We apply the incomplete Gauss-Newton full-waveform inversion (TDIGN-FWI) to Gulf of Mexico (GOM) data in the space-time domain. In our application, iterative least-squares reverse-time migration (LSRTM) is used to estimate the model update at each non-linear iteration, and the number of LSRTM iterations is progressively increased after each non-linear iteration. With this method, model updating along deep reflection wavepaths are automatically enhanced, which in turn improves imaging below the reach of diving-waves. The forward and adjoint operators are implemented in the space-time domain to simultaneously invert the data over a range of frequencies. A multiscale approach is used where higher frequencies are down-weighted significantly at early iterations, and gradually included in the inversion. Synthetic data results demonstrate the effectiveness of reconstructing both the high- and low-wavenumber features in the model without relying on diving waves in the inversion. Results with Gulf of Mexico field data show a significantly improved migration image in both the shallow and deep sections.