Some properties of thin beds
Hai-Man Chung, Donald C. Lawton
Six thin-bed models as represented by six two-termed reflectivity series are convolved with a Ricker 31 Hz zero-phase wavelet. The absolute maximum amplitude (AMA) and the peak frequency (PF) of the resultant composite wavelet are studied. It is found that for unequal polarity, the AMA increases with thickness, and vice versa for equal polarity in the range of thickness between one-eighth and one-quarter of the predominant wavelength. The functional dependence is, in general, nonlinear, except in the case of unequal polarity and equal strength. The PF decreases quadratically as a function of thickness for the equal polarity models. For the unequal polarity models, it first increases with thickness and then decreases. But for the unequal polarity and equal strength model (Widess' model, 1973), the PF of the composite wavelet is found to be /3/2fo for thickness for which the thin-bed assumption is valid, where fo is the PF of the input wavelet. Mathematical expressions for the AMA and the PF have also been derived. To study the phase, complex attributes are used. However, the results are not conclusive and more study is needed.