AMPLITUDE RESPONSES OF THIN BEDS - SINUSOIDAL APPROXIMATION VERSUS RICKER APPROXIMATION

The amplitude response of a thin bed with arbitrary upper and lower normal incidence reflection coefficients is studied. Two analytical expressions for the normal incidence amplitude response as a function of the thickness are derived and are both valid for weak reflectivities and for thicknesses below (1/8)lambda(d), where lambda(d) is the dominant wavelength. The first expression is based on the substitution of a cosine wave for the source wavelet, and the second is based directly on the analytical expression for a Ricker wavelet. The results calculated from these two expressions are compared to numerical modeling results for a Ricker wavelet for several models. We found that the differences between the two expressions are small, and both are good approximations. Above the (1/8)lambda(d) thickness, the percentage differences increase rapidly for both expressions, implying that the thin-bed assumptions in both derivations break down rapidly beyond the (1/8)lambda(d) thickness. Below the (1/8)lambda(d) thickness, except in the case where the two reflection coefficients are equal in magnitude but opposite in sign, the amplitude dependence on the thickness is nonlinear.