Full model wavenumber inversion: Identifying sources of information for the elusive middle model wavenumbers

We recognized over the years that our conventional surface seismic recording can effectively identify two main features of the earth: its seismic propagation attributes and those attributes resulting in echoes or reflections. Thus, the resulting expression of the earth is dominated by the generally smooth (long-wavelength) features that control wave propagation, which we use to invert for the short-wavelength features causing reflections in a process we refer to as migration velocity analysis and imaging, respectively. The features of the earth that fall in between these two model scales - the middle wavenumbers - have been elusive, which is a dilemma for full-waveform inversion because we need to build the full velocity model (a broad band of model wavenumbers). We analyze the middle model wavenumber gap, but we focus more here on potential sources of information for such middle model wavenumbers. Such sources include regularization, objective function enhancements, and multiscattered energy. Regularization, provided by a total variation (TV) constraint admits middle and high model wavenumber components into the model to enforce the model's compliance with such a constraint. As opposed to minimizing the TV, such a constraint merely reduces the model space, and thus, these injected middle model wavenumbers are as good as the projected data information to the reduced model space. Such data information includes large offsets, but also multiscattered energy, in which the energy through wavepath and scattering updates can admit more of the elusive middle-wavenumber information that comes from the data. The combination of the right level of allowable model variations with the added data information from large offsets and multiscattering can help in filling the elusive middle model wavenumber gap and admit plausible models.