We classify full-waveform inversion (FWI) projects according to the types of events used to invert marine streamer data. In general, an adequate model update requires the seamless introduction of wavenumbers that are missing in the starting model. It has been our experience that a seamless update may require extraction of the lowest possible wavenumbers from the data, as well as the application of preprocessing procedures and scattering kernels that are optimal for each type of arrival. In a shallow-water environment, and with sufficient offsets, refracted arrivals and diving waves can provide an adequate inversion for shallow velocity structures. We demonstrate this principle using the linearized (Born) scattering kernel for field data from the North Sea.