Low Frequency Reconstruction Using Extended Modeling

The band-limited nature of seismic data has been prohibiting full waveform inversion from success due to the gap in information between the low frequency tomography map and the high frequency reflectivity map. In this paper, we present a method to fill in the gap utilizing the kinematic and amplitude information one can obtain from the high frequency data. The frequency continuation relies on an explicit scale separation between the background propagation velocity and the high wavenumber velocity contrast (reflectivity map). In order to preserve the full kinematic information in the recorded data, the high wavenumber reflectivity map are extended in the subsurface offset domain. We perform event tracking on the image gathers to extrapolate the reflectivity information beyond the recorded frequency band, based on the assumption that the location and reflectivity of a reflector are frequency independent. The low frequency data is then synthesized via extended Born modeling, using a low frequency wavelet, the migration velocity which can be arbitrarily inaccurate, and the extrapolated extended image gathers. This workflow provides a data-processing solution to synthesize the kinematically and dynamically correct approximation to the low frequency data that we could have recorded in the field.