Both model seismic data and broad-band field data acquired to delineate complicated stratigraphy have been converted to displays of the instantaneous attributes of the complex seismic trace. Attribute sections enhance the interpretation of conventional sections not only by qualitatively highlighting specific properties of conventional displays, but also by quantitatively defining wavelet characteristics like dominant frequency, and stratigraphic variables like formation thickness. An example of the quantitative use of complex attributes in wavelet definition is the phenomenon that the maximum instantaneous frequency of a zero-phase Ricker wavelet is synchronous with the central peak of the wavelet and exactly equal to the frequency corresponding to the center of gravity o the wavelet's amplitude spectrum. Peak instantaneous frequency thus is a physical meaningful measure of the spectral content of a zero-phase Ricker wavelet. If the signal in a seismic section can be approximated by zero-phase Ricker wavelets, and if the geophysicist can identify occasional wavelet peaks in the sections which are uncontaminated by noise or interference, instantaneous frequencies at these samples are direct estimates of a significant and absolute spectral characteristic of the signal.

An example of the quantitative use of attribute sections in seismic stratigraphy is their application to estimation of the thickness of thin, porous sands. Pods of porous sand which are encased in high-velocity material and whose thicknesses are of the order of half the peak-to-peak period of the dominant seismic energy show up as anomalously high amplitude zones on instantaneous amplitude displays. These anomalies result from the well-known amplitude tuning effect which occurs when reflection coefficients of opposite polarity a half-period apart are convolved with a seismic wavelet. As sand members thin to a quarter-period of the dominant seismic energy, the thinning is revealed by an anomalous increase in instantaneous frequency. This behavior results from the less well-known but eq ally important phenomenon of frequency tuning by thinning beds. Frequency tuning reaches a maximum when sand thickness is about a quarter-period and remains evident as the sand continues to thin. The instantaneous frequency section thus can be a sensitive analytical tool for investigating stratigraphic sequences composed of very thin layers. Frequency and amplitude tunings are accompanied by changes in the character of the complex of interfering reflections from various impedance boundaries in a formation of thin beds, and these changes are highlighted by the instantaneous phase display.

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