Efficient full waveform inversion using the excitation representation of the source wavefield

Full waveform inversion (FWI) is an iterative method of data-fitting, aiming at high-resolution recovery of the unknown model parameters. However, its conventional implementation is a cumbersome process, requiring a long computational time and large memory space/disk storage. One of the reasons for this computational limitation is the gradient calculation step. Based on the adjoint state method, it involves the temporal cross-correlation of the forward propagated sourcewavefield with the backward propagated residuals, inwhichwe usually need to store the source wavefield, or include an extra extrapolation step to propagate the source wavefield from its storage at the boundary. We propose, alternatively, an amplitude excitation gradient calculation based on the excitation imaging condition concept that represents the source wavefield history by a single, specifically the most energetic arrival. An excitation based Born modelling allows us to derive the adjoint operation. In this case, the source wavelet is injected by a cross-correlation step applied to the data residual directly. Representing the source wavefield through the excitation amplitude and time, we reduce the large requirements for both storage and the computational time. We demonstrate the application of this approach on a two-layer model with an anomaly, the Marmousi II model and a marine data set acquired by CGG.