Full waveform inversion with extrapolated low frequency data

TL;DR

This paper presents a method to synthesize low frequency seismic data from high-frequency data using phase tracking, enabling effective full waveform inversion without the need for challenging low-frequency acquisition.

Contribution

The authors introduce EFWI, a novel approach that extrapolates low frequencies from high-frequency data to improve FWI initialization and convergence.

Findings

Extrapolated low frequencies can effectively replace recorded low frequencies in FWI.

EFWI demonstrates robustness to inaccuracies in the extrapolated data.

Synthetic examples show successful low-wavenumber velocity model estimation.

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. As a signal processing problem, bandwidth extension is a very nonlinear and delicate operation. It requires a high-level interpretation of bandlimited seismic records into individual events, each of which is extrapolable to a lower (or higher) frequency band from the non-dispersive nature of the wave propagation model. We propose to use the phase tracking method for the event separation task. The fidelity of the resulting extrapolation method is typically higher in phase than in amplitude. 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, EFWI for short, demonstrates surprising robustness to the inaccuracies in the extrapolated low frequency data. With two synthetic examples calibrated so that regular FWI needs to be initialized at 1 Hz to avoid local minima, 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.