Interferometric frequency-domain gradiometry

Estimating accurate initial long-wavelength Earth models is an important consideration in elastic full waveform inversion (E-FWI) workflows for preventing cycle-skipping and convergence to local minima; however, obtaining such models is challenging because conventional marine seismic sources generate limited sub-2 Hz energy. Long duration ocean-bottom node (OBN) recordings, though, capture ambient wavefield energy that commonly carries long-wavelength surface-wave information, allowing coherent sub-2.0 Hz wavefields to be extracted through seismic interferometry in the form of virtual shot gathers (VSGs). While the analysis of field VSG data has shown that sub-1.0 Hz Scholte waves are indeed sensitive to local shallow salt structures, most current surface-wave analysis methods provide more global surface-wave phase-velocity estimates based on dispersion curve calculations that effectively average over the array aperture and obscure the often significant lateral heterogeneity. Seismic gradiometry applied to raw ambient data has shown promise in obtaining localized surface-wave phase-velocity estimates, though with currently limited depth sensitivity enabled by narrow-band filtering over multiple discrete central frequencies. To address this issue, we extend time-domain seismic gradiometry on raw ambient data to frequency-domain gradiometry on VSG data. This recasting allows for the reconstruction of frequency-dependent surface-wave phase-velocity estimates appropriate for use in local surface-wave inversion for recovering long-wavelength 3-D shear-wave velocity depth models. We illustrate the utility of interferometric frequency-domain gradiometry (I-FDG) by applying the framework to a synthetic VSG data set simulated through a 3-D elastic model with shallow salt pinnacles and a complex salt body that exhibit high-velocity contrasts compared to the background and pose complex imaging challenges. The results demonstrate that I-FDG can accurately recover the frequency-dispersion trends of the background 1-D shear-wave velocity model and provide long-wavelength (e.g. km-scale) constraints on, and depth sensitivity to, strong 3-D lateral shear-wave velocity heterogeneity. These results suggest that I-FDG applied to OBN-recorded interferometric VSG data volumes when coupled with local 1-D surface-wave inversion represents a promising candidate for developing long-wavelength shear-wave velocity models required as input for E-FWI analysis.