The Influence of Reflection Coefficient Statistics on the Seismic Method: Scattering and the Minimum Detectable Reflection Coefficient
Propagation of seismic reflection energy through layered media is discussed in terms of one-dimensional elastic scattering and the effect of a layered overburden on the detectability of the underlying target horizons is investigated. In a previous paper, using Walden & Hosken's statistical models of real reflection series, Q-like attenuation laws were derived for the two-way transmission. Considerable use was made of the O'Doherty and Anstey relation between the amplitude spectrum of the two-way transmission and the energy spectrum of the reflection coefficients. With reference to the seismic reflection bandwidth, in general the equivalent Q is seen to increase with frequency, except over an intermediate band of frequencies where it often decreases with frequency. Also, the minimum phase wavelet predicted by the theory was 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 was approximately described in terms of the statistical parameters of the reflection coefficients in the overburden. The spectrum of the back-scattered energy can be determined from the conservation of energy into and out of the overburden and is seen to be complementary to the forward scattered signal and thus it can also be described in terms of the Walden and Hosken statistical parameters. The back-scattered energy can be divided into two components: (i) the primary reflections from within the overburden together with their associated short period multiples and (ii) the long period internal multiple noise which may arrive at the same time as the reflections from the underlying target horizons, obscuring them. The ratio of forward-scattered signal to back-scattered noise is a function of frequency and travel time through the overburden and it sets a fundamental signal-to-noise ratio for the section. An approximate expression is derived for the signal-to-noise peak power ratio which we use to determine both a natural cut-off frequency above which the noise dominates over signal from a given target strength, and α min, the minimum reflection coefficient detectable below the overburden. α min is seen to depend on the statistical properties of the overburden and can usually be decreased by decreasing the high and low-cut frequencies of the seismic bandwidth. There is thus a trade-off between detectability level and resolution.
Proceedings of the Royal Society of London Series A
- Pub Date:
- February 1993