A plane wave solution in a multi-layered dipping medium with arbitrary dips is not available in practical form, but we show that algorithms based on a partial ray expansion using asymptotic ray theory presents no difficulties. The selection of multiple and converted phases is done automatically by the computer to minimize the error in the partial ray expansion below any desired level. For modest dips, the peak positions in the ratio of the vertical to the horizontal crustal transfer functions do not shift significantly. However, the relative peak amplitudes are modified considerably. Therefore, it seems feasible to use the ratio of transfer functions to obtain a suitable layered model, and dip determinations may be carried out as a secondary stage of iteration to improve the agreement between field experiment and model theoretical computations. As an example we obtain a crustal model, 35 km thick, near the Edmonton observatory with a steeply dipping sill, 2 km thick, at a depth of about 19 km and most likely made up of high-velocity material.