FREQUENCY-WAVE-NUMBER ELASTIC INVERSION OF MARINE SEISMIC DATA

We present an inversion method for determining the velocities, densiti es, and layer thicknesses of a horizontally stratified medium with an acoustic layer at the top and a stack of elastic layers below. The mul tioffset reflection response of the medium generated by a compressiona l point source is transformed from the time-space domain into the freq uency-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 reflec tivity method where the solution for each frequency-wavenumber compone nt is found by computing the generalized reflection and transmission m atrices recursively. The gradient of the objective function is compute d 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 simulta neously with the reflection response by layer-recursive formulas. The limited-aperture and discretization effects in time and space of the r eference data are included by applying a pair of frequency and wavenum ber dependent filters to the predicted data and to the Jacobian matrix at each iteration. Numerical experiments performed with noise-free sy nthetic data prove that the proposed inversion method satisfactorily r econstructs the elastic parameters of a stratified medium. The low-fre quency trends of the S-wave velocity and density are found when the in itial P-wave velocity model gives approximately correct traveltimes. T he convergence of the iterative minimization algorithm is fast.