When a layer is overlying a half-space with a tilted interface, the refraction of seismic waves emerging from the half-space generally results in their reorientation away from the vertical plane of incidence, with the following consequences:
The angle of emergence at the free surface and, thus, dT/dΔ will become azimuth dependent.
The apparent direction of approach of the wave front along the free surface will, in general, be different from the true azimuth. The azimuthal deviation also varies with azimuth.
A general formulation for the computation of the apparent azimuth and the angle of incidence at the free surface is obtained. The numerical corrections to the observed dT/dΔ and apparent azimuth, for a number of combinations of various dip angles and velocity contrasts, are tabulated.
The tables may be helpful when the first and second derivatives of the travel time data are to be analyzed. Their comparison with observation can also be useful for making inferences about the underlying crustal structure. The latter approach has been applied to the P arrivals across the Tonto Forest Seismological Observatory (TFSO) array, Arizona. On the basis of these observations, the Mohorovičić discontinuity under the observatory appears to be dipping locally as much as eight degrees in the N70° ± 5°E direction.