Thin layers are considered from the point of view of the quasi-linear relation that exists between their thickness and their reflection response to a seismic signal. The range within which this quasi-linearity exists is investigated; for a continuous sine wave, this is done by means of the equation for the response given in Rayleigh (1945), and for a seismic wavelet by means of a synthetic seismogram program. For a wavelet, the limiting value of the dominant frequency is found to be smaller than that for a continuous sine wave, the difference being in the order of magnitude of 15 percent.Within the linearity range, a thin layer may be replaced by an equivalent layer which gives the same reflection response but differs in thickness and in acoustic impedance. In the construction of synthetic seismograms over coal seams, this equivalent replacement may be utilized to replace the seams by layers, for which the two-way traveltime is equal to an integer number of sampling intervals; by this procedure the usual rounding-off errors are avoided. The method of equivalent replacement is also applicable when the host rock above and below the seam have different velocities.

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