A Bayesian nonlinear inversion scheme is used to invert traveltime and amplitude data from supercritical reflections. Reflection amplitudes are determined using a spherical‐wave model, where the amplitude of a reflected spherical wave is given by a Sommerfeld integral. This integral is evaluated numerically by integrating over a contour in the complex plane. The spherical‐wave model differs from plane‐wave models in the regions around the critical points for P and S refraction. In these regions, the spherical‐wave amplitudes are sensitive to frequency with a dependance on the ratio H/λ, between the reflector depth H and the seismic wave‐length λ. The accuracies of the inversion scheme and the spherical reflection model are tested using control data from the University of Houston physical‐model tank. The solution obtained by inversion agrees with the known solution to within 3 percent for all parameters and the amplitudes predicted by the spherical‐wave model agree remarkably well with the observed data.