Because the spectral behavior of seismic first arrivals contains much information about the nature of the transmission path, the Thomson-Haskell matrix formulation for the response of layered systems has received much attention. In particular, the transfer ratio, i.e., the ratio between the vertical and horizontal transfer functions, invites study because it can be compared with the ratio spectrum, an observable quantity, independent of the source function and characterizing the model alone. An investigation of this quantity as a function of the parameters in the layered model shows that it is insensitive to densities in the model, that the shear velocities in the model are less critical than the layer thicknesses and compressional velocities, and that it is probably impossible to numerically invert the problem uniquely, that is, to find a unique model whose calculated transfer ratio matches the observed ratio spectrum of a seismogram. The transfer ratio can provide a useful and sensitive constraint on models derived from other methods, however. By searching the parameter space around several different types of models, models which satisfy observed ratio spectrums in the least square sense can be found. Inspection of these models' transfer ratios and response functions discriminates between model types which are acceptable and those which are not.

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