FULL WAVEFORM INVERSION OF THE SECOND-ORDER TIME INTEGRAL WAVEFIELD

Abstract

We proposed a new full waveform inversion (FWI) method, namely full waveform inversion of the second-order time integral wavefield, by enhancing low-frequency components of seismic data with a second-order time integration of seismic wavefield, which can efficiently reduce the initial model dependence of FWI. According to the propagation equation of scattering wavefield in scattering theory, we derived a propagation equation for the scattering wavefield with second-order time integral, and used the leading order Born approximation for the linearization of the propagation equation. Based on the propagation equation for the scattering wavefield with second-order time integral, using the scattering wavefield to invert for the distribution of scattering sources in subsurface, and using wavefield modeling to construct the incident wavefield, and according to the linear relationship between the scattering wavefield and the incident wavefield and velocity perturbation in the linear propagation equation for the scattering wavefield with second-order time integral, we applied a formula similar to the imaging formula of migration to obtain the estimation of velocity perturbation, and established an iterative inversion method for the full waveform inversion of second-order integral wavefield. Applying the inversion result of full waveform inversion of second-order integral wavefield as the initial velocity model for the conventional FWI can efficiently reduce the initial model dependence of FWI. Numerical tests using synthetic data of the Marmousi model demonstrated the validity and feasibility of the proposed method. The final results of the new method can deliver much improved results than the conventional FWI. Furthermore, to test the independence from the seismic frequency-band, we use a low-cut source wavelet (cut from 4Hz below) to generate the synthetic data. The inversion results by our new method show no appreciable difference from the full-band source results.