ANALYSIS OF DIFFRACTION PATTERN FILTERING OF VARIABLY DENSITY AND VARIABLY AREA RECORDINGS

When a small, transparent replica of a seismic section is illuminated by a homogeneous beam of coherent, monochromatic parallel light a diffraction pattern is created that is representation of the double Fourier spectrum of the recorded seismic waves, i.e. their spectrum in terms of frequency, f, and apparent wave number, k. Masking selected parts of this diffraction pattern causes the spectrum to be filtered: the recomposition of the filtered spectrum then provides a filtered section. The ideal seismic section for this purpose would be a continuous variable density section obtained from recording made at every point of the seismic line. The light transmission coefficient (in terms of light amplitude) at each spot of the replica should be linearly related to the instantaneous seismic signal strength at the spot on the seismic section to which it refers. Unfortunately we cannot make recordings at every point of a seismic line and in our practically realisable recordings we have to be content with sampling in the direction of the location coordinate x. This means that with variable density recordings aliasing will be present and evident in the spectrum obtained in the direction of k; furthermore, the aliased spectrum is also multiplied by a sine function of k because the recording obtained at a given station is not presented on the seismic section as a single line along the time axis, but occupies the entire width of the trace. The diffraction patterns created by variable density recordings of dipping sine waves, including clipped recordings, and of the effect of dip filtering in such sections are discussed. The efficiency of dip rejection is shown to decrease with increasing dip. The diffraction pattern of a variable density recording is found to be characterised by a relationship between point pairs in the pattern. No such simple relationship has been found for the diffraction pattern of a variable area section; the spectra of such VAR sections belong to a very special class, because the amplitude transmission coefficient has only two values, viz. 0 and 1. Consequently, selective masking of the diffraction pattern of a VAR section may give rise to a filtered profile that does not look like a VAR section at all. General statements about the diffraction pattern of VAR sections are hard to give, because the transmission coefficient at a given point in the replica is not proportional to the signal level in the seismic section at the relevant point. In the case of VAR presentation of harmonic waves it was found that, as well as the aliasing effect in the k direction, higher harmonics of the frequency are also introduced. Some synthetic examples are given that show dip filtering to be less effective with VAR than with variable density recordings. Some arguments are advanced in favour of the opinion that high-pass filtering of VAR sections will have less success than low-pass filtering. This is demonstrated by two synthetic examples.