Inversion of reflection traveltimes and amplitudes

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/lambda , between the reflector depth H and the seismic wavelength lambda . 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.