Extrapolated full-waveform inversion: An image-space approach

Abstract

The primary factor that prevents full waveform inversion from universal success is the band-limited nature of seismic data, resulting in a gap between the low wavenumber background velocity model and the high wavenumber seismic images. In this paper, we propose to bridge the wavenumber gap in the extended image space, where full kinematic information in the data is preserved in spite of the inaccuracy of the background migration velocity model, and where the wavenumber range of the extended image is extrapolated using total-variation constrained deconvolution. This explicit wavenumber extrapolation is nested within least-squares reverse time migration iterations to ensure that the resulting extended images match the recorded band-limited data. We then synthesize reflection data using extended Born modeling with the extrapolated images. Numerical experiments show that although the total variation projection has limited the high frequencies that can be recreated by extended Born modeling, the low frequencies are reliably extrapolated at all offsets, given a reasonable starting velocity model. When the initial model is too crude, the proposed frequency extrapolation breaks down near the complex structures. Keywords: data reconstruction; deconvolution; full-waveform inversion; least-squares migration