A ray-theory development of the effect of dip on P-wave transmission through a single layer over a half-space permits an assessment of errors due to dip in estimates of crustal thickness from observed P-wave spectral properties using transmission coefficients for a nondipping interface. The possibility of simultaneously deriving depth and dip from such observation is also shown. The theory has been tested by experiments in a two-dimensional laboratory model and applied to observations of deep South American earthquakes at small epicentral distances.
Theory and laboratory results show that errors in depth reflecting dip are less than 5 per cent for dips up to 25°. Dip can be estimated by matching observed and theoretical curves, once a velocity contrast has been fixed independently. A curve-matching technique for objectively selecting the best match has been developed.
A variation of parameter study shows that changes in velocity contrast do not change the shape of the crustal transfer function, but peak-to-trough differences increase with increasing velocity contrast. A change in depth of a dipping layer produces no change in the crustal transfer function plotted in dimensionless frequency. The transfer function changes with dip more rapidly for waves incident downdip. If the data window is long enough to include P and PPP (three P legs in the layer), the depth determination is not sensitive to window length, but dip determination is not possible for short windows.
The data for Antofagasta permit one of two solutions, a crust either 46.1 or 56.7 km thick, with the M discontinuity dipping 5° east, with the 46.1 km thickness preferred. This result agrees well with refraction results of others. A less firm result for Naña is a crust 74.7 km thick, with dip 15° to the southeast.