We present an inversion method for determining the velocities, densities, and layer thicknesses of a horizontally stratified medium with an acoustic layer at the top and a stack of elastic layers below. The multioffset reflection response of the medium generated by a compressional point source is transformed from the time-space domain into the frequency-wavenumber domain where the inversion is performed by minimizing the difference between the reference data and the modeled data using a least-squares technique. The forward modeling is based on the reflectivity method where the solution for each frequency-wavenumber component is found by computing the generalized reflection and transmission matrices recursively. The gradient of the objective function is computed from analytical expressions of the Jacobian matrix derived directly from the recursive modeling equations. The partial derivatives of the reflection response of the stratified medium are then computed simultaneously with the reflection response by layer-recursive formulas.
The limited-aperture and discretization effects in time and space of the reference data are included by applying a pair of frequency and wavenumber dependent filters to the predicted data and to the Jacobian matrix at each iteration. Numerical experiments performed with noise-free synthetic data prove that the proposed inversion method satisfactorily reconstructs the elastic parameters of a stratified medium. The low-frequency trends of the S-wave velocity and density are found when the initial P-wave velocity model gives approximately correct traveltimes. The convergence of the iterative minimization algorithm is fast.