Surface seismic data with a known source pulse are used to estimate parameters in a stack of homogenous layers. The unknown parameters in each layer are the P wave velocity, the S wave velocity, the density, the layer thickness, and the quality factor. The forward problem is solved by dynamic ray tracing. Primary and multiple P wave reflections are considered. The S wave velocities are estimated from the PP transmission and reflection coefficients. The model is fitted to the data using a stabilized least squares procedure. The Jacobian is computed analytically in each step. By introducing the layer thicknesses as known parameters, it is possible to keep the number of unknowns at a tractable level, and the Gauss-Newton approximation to the Hessian matrix can be inverted exactly at each iteration. When only one event is considered, the scheme provides a nonlinear solution to the amplitude versus offset problem, where offset dependent corrections for absorption, geometrical spreading, and transmission losses are automatically included. All parameters are successfully estimated from synthetic data. We also perform a sensitivity analysis for the different parameters and discuss the reliability for the estimates in each parameter group. ¿American Geophysical Union 1991