This dissertation addresses the problem of inverting two-dimensional seismic data to determine the compressional wave velocity as a function of the spatial position in the medium. An automatic procedure for velocity estimation is set up using a bi-dimensional cross-correlation function to compare the modelled seismograms with the data. The standard wave-equation traveltime inversion algorithm treats each recorded seismic trace independently, and ignores the offset-dependence of reflected and diffracted arrivals in an ensemble of traces in a shot gather. My new inversion method, wave-equation traveltime-offset inversion, focuses on reflected or diffracted waveforms and introduces the bi-dimensional (offset-time) cross-correlation function to tackle this offset dependence. The velocity model is updated using the current velocity model, the observed pressure field, and the fields computed by reverse time propagation of two pseudo-residual functions acting as sources in a particular location. The wave-equation traveltime-offset inversion reconstructs the low frequency content of the velocity model when transmitted arrivals are used. Combined with the full waveform inversion, it succeeds in inverting a synthetic fault model in the crosshole configuration. The proposed method also succeeds in inverting surface reflection datasets while the standard traveltime inversion fails. By taking into account the moveout between traces, the convergence is more stable than with the conventional method. When inverting datasets with surface reflection geometries, the dominant event and the velocity above it are recovered using the traveltime and offset information. The remaining interfaces are defined as well. However, as there is a gap in resolution between the long and short wavelengths, the blocky variations in the velocity model are not observed.