Amplitude responses of thin beds: Sinusoidal approximation versus Ricker approximation

Hai-Man Chung, Donald C. Lawton

The amplitude responses of thin beds whose thicknesses are below (1/8)d, where d is the predominant wavelength, are studied. Two analytical expressions for the amplitude response as a function of the thickness are derived. The first one is based on the substitution of a sine wave for the input wavelet, and the second one is based directly on the analytical expression for the Ricker zero-phase wavelet. The numerical results of these two expressions are compared to the numerical results of several models. It is found that below (1/8)d, the differences between the two expressions are very small, and both are good approximations, assuming that the limit of good agreement between the analytical results and the modelling results is about 10%. Above the (1/8)d thickness, the percentage differences increase rapidly for both expressions, implying that the thin-bed assumptions in both derivations breaks down rapidly beyond the (1/8)d thickness.