Frequency-domain FWI for 2D VTI media using pseudo-acoustic and pure-acoustic wave equations

Abstract

Describing the exact wavefield movement is required to obtain a more accurate subsurface velocity model during full waveform inversion (FWI). Real rock environments are composed of many anisotropy factors, but the conventional FWI assumes that the subsurface is an isotropic medium. Because of these assumptions, it is difficult to describe realistic wavefield motion. This is not sufficient to obtain the appropriate subsurface velocity model. To more closely simulate realistic wavefield motion, we selected the pseudo-acoustic wave equation and the pure-acoustic wave equation suggested by Fletcher et al., 2009, and Chu et al., 2011. When we apply both equations to FWI, a large difference in performance is expected because both equations have different formulations. One of the important considerations in the multiparameter FWI is the radiation pattern of the parameters. The radiation pattern can be calculated using a partial derivative wavefield, and many researchers have proposed that setting the parameters that do not influence the other parameters is good for parameterization when analyzing the radiation patterns. We simulated both equations in the frequency-domain, and we calculated the radiation patterns of P-wave, epsilon, and delta in the time-domain. To determine whether the behavior is good and the possibility of the two algorithms, we tested synthetic data generated in the frequency-domain using the same equation and modeling scheme. Considering a more realistic situation, we generated a synthetic dataset under the time-domain using an elastic wave equation with a marine environment assumption and applied two algorithms. The tests of the time-domain synthetic dataset used 6 cases of initial models and updating strategies. Additionally, we applied conventional isotropy FWI to the same synthetic dataset and calculated the relative percentage errors between the true model and the inverted model. Through the relative percentage errors called model misfits, we compared the performance of conventional FWI with the proposed FWI. Finally, we applied both algorithms to the 2D TTI model officially provided by BP Exploration Operation Company, and reconfirmed the importance of anisotropy factors.