Extrapolated full-waveform inversion (EFWI) with synthesized low-frequency data

Abstract

The availability of low frequency data is an important factor in the success of full waveform inversion (FWI) in the acoustic regime. The low frequencies help determine the kinematically relevant, low-wavenumber components of the velocity model, which are in turn needed to avoid convergence of FWI to spurious local minima. However, acquiring data below 2 or 3 Hz from the field is a challenging and expensive task. In this paper we explore the possibility of synthesizing the low frequencies computationally from high-frequency data, and use the resulting prediction of the missing data to seed the frequency sweep of FWI. To demonstrate the reliability of bandwidth extension in the context of FWI, we first use the low frequencies in the extrapolated band as data substitute, in order to create the low-wavenumber background velocity model, and then switch to recorded data in the available band for the rest of the iterations. The resulting method, extrapolated FWI (EFWI), demonstrates surprising robustness to the inaccuracies in the extrapolated low frequency data. With a synthetic Marmousi model, we demonstrate that FWI based on an extrapolated [1,5] Hz band, itself generated from data available in the [5,15] Hz band, can produce reasonable estimations of the low wavenumber velocity models.