An efficient iterative method is discussed for solving the 3-D nonline
ar seismic inverse problem. The method is based on high-frequency asym
ptotic methods for both computing the data misfit function and acceler
ating the rate of convergence by means of preconditioning. The method
is applied to synthetic and real data and, for the simple models consi
dered here, it is concluded that it appears to be capable of resolving
both background velocity and contrast parameters. For a typical three
-dimensional data-acquisition geometry, the method seems to be :ess se
nsitive to sparse-sampling effects than imaging methods.