Introduction

Recent work Spitz (1991) has demonstrated the use of prediction filters in the $x-\omega$ domain to interpolate aliased data. Spitz's method uses the predictability of the filters as a function of frequency to overcome the problems of aliasing. The filters from low frequencies at one trace spacing are used to predict the filters at a higher frequency for a finer trace spacing.

This method has two major limitations; first the use of prediction in the x-direction requires that the input traces be sampled on a regular grid; second, if the dips at low frequencies are not the same as the dips at high frequencies the low frequency filter from the original spacing is not a good estimate of the high frequency filter at a finer spacing.

I have chosen to use a simpler property of the spectrum of dipping events to remove the aliased energy from sampled data. In the $p-\omega$ domain a band limited dipping event has a locally continuous amplitude spectrum at the true dip and a discontinuous amplitude spectrum at the aliased dip. I perform a least-squares inverse transform (see e.g. Kostov (1990)) to the $p-\omega$domain with constraints in the $p-\omega$ domain that are based on a measure of local continuity as a function of frequency. Once I have found an unaliased representation of the data in the slant stack domain I can transform back to the x-t domain at an arbitrary trace spacing.

This method does not suffer from the same limitations as Spitz's method. The use of a least-squares inverse slant stack means that irregular trace geometries can be handled satisfactorily. By using a local continuity constraint I can handle events at different dips that have different bandwidths. My only requirement is that events be continuous in frequency over some (user definable) length. If this length is too long the method may reject valid dipping events with a narrower bandwidth. If it is too short the method may fail to reject aliased energy.