The influence of reflection coefficient statistics on the seismic method: scattering attenuation and transmission wavelets

The propagation through layered media of seismic energy from reflection seismic surveys is discussed in terms of one dimensional elastic scattering. The effect of a layered overburden on the detectability of the underlying target horizons is investigated. The required signal from the target reflectors arises from the two-way forward-scattered component whereas the internal multiple noise (which tends to obscure the target reflections) arises from the back-scattered component. The starting point of the investigation is the O’Doherty-Anstey relation for the two-way transmission response. In this paper, using statistical models of real reflection series, we derive Q-like attenuation laws for the two-way transmission. Most real sequences of reflection coefficients have spectra which rise with frequency in the seismic band and this leads to signal attenuation which only approximates to that of a 'constant Q’ type over small bands of frequency. The implications of the theory are checked for two very different types of overburden, one being a repetitive type of sedimentary sequence with a large mean square reflection coefficient and the other a non-repetitive sequence with a small mean square reflection coefficient, against synthetic seismograms derived from real sonic logs. The minimum phase wavelet predicted by the theory is shown to model adequately the first pulse of the two-way transmission waveform, carrying the greater part of the energy, and the lag of the first peak is given approximately in terms of the statistical parameters of the reflection coefficients in the overburden.

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