The travel times of P in the upper mantle are considered. Usually the phases are more clearly recorded at epicentral distances beyond 15° and here the time-distance curves have appreciable curvature. At smaller distances the time-curves are nearly straight lines, that sometimes are cut off at distances less than 15°.
Travel times have been calculated on various velocity assumptions so as to agree with the empirically determined travel times.
For the uppermost mantle the velocity has been taken either to be constant or slightly increasing down to a depth sufficiently great for the phases to be recorded, though with small amplitudes, at least to distances of 15°, or a low velocity layer has been inserted that cuts off the time-curve at smaller distances.
The bending branch of the time-curve from about 15° onwards can be produced by a slow, gradual increase of velocity downwards from about 100 km depth, or by a somewhat faster increase causing a reversal of the time-curve and a cusp at about 15°, or else by an abrupt increase of velocity and velocity gradient at a depth somewhat greater than 200 km. In this last case reflections and refractions emerge at distances smaller than 15°.