can easily be programmed for a digital computer.The conventional fan filtering technique allows one to pass only those events whose apparent velocities fall within a certain fan-shaped region in the (frequency, wavenumber), or (f, k) plane. In some applications it becomes desirable to perform the complementary operation; that is, we wish to reject those events whose apparent velocities fall within this fan-shaped region in the (f, k) plane. These two operations are called fan pass and fan reject filtering, respectively. We derive the formulas allowing one to compute the operator coefficients for the fan reject filter, and generalize the algorithm obtained for the fan pass case so that it may be used for the fan reject case as well. The fan reject filter is applied to a set of traces from a vertical seismic array, where it becomes desirable to distinguish between upward and downward traveling events.

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