Frequency‐wavenumber inversion of acoustic data

Abstract

We describe an inversion procedure for obtaining velocities, densities, and layer thicknesses from multioffset reflection seismograms generated by a point source excitation in a stratified acoustic medium. The reference seismograms are decomposed into cylindrical waves in the frequency‐wavenumber domain, where the inversion is performed by minimizing the difference between the reference data and modeled data using a least‐squares technique. The modeling algorithm is based on the classical reflectivity method. We include the effects of limited temporal and spatial apertures by applying a frequency and wavenumber dependent filter in the modeling process. This inversion is suited for Jacobian matrix methods where the first derivatives of the model‐generated data with respect to the model parameters are calculated from analytical expressions together with the modeling. The numerical examples show that the inversion algorithm recovers with reasonable accuracy the parameters used to generate the reference data. The low frequency trends of both the velocity and the density are restored. The convergence of the iterative minimization algorithm is fast.