Abstract
Various postprocessing methods can be applied to seismic data to extend the spectral bandwidth and potentially increase the seismic resolution. Frequency invention techniques, including phase acceleration and loop reconvolution, produce spectrally broadened seismic sections but arbitrarily create high frequencies without a physical basis. Tests in extending the bandwidth of low-frequency synthetics using these methods indicate that the invented frequencies do not tie high-frequency synthetics generated from the same reflectivity series. Furthermore, synthetic wedge models indicate that the invented high-frequency seismic traces do not improve thin-layer resolution. Frequency invention outputs may serve as useful attributes, but they should not be used for quantitative work and do not improve actual resolution. On the other hand, under appropriate circumstances, layer frequency responses can be extrapolated to frequencies outside the band of the original data using spectral periodicities determined from within the original seismic bandwidth. This can be accomplished by harmonic extrapolation. For blocky earth structures, synthetic tests show that such spectral extrapolation can readily double the bandwidth, even in the presence of noise. Wedge models illustrate the resulting resolution improvement. Synthetic tests suggest that the more complicated the earth structure, the less valid the bandwidth extension that harmonic extrapolation can achieve. Tests of the frequency invention methods and harmonic extrapolation on field seismic data demonstrate that (1) the frequency invention methods modify the original seismic band such that the original data cannot be recovered by simple band-pass filtering, whereas harmonic extrapolation can be filtered back to the original band with good fidelity and (2) harmonic extrapolation exhibits acceptable ties between real and synthetic seismic data outside the original seismic band, whereas frequency invention methods have unfavorable well ties in the cases studied.
Highlights
Resolution of seismic data is a function of data bandwidth and dominant frequency (Widess, 1973; Kallweit and Wood, 1982)
The theoretical validity of the various spectral extension methods in increasing the seismic resolution can be reasonably demonstrated on synthetic tests, whereby a low-frequency synthetic is bandwidth extended and compared with a high-frequency synthetic derived from the same earth-reflectivity model
The residual spectrum shows a roughly increasing trend from low to high frequency. These synthetic tests suggest that the harmonic extrapolation method can stably predict the missing frequencies under the circumstance of a blocky earth model providing the noise level is small and the bandwidth extension is limited
Summary
Resolution of seismic data is a function of data bandwidth and dominant frequency (Widess, 1973; Kallweit and Wood, 1982). The ability of harmonic extrapolation to achieve useful bandwidth extension for a blocky earth model, and its superiority over frequency invention methods, will be demonstrated in the following comparative studies (synthetic and real data examples).
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