Comparative study of objective functions to overcome noise and bandwidth limitations in full waveform inversion

Abstract

Ongoing works on full waveform inversion (FWI) are yielding an increasing number of objective functions as alternative to the traditional L2-waveform. These studies aim at designing more robust functions and inversion strategies to reduce the intrinsic dependence of the FWI results on (1) the initial model and (2) the lowest frequency present in field data. In this work, we perform a comparative study of five objective functions in time domain under a common 2-D-acoustic FWI scheme using the Marmousi model as benchmark. In particular, we compare results obtained with L2-based functions that consider the minimization of different wave attributes; the waveform-based, non-integration-method; instantaneous envelope; a modified version of the wrapped instantaneous phase and an improved version of the cross-correlation travel time (CCTT) method; and hybrid strategies combining some of them. We evaluate the robustness of these functionals as a function of their performance with and without low frequencies in the data and the presence of random white Gaussian noise. Our results reveal promising strategies to invert noisy data with limited low-frequency content (≥4 Hz), which is the single strategy using the instantaneous phase objective function followed by the hybrid strategies using the instantaneous phase or CCTT as initial models, in particular the combinations [I. Phase + Waveform], [CCTT + Waveform] and [CCTT + I. Phase]. © The Authors 2015. Published by Oxford University Press on behalf of The Royal Astronomical Society