Accurate near-surface characterization and velocity model building are important for a number of geotechnical and geophysical applications. 3D full waveform inversion can be used to generate a detailed velocity model, but must be provided with a good initial velocity model. A method for producing such an initial velocity model is explored in this paper. Assuming that the near-subsurface can be locally approximated by an effective flat-layered medium, a specialized form of acoustic full waveform inversion is proposed. The inversion is based on regularized least-squares in the Laplace-Fourier domain as a measure to mitigate the cycle-skipping problem. Forward modeling is carried out by solving a number of independent finite-difference problems in parallel, for a set of horizontal wavenumbers. The set is determined adaptively, using a pair of algorithms discussed in detail. A numerical implementation of the inverse Hankel transform, used to synthesize data in the frequency-offset domain, is also described. The forward modeling scheme is validated against analytic solutions of the Helmholtz equation, showing good agreement between the two. Full waveform inversion is tested by inverting a synthetic dataset consisting of flat layers with embedded velocity anomalies. Important features are recovered after inversion at a small number of complex frequencies, providing a detailed initial model for successive 3D full waveform inversion.