The boundary-value or 'bending' method of ray tracing may be simply extended to give the first-order change in ray path due t o a change in wavespeed structure. If the wavespeed of the medium depends on a finite number of parameters, the method yields the partial derivatives of ray path coordinates with respect t o these parameters. A further extension of the method enables calculation of the partial derivatives of the geometrical spreading factor associated with a ray with respect t o wavespeed parameters. These amplitude partial derivatives are used in an attempt t o interpret variations in the relative amplitudes of 1-3 Hz teleseismic P-wave arrivals observed across NORSAR in terms of laterally varying wavespeeds in the lithosphere below. Some observational evidence is presented to support the assumption that near receiver structure controls the relative amplitude distribution. The wavespeed model is described by cubic spline interpolation between values on a 3-D mesh of knots. The amplitude data are used to derive damped leastsquares estimates for the inverse wavespeed or slowness at the knots. Nonlinearity necessitates an iterative solution. Calculations with synthetic amplitude data indicate that relative amplitudes have difficulty resolving the average horizontal velocity gradient below the array. Only two parameterizations have so far been tried with real amplitude data and the results compare only moderately well with models derived from travel-time data. Several possible reasons for this are discussed. These include the reduction of the data, which show signs of internal inconsistency, the model parameterizations so far tried, the resolution problem just mentioned and, of course, the assumption that geometrical ray theory is adequate.
